UNIVERSITÀ DEGLI STUDI DI MILANO - BICOCCA
Facoltà di Scienze Matematiche, Fisiche e Naturali
corso di Laurea Magistrale in Fisica
Study of the Bc → J/ψ π and Bc → J/ψ 3π decay
channels in the CMS experiment at LHC
Relatore:
Prof. L. Moroni
Correlatore: Dott.ssa S. Malvezzi
Simone COLOMBO
Matr. 704371
Anno Accademico 2010/2011
Contents
1 CMS at LHC
1.1 The accellerator . . . . . . . . . . .
1.2 The detector . . . . . . . . . . . . .
1.2.1 Tracker . . . . . . . . . . .
1.2.2 Electromagnetic Calorimeter
1.2.3 Magnet . . . . . . . . . . .
1.2.4 Hadronic Calorimeter . . . .
1.2.5 Muon System . . . . . . . .
1.3 The trigger . . . . . . . . . . . . .
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1
1
2
5
9
10
10
12
14
2 Physics at CMS
2.1 B physics at CMS . . . . . . . . . .
2.2 The Bc meson . . . . . . . . . . . .
2.2.1 Bc production . . . . . . . .
2.2.2 Bc decay . . . . . . . . . . .
2.2.3 Experimental measurements
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19
20
21
22
24
25
3 Event Selection
3.1 Datasets and JSON Files
3.2 Triggers . . . . . . . . .
3.2.1 Analysis Triggers
3.2.2 Trigger Match . .
3.3 Track Combination . . .
3.4 Signal optimization . . .
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29
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4 Monte Carlo studies
41
4.1 Testing the generator . . . . . . . . . . . . . . . . . . . . . . . 42
4.1.1 MC signal - Data signal . . . . . . . . . . . . . . . . . 42
iii
CONTENTS
iv
4.1.2
4.1.3
MC signal - Data background . . . . . . . . . . . . . . 43
Additional MC studies . . . . . . . . . . . . . . . . . . 48
52
5 Bc± → J/ψπ ± and Bc± → J/ψπ ± π ± π ∓ analysis
5.1 Bc± → J/ψπ ± signal . . . . . . . . . . . . . . . . . . . . . . . 52
5.2 Bc± → J/ψπ ± π ± π ∓ signal . . . . . . . . . . . . . . . . . . . . 59
6 Branching Ratio evaluations
68
σ(Bc± )×Br(Bc± →J/ψπ ± )
6.1 σ(B ± )×Br(B ± →J/ψK ± ) . . . . . . . . . . . . . . . . . . . . . . . . 68
6.2
Br(Bc →J/ψ3π)
Br(Bc →J/ψπ)
. . . . . . . . . . . . . . . . . . . . . . . . . . . 70
7 Bc lifetime
73
Conclusions
77
Bibliography
78
Introduction
The Compact Muon Solenoid (CMS) is a high luminosity experiment located at Large Hadron Collider (LHC) at CERN. LHC aims
√ at accelerating
and colliding protons at a centre of mass energy up to s = 14 T eV and
istantaneous luminosities up to 1034 cm−2 s−1 , opening new frontiers for highenergy physics. However, during the first years of operations,
the machine
√
has worked at a reduced centre of mass energy of s = 7 T eV and at a
luminosity that reached the value of 5 × 1033 cm−2 s−1 in the last 2011 run.
The physics program of CMS extends from the discovery of the Higgs
Boson, the particle responsible for the mass generation in the Standard Model
(SM), to the search for evidences of physics beyond the SM.
In this context, the B physics sector represents an interesting field of
observation: rare decays could indicate signatures of New Physics while the
properties of a wide number of B-hadrons can be precisely tested thanks to
the great production rate expected. The operational conditions reached by
the LHC and the detector performances enable CMS to be an ideal laboratory
for the study of the high mass B hadrons (Bc , Λb , Ωb , Ξb and Σb ).
Among these, the Bc meson is a unique candidate for the study of the
heavy flavor dynamics since it is formed by two different heavy quarks. In
spite of the rich theoretical literature, only few decay modes have been experimentally observed and many properties have still to be investigated. Indeed,
its production cross section at the LHC energy and decay branching fractions are under study and the only lifetime measurement comes from the
semileptonic channel Bc± → J/ψl± ν, for which heavy Monte Carlo corrections, taking into account the neutrino missing energy, are required.
The studies of the Bc meson presented in this thesis are based instead
on the reconstruction of kinematically closed decay modes for the 2011 data
samples, respectively Bc± → J/ψπ ± and Bc± → J/ψπ ± π ± π ∓ .
The Bc± → J/ψπ ± π ± π ∓ is the third and most recent experimentally
observed mode and the signal presented in this thesis represents the first
evidence for the channel in CMS.
The B ± → J/ψK ± process is topologically equivalent to the Bc± →
J/ψπ ± decay mode and is thus studied to perform consistency checks for
the Bc signals and as normalization mode.
σ(Bc )×Br(Bc →J/ψπ)
The ratio σ(B
+ )×Br(B + →J/ψK) is calculated for a 7 T eV production and its
preliminary estimate, the first in CMS, is (0.982 ± 0.214)%. This result is in
agreement with a preliminary value from LHCb and the CDF measurement.
c →J/ψ3π)
at 7 T eV is presented, leading
A measurement of the ratio Br(B
Br(Bc →J/ψπ)
to a preliminary result of 3.55 ± 1.79. The big statistical error comes from
the still limited Monte Carlo (MC) samples and will be reduced as soon as
the next MC production will be avalaible. Nevertheless, the branching ratio
measurement is compatible with recent theoretical predictions and with the
only other experimental measurement, performed by LHCb.
The first lifetime measurement on a full reconstructed decay channel is
also performed, with a preliminary result of 0.453+0.042
−0.038 ps that should be
compared with the PDG average τP DG = 0.45 ± 0.04 ps.
Chapter 1
CMS at LHC
1.1
The accellerator
The Large Hadron Collider (LHC) is the two-ring particle accelerator and
collider installed in the 27 km LEP tunnel at CERN. It is designed to provide
√
proton-proton (pp) collisions having a center of mass energy up to s =
14 T ev, a nominal luminosity of L = 1034 cm−2 s−1 and a bunch crossing of
25 ns. In the 2010 and 2011 data taking, the machine has been operated at
√
s = 7 T ev and an istantaneous luminosity of L = 5 × 1033 cm−2 s−1 has
been delivered in the last runs. This unique features allow it to reach the
TeV energy scale, opening a new domain for physics studies.
The aims of LHC are various and complementary: they range from the
discovery of new physics phenomena (e.g. the search for the Higgs Boson
and for supersimmetric particles) to new and more precise measurements for
the properties of the known particles of the Standard Model (SM). The high
beam intensities needed for a luminosity of 1033 cm−2 s−1 exclude the use
of antiprotons and a single vacuum pipe: two different pipes are therefore
needed, each one provived with a set of bending dipole magnets.
The solution is a pp collider with separate magnet fields and vacuum
chambers in the main arc and common straight sections in the interaction
regions. Some machine parameters relevant for detectors operations are listed
in Table 1.1.
The bunches are formed in the Proton Sincrotron (PS) with the nominal
spacing and an energy of 26 GeV ; the beam is then accelerated in the Super
Proton Synchrotron (SPS) to 450 GeV and inserted in one of the LHC rings.
1
CHAPTER 1. CMS AT LHC
2
Once both the rings are filled, the beams are accelerated to the nominal collision energy. Various bunch gaps are used for the purposes of synchronization,
acquiring calibration data and providing resets to front-end electronics. In
order to constrain the beam inside the LHC tunnel, a bending magnetic field
of 8.33 T is provided by 1232 cryodipoles, superconducting magnets working
at 1.9 K.
Energy per nucleon
Design Luminosity
Dipole field at 7 TeV
Bunch separation
No. of bunches
No. of particles per bunch
E
L
kB
Np
pp
7
1034
8.33
25
2808
1.15 × 1011
HI
2.76
1027
8.33
100
592
7.0 × 107
T eV
cm−2 s−1
T
ns
Table 1.1: Parameters relevant for LHC detectors.
The LHC has two high luminosity experiments, ATLAS and CMS, aiming
at a peak luminosity of L = 1034 cm−2 s−1 and two low luminosity experiments, LHCb for B physics and TOTEM for the detection of protons from
elastic scattering at small angles. A dedicated ion experiment, ALICE, is
built for Pb-Pb ion operation. The LHC structure, shown in Fig.1.1, consists of eight arcs and straights sections, with four points of bunch crossing.
ATLAS and CMS are located at diametrical opposite sections, at point 1 and
5 respectively, whereas ALICE and LHCb are located at point 2 and 8, in
the two other interaction regions. The bending magnets are installed in the
eight curved sections.
1.2
The detector
With the energy and the designed luminosity given by LHC, a wide range
of physics is possible; however many experimetal challenges have to be overcome. The design of the detector plays a crucial role in this scenario.
The two main aspects of the collisions that must be taken into account
are the rate at which they occur and the huge number of particles interested.
About 1000 charged particles are expected to emerge from the interction
point every 25 ns, leading to an event rate of approximately 109 inelatic
CHAPTER 1. CMS AT LHC
3
Figure 1.1: Schematic layout of the LHC.
events per second. The online event selection progress (”trigger”) must reduce such a huge rate to about 100 events/s for storage in a relative short
time, taking into account the time of the next bunch crossing.
In addition, at the nominal machine parameters, a mean of 20 inelastic
collisions will be superimposed on the event of interest and the reconstruction
of the event under study is made more difficult by pile-up effects (in the 2011
a mean of about 6 primary vertices of interaction is reached). These effects
are reduced by using high granularity detector with good time resolution,
resulting in low occupancy, and a fast electronic readout chain for online
selection. The result is a large number of detector channels that require very
good syncronization. The high radiation levels the detectors have to sustain
must be also considered in their choice and realization.
The detector requirements for CMS, to meet the goals of the LHC physics
program, can be summarized as follows:
• Good muon identification and momentum resolution over a wide range
of momenta in the region |η| < 2.5, good dimuon mass resolution,
and the ability to determine unambiguously the charge of muons with
p < 1 T eV /c.
CHAPTER 1. CMS AT LHC
4
• Good charged particle momentum resolution and reconstruction efficiency in the inner tracker. Efficient triggering and offline tagging of τ
and b jets, requiring pixel detectors close to the interaction region.
• Good electromagnetic energy resolution, good diphoton and dielectron
mass resolution (≈ 1% at 100GeV), wide geometric coverage (|η| <
2.5), measurement of the direction of photons and correct localization
of the primary interaction vertex, π 0 rejection and efficient photon and
lepton isolation at high luminositiy.
• Good ETmiss and dijet mass resolution, requiring hadron calorimeters
with a large hermetic geometric coverage (|η| < 5) and with fine lateral
segmentation.
The design of CMS, depicted in Fig.1.2, meets these requirements with
a high field solenoid, a full silicon inner tracking system and a homogeneous
crystal-based electromagnetic calorimeter.
Figure 1.2: View of the CMS detector. Different colors correspond to the
various detectors. From innermost to outermost: the Tracker (pink), the
Electromagnetic Calorimeter (green), the Hadronic Calorimeter (blue) and
the Muon Chambers (yelow).
CHAPTER 1. CMS AT LHC
5
The overall dimensions of the CMS detector are 21.6 m (length) × 14.6 m
(diameter) for a total weight of 12500 tons. A superconducting solenoid 13 m
long, with a 6 m inner diameter, provide a magnetic field of 3.8 T . The
return field saturates 1.5 m of iron, in which 4 muon stations are placed.
These features ensure robustness and full geometric coverage and a good
momentum resolution within a compact structure.
1.2.1
Tracker
Robust tracking and detailed vertex reconstruction are expected to play an
essential role for an experiment designed to address the full range of physics
that can be accessed at the LHC. Tracker measurements, combined with
track segments in the muon chambers, provide a good reconstruction of the
topology of the collision products emerging from the point of interaction.
Aiming at high luminosity, CMS needs a detector technology featuring high
granularity and fast response, so that the trajectories can be identified and
assigned to the correct bunch crossing. Resistance to high level of radiations
must be taken into account too.
To satisfy the performance requirements and constrains it is chosen the
strategy of providing a set of coordinate measurements of sufficient precision
so that the track reconstruction is made using a small number of measurements. Fine detector granularity is therefore required, so that single channel
occupancy at high luminosity for detectors with at least one hit in them is
kept at ≈ 1-3% everywhere. The active region surrounds the interaction
point and has a lenght of 5.8 m and a diameter of 2.5 m and is divided into
a central barrel and two endcaps, consisting in several layers of detector (see
Fig 1.3).
The high hit resolution and granularity requests (from 15 µm to 40 µm in
the trasverse plane) are fulfilled with Pixels and Silicon Strips technologies.
They are fast on the scale of 25 ns and are arranged in three regions respect
to the beam pipe, according to different particle flux areas:
• the region below 20 cm, where the particle flux is the highest, with
pixel detectors with a cell size of 150 µm × 150 µm;
• the intermediate region between 20 cm and 55 cm, equipped with silicon
microstrips with minimum cell size of 10 cm × 80 µm;
CHAPTER 1. CMS AT LHC
6
• the outermost region, from 55 cm to 125 cm, where the flux i low enough
to allow the use of larger-pitch silicon microstrips (25 cm × 180 µm).
Figure 1.3: The CMS tracker section: each line represents a detector module,
double lines are back to back modules.
Pixel Tracker
The CMS pixel detector is the part of the tracker closest to interaction point.
It is made of three barrel layers and two end layers (end disks) on each side of
the barrel. The barrel layers are located at mean radii of 4.4 cm, 7.3 cm and
10.2 cm and the endcaps cover radii from 6 cm to 15 cm; both are composed
of modular detector units. The system provides efficient three-hit coverage
in the region of pseudorapidity |η| < 2.2 and efficient two-hit coverage in the
region |η| < 2.5. The active element consists of a thin, segmented sensor
plate with integrated readout chips wire-bonded to the active surface. The
chips are connected through bond wires to hybrid circuits, kept at a low
temperature by cooling frames integrated in the structure.
The pixel dimensions are dictated by the high resolution performance
needed and the readout circuit area associated to each pixel. Squared pixel
of 100 µm × 150 µm with n-on-n doping are chosen as the most appropriate.
The geometry of the detector is arranged so that large charge sharing across
neighbouring cells occurs and the resolutions can reach values between 10 µm
CHAPTER 1. CMS AT LHC
7
and 15 µm in the barrel and between 15 µm and 20 µm in the endcaps,
both in rφ ad z directions, improving spatial reconstrution. The total active
surface of close to one square metre provides three 3D position measurements
over almost the full η range. The performance of the tracker is illustrated in
Figure 1.4.
Figure 1.4: Resolution of transverse momentum, transverse and longitudinal impact parameter in the Pixel Tracker for single muons with transverse
momenta of 1, 10 and 100 GeV /c.
Strip Tracker
The strip tracker mirrors the structure of the Pixel Detector and is divided
in barrel and endcaps too. It uses silicon sensors with variable thickness
and pitch depending the region (see Table 1.2). The barrel tracker region
is divided into 2 parts: a TIB (Tracker Inner Barrel) and a TOB (Tracker
Outer Barrel). The TIB consist in 4 layers and covers up to |z| < 65 cm.
The first two provide measurement in both rψ r − z coordinates with stereo
CHAPTER 1. CMS AT LHC
8
modules (100mrad of stereo angle), resulting in a single-point resolution of
between 2334 µm in the rψ direction and 230 µm in z. The lower radiation
levels in the TOB allow its 6 layers, with half-leght |z| < 110 cm, to mount
thicker sensors. Stereo modules with the same stereo angle are equipped in
the first 2 layers and the single-point resolution varies from 3552 µm in the
rφ direction and 530 µ in z.
(a) Pixel sensors and readout electronic
(b) Silicon strip sensor
Figure 1.5: CMS tracker detectors.
The endcaps are divided into the TEC (Tracker End Cap) and the TID
(Tracker Inner Disks). Each TEC comprises 9 disks that extend into the
region 120 cm < |z| < 280 cm, and each TID comprises 3 small disks that fill
the gap between the TIB and the TEC. Each module is arranged in rings and
have strips of variable pitch pointing towards the beam line. Stereo modules
are mounted on the first 2 rings of the TID and the innermost 2 rings and the
fifth ring of the TEC. The operating temperature of the total 15400 modules
is around −20o C.
Part
No detectors
TIB
2724
TIB
2724
TOB
5208
TID
816
TEC
2512
TEC(2)
3888
thickness (µm) mean pitch (µm)
320
81/118
320
81/118
500
81/183
320
97/128/143
320 96/126/128/143
500
143/158/183
Table 1.2: Different strip parameters in the silicon tracker.
CHAPTER 1. CMS AT LHC
1.2.2
9
Electromagnetic Calorimeter
The Electromagnetic Calorimeter (ECAL) is a hermetic, homogeneous calorimeter comprising 61 200 lead tungstate (PbWO4 ) scintillating crystals mounted
in the central barrel part, closed by 7324 crystals in each of the two endcaps.
Lead tungstate scintillating crystals have short radiation (X0 = 0.89 cm) and
Moliere (2.2 cm) lengths, are fast (80% of the light is emitted within 25 ns)
and radiation hard (up to 10 Mrad). The choice of PbWO4 crystals is driven
by the requirements of a compact calorimeter inside the solenoid that is fast,
has fine granularity, and is radiation resistant.
Figure 1.6: The CMS Electromagnetic Calorimeter layout.
The relatively low light yield (30 γ/M eV ) implies the use of photodetectors with intrinsic gain that can operate in a magnetic field. Silicon avalanche
photodiodes (APDs) are used as photodetectors in the barrel and vacuum
phototriodes (VPTs) in the endcaps. In addition, the sensitivity of both the
crystals and the APD response to temperature changes requires a temperature stability.
The barrel section (EB) has an inner radius of 129 cm. It is structured as
36 identical ”supermodules”, each covering half the barrel length and corresponding to a pseudorapidity interval of 0 < |η| < 1.479 . A ”supermodule”
is composed of four modules, each formed by submodules with five pairs
of crystals. The crystals are in quasi projective geometry, pointing to the
interaction vertex, and ensure a coverage of 24.7 X0 .
CHAPTER 1. CMS AT LHC
10
The endcaps (EE) are located at a distance of 314 cm from the vertex
and cover a pseudorapidity range of 1.479 < |η| < 3.0; they are structured
as “Dees” consisting of semi-circular aluminium plates from which are cantilevered structural units of 5 × 5 crystals, known as “supercrystals”. The
endcap crystals, like the barrel crystals, off-point from the nominal vertex
position, but are arranged in an xy grid (Fig. 1.6).
A preshower device is placed in front of the crystal calorimeter over much
of the endcap pseudorapidity range. The active elements of this device are
two planes of silicon strip detectors, with a pitch of 1.9 mm, which lie behind
disks of lead absorber at depths of 2 X0 and 3 X0 .
The energy resolution of the ECAL can be parametrized as a function of
energy:
!2 2
2
S
N
σ
= √
+ C2
+
E
E
E
where S is the stochastic term, N the noise and C the constant term, due to
intercalibration.
1.2.3
Magnet
One of the requirement for the CMS detector is the capability to perform
good momentum resolution measurements, and hence a good bending power
is a key point. It is provided by a 3.8 T magnetic field created by a 13 m long,
5.9 m inner diameter superconducting solenoid. This choice affects largely
the detector design and the technologies for the readout electronics: each
device in the tracker and in the calorimeters must work reliably under this
magnetic field.
1.2.4
Hadronic Calorimeter
The design of the hadron calorimeter (HCAL) is strongly influenced by the
choice of magnet parameters since, as mentioned before, most of the CMS
calorimetry is located inside the magnet coil and surrounds the ECAL system.
An important requirement of HCAL is to minimize the non-Gaussian tails
in the energy resolution and to provide good containment and hermeticity for
the ET measurement. Hence, the HCAL design maximizes material inside
the magnet coil in terms of interaction lengths. This is complemented by an
additional layer of scintillators lining the outside of the coil. Brass has been
CHAPTER 1. CMS AT LHC
11
Figure 1.7: The CMS Hadronic Calorimeter layout.
chosen as absorber material as it has a reasonable short interaction length,
is easy to machine and is non-magnetic.
In order to maximize the amount of absorber before the magnet, the
tile-fibre technology is adopted. It consists of plastic scintillator tiles read
out with embedded wavelength-shifting fibres. The fibres are spliced to high
attenuation length clear fibres outside the scintillator that carry the light to
the readout system.
The photodetection readout is based on multi-channel hybrid photodiodes. The absorber structure is assembled by bolting together precisely
machined and overlapping brass plates so as to leave space to insert the
scintillator plates, which have a thickness of 3.7 mm.
A crucial test to gauge the HCAL performance is the measurement of jet
energy resolution and missing transverse energy resolution. Studies have been
made on 3 parts of the calorimeter, chosen such that the jet energy resolution,
as a function of ET , is similar in all 3 parts.√ The missing transverse energy
ETmiss resolution is given by σ (ETmiss ) ≈ 1.0 ΣET
CHAPTER 1. CMS AT LHC
1.2.5
12
Muon System
Muon identification becomes more crucial for physics analysis as the centerof-mass energy and the luminosity increase and much of the new physics
is expected to be gleaned within the muon channels. Dealing with a great
bunch crossing rate (40 MHz) means that the CMS trigger must achieve an
enormous reduction and scant but efficient selection of events, togheter with
a good momentum measurement.
To achieve this challenging goal the CMS experiment is provided with
a robust muon system with three muon detectors [9]: Drift Tubes (DTs),
Cathode Strip Chambers (CSCs), and Resistive Plate Chambers (RPCs),
arranged in a barrel section and two planar endcaps. The choice of the
detector technologies has been driven by the very large surface to be covered
and by the different radiation environments (Fig.1.8).
The trigger and momentum measurement of the muons are performed by
the DTs in the barrel region and by the CSCs in the endcap region. The
RPCs operate in avalanche mode as dedicated fast muon trigger and are
installed both in the barrel region and in the endcap region, coupled with
DTs and CSCs.
Figure 1.8: Side view of the Muon Chambers. Various eta regions are separated with dashed lines.
CHAPTER 1. CMS AT LHC
13
The barrel muon system of the CMS detector consists of four stations
integrated in the return yoke of the magnet that cover a seudorapidity of
|η| < 1.2. Two stations are mounted on the inner and outer face of the yoke;
the remaining two are located in slots inside the iron. The segmentation
of each station is dictated by the longitudinal segmentation of the iron in
five rings, each 2.5 m long. In total, 60 chambers compose each one of the
inner three stations, while 70 chambers are used in the outer station. The
basic chambers detector is a drift cell of approximately 400 ns maximum
drift time. The twelve planes of drift tubes present in every chamber are
organized in three independent subunits called Super Layers (SL) made up
of four planes with parallel wires. Two SLs measure the coordinate in the
transverse plane,while the third measures the z coordinate. Thick honeycomb
place acts as a spacer between them. The four layers of each SL are staggered
by half a cell, making it possible to use the correlation of the drift times in
the different planes to compute the coordinate and the angle of the crossing
tracks without any external time tag.
In each endcap region, four muon stations of CSC (ME1 to ME4) are
demanded to detect the muons. These chambers have trapezoidal shape and
are arranged in a series of concentric rings centered on the beam line. The
stations are separated by the iron disks of the flux return yoke, with different
thickness, that isolate the electrons in showers and shield the detector from
backsplash backgrounds. The first station has three rings of chambers, at
increasing radius, and is placed inside the solenoidal magnet, while the other
three stations are composed of two rings of chambers working in a lower magnetic field. Therefore, the sagitta measurement at the first station is crucial
and leads to more stringent requirements on the resolution and alignment in
this station than in the other ones. The chambers overlap, so no dead area in
azimuthal range is left. Muons with typical pseudorapidity of 1.2 < |η| < 2.4
crosses 3 or 4 CSCs.
Planes of resistive plate chambers (RPCs) are mounted in both the barrel
and endcaps to provide an additional, complementary trigger. RPCs are
gaseous parallel-plate chambers with a reasonable level of spatial resolution
and excellent time resolution, comparable to that of scintillators. In the muon
system, these chambers will cover roughly the same area as the DTs and
CSCs but will provide a faster timing signal and have a different sensitivity
to background. The use of RPCs in the trigger selection is discusser later, in
a more dedicated section. Details on the three detectors are listed in Table
1.3.
CHAPTER 1. CMS AT LHC
Detector
η region
Stations
Layers
Chambers
Channels
DTs
0.0 - 1.3
4
Rφ8, Z4
250
195000
CSCs
0.9 - 2.4
4
6
540
Strips 273024
Wire groups 210816
Spatial
per wire 250µm
Rφ(6pts) 75µm
resolution
Rφ(6/8pts) 100µm
(outer CSCs) 150µm
√
(σ)
Z (3/4 pts) 150µm R(6pts) (15-50)/ 72µm
Time resolution
5 ns
6ns
Within 20ns
> 98%
> 92%
window
14
RPCs
0.0 - 2.1
Bar 4 - End 6
2
360 - 252
80640 - 80642
Cell Size
3ns
98%
Table 1.3: Drift Tubes (DTs), Cathode Strip Chambers (CSCs) and Resistive
Plate Chambers (RPCs) properties and statistics.
1.3
The trigger
Given the nominal luminosity of 1034 cm−2 s−1 , an event rate of 109 Hz
is expected. Therefore it is crucial to have an efficient and robust event
selection. The main physics requirements on the L1 trigger and the HLT
are:
• the selection must fulfill the needs of the CMS physics program; the
efficiency for the physics objects must be as high as possible;
• the selection must be as inclusive as possible, in order to keep every
possible hint of new physics;
• the rate of events accepted by the HLT should be within limits allowed
by the data storaging, taking down the the rate of event to 100 Hz;
• the final selection of events should include data samples for the calculation of all trigger and reconstruction efficiencies offine;
• the events selected should be tagged to indicate the reasons for their
selection.
CHAPTER 1. CMS AT LHC
15
The tighter constrain on the event selection is the bunch crossing time of
25 ns. In such a short time interval the trigger cannot access all the raw data
from the detector. CMS thus adopts a multi-level structure in which each
step accesses only a part of the whole data, with the main goal of minimizing
the overall CPU usage. The trigger is divided in two steps called Level-1
Trigger (L1) and High-Level Trigger (HLT) [10]. The L1 is based on custom
hardware and uses only coarsely segmented data from calorimeters and muon
detectors. Fig.1.9 shows the structure of the L1 trigger; the first action is the
analysis, made by Local Triggers, of the energy deposits in calorimeter trigger
towers and track segments or hit patterns in muon chambers. Regional Triggers combine informations of Local Triggers to determine and rank trigger
objects, physics candidates like particles, jets and global physical quantities.
The rank is determined as a function of energy or momentum and quality, reflecting the level of confidence attributed to the L1 parameter measurements.
The highest-rank trigger objects are selected by the Global Calorimetes and
Global Muon Triggers and sent to Global Trigger, that takes the decision to
accept or reject the event. During the Level-1 decision-making period, all
the high-resolution data is held in pipelined memories.
Figure 1.9: Structure of the Level-1 Trigger system.
After a fixed time interval of about 3.2 µs, the data from the pipelines
are transferred to front-end readout buffers and, through the event building,
CHAPTER 1. CMS AT LHC
16
data from a given event are transferred to a processor. Each processor runs
the HLT software code to reduce the output rate to the final 100 Hz. The
HLT code performs the reconstruction and selection of physics objects using
the full event data in less than 1 s; this results in a significant constraint
on the resources that the algorithms can use [24]. It is also necessary for
the algorithms to be solid and reliable. Rather than reconstruct all possible
objects in an event, the HLT implements the idea of partial reconstruction,
arranging a chain of virtual trigger levels that access the data from the different detectors. The Level 2 uses calorimeter and muon detector information,
the Level 2.5 additionally uses the tracker pixel information, and the Level
3 accesses the full event information.
The Muon Trigger, interesting for this thesis since the analysis will be
based on muon identification and reconstruction.
Muon trigger and reconstruction
The muon trigger system consists of the following items:
• Drift Tube (DT) Trigger
• Cathode Strip Chamber (CSC) Trigger
• Pattern Comparator Trigger (PACT) based on Resistive Plate Chambers (RPC)
• Global Muon Trigger
The DT an CSC ensure, thanks to their excellent spatial precision, sharp
momentum threshold and background rejection. The RPCs act as bunch
crossing identificators because of their faster time resolution. Time information and both spatial coordinates of a detected particle are carried by the
same signal, as a result ambiguities typical for wire detectors are eliminated.
The different and complementary features of DT/CSC and RPC build two
trigger subsystems which deliver independent information about detected
particles to the Global Muon Trigger (Fig.1.10).
DT and CSC electronics first process the information from each chamber
locally and for that are named local triggers. They produce a vector of position and angle for each muon crossing each station. The vectors are collected
by the Track Finder, which combines them to form muon candidates and
determinates their transverse momenta. The track finding principle relies on
CHAPTER 1. CMS AT LHC
17
extrapolation from a source track segment in one muon station to a possible
target segment in another station according to a pre-calculated trajectory
originating at the vertex. If a target segment of compatible location and
bending angle is found, it is linked to the source segment, for a maximum
combination of four segments to form a complete track. The Muon Sorter
select the four highest pt muons from each subsystem and sends them to
the Global Muon Trigger, that combines the information from the various
detectors. The merging takes into account trasverse momentum as well as
information about the tracks quality and presence in both systems; the data
leads to improved momentum resolution and efficiency compared to the standalone systems performances. The four muons that result as the best after
the Global Muon Trigger evaluation are sent to the Global Trigger and take
the name of Global Muons.
Figure 1.10: The Level-1 Muon Trigger.
The muon HLT is structured in two main levels. The Level-2 uses muon
chambers information to perform a stand-alone reconstruction, with the full
detector resolution. An iterative method reconstructs track segments and
builds the trajectory from inside out, then the track fitting is performed
from the outermost muon station inwards. A separate module computes the
isolation of each muon candidate using calorimeters information. The Level-3
extends the muon trajectories to include the full tracker system starting from
CHAPTER 1. CMS AT LHC
18
the Level-2 track and adding the pixel information. After each reconstruction
level, a selection is applied on the muon candidates with various variable. The
software module corresponding to this selection process is called filter, and a
sequence of filter steps is a trigger path. By changing the filter cuts different
trigger paths are created: in this way the muon trigger can be specialized to
match the needings of different physiscs analysis.
The main algorithm anternative to the muon reconstruction, explained
so far, is the so called muon identification. It considers all the inner tracker
tracks and then look for matching segments in the muon chambers. The
candidates produced via this strategy are called Tracker Muons (Fig.1.11). In
the creation of Tracker Muon candidates it is possible that a given segment is
associated to more than one silicon track; an Arbitration process assigns each
segment uniquely to a single candidate. The arbitration algorithm calculates
the quantity ∆R2 = ∆X 2 + ∆Y 2 for each possible candidate, with ∆X
and ∆Y being the distances between the extrapolated silicon track and the
segment in local X and Y coordinates. The one with minimum ∆R is chosen.
Figure 1.11: Different muon types reconstruction.
Chapter 2
Physics at CMS
The main goals for the CMS physics program can be framed in three main
areas of work: Standard Model processes, Higgs searches and measurements
and searches beyond the Standard Model.
The Standard Model sector contains studies of the strong interactions, top
quark physics and electroweak physics. B-hadrons will be copiously produced
at the LHC and B, Bs and the elusive Bc can be produced. At the LHC,
about one top quark pair is produced per second. Such a huge sample of top
quarks allows to perform detailed measurements of the top quark properties,
such as cross sections, spin properties, single top production, and searches for
new physics in top decays. A detailed study on the mass measurement precision, limited till LHC by the systematics errors, is then expected. The LHC
will also allow studies of QCD, electroweak, and flavour physics. Measuring
properties of the known particles with the highest precision as possible is a
complementary approach to direct searches for something new: any deviation
from the SM expectation is a signal of new physics.
One of the main missions of the LHC is to discover the origin of the
electroweak symmetry breaking mechanism. Therefore, the search for the
Higgs particle is a major task for the experiments. The Higgs particle search
is studied for the SM and MSSM Higgs(es) in the full mass range starting
from the LEP exclusion limits. Detailed systematic studies are included in
the estimates for the integrated luminosity needed for a 5σ discovery. MSSM
Higgs discoveries are studied both for neutral and charged Higgs.
The LHC is expected to break new ground at the TeV energy scale.
Search for new physics is therefore an extremely challenging field. If low
mass supersymmetry exists, it will be within the reach of the LHC. The multi19
CHAPTER 2. PHYSICS AT CMS
20
purpose nature of CMS detector allows it to test the discovery potential in
many different channels, with a wide choice of benchmark points that cover
large part of different signatures.
The discovery reach for scenarios with extra dimensions, and new vector
bosons high mass states are analyzed, using several different experimental
signals. Finally, alternative signatures for new physics such as contact interactions, heavy Majorana neutrinos, heavy top in Little Higgs models, and
same sign top quarks have been taken into account and are object of study.
2.1
B physics at CMS
The Heavy Flavor sector has been deeply investigated in the last decades.
The B-physics is a wide field of observation, both for precise electroweak
testing and physics beyond the SM probing. The b quark belongs to the
third generation of quarks as the weak doublet partner of t quark and, being
the lightest of the two, can only decay through flavor-changing processes.
In this perspective, the study of B systems at high statistics can improve
the constrains and test the SM for various decay channels. While B + and
B 0 mesons properties have been well studied in the Beauty Factory, proving
excellent agreement with the SM expectations, the higher energy available
at colliders opens a new frontier of study on heavier particles, such as Bs ,
b-baryons and the Bc meson. The LHC ensures a new era for this physics:
the center of mass energy avalaible is so high that the bb cross section will
be up to ∼ 5 time larger than the Tevatron. Both CMS and LHCb have
defined a rich program of measurements, focusing on their different strong
points. LHCb is optimized for the measurements of the B meson properties
at 2 < |η| < 4.5, while CMS is designed to give the best performances in the
complementary pseudorapidity region.
The more relevant detector components for B physics are the tracking
system and the muon chambers: the fine granularity of Pixels and Silicon
Strips allows to obtain a good track resolution even with few hits. This
means that low luminosities facilitate B physics studies, as the pile up effects
on track reconstruction are under control. An increased luminosity provides
on one hand an increment in statistics, but on the other also an increase
in the number of interactions per crossing so that the event reconstruction
becomes more challenging.
A particle that deserves careful study is the Bc meson. Its small cross-
CHAPTER 2. PHYSICS AT CMS
21
section has limited, so far, its experimental investigation. The CMS experiment, due to the excellent muon identification systen and tracker detectors,
allows the Bc± → J/ψπ ± and Bc± → J/ψπ ± π ± π ∓ final state studies in the
|η| < 2.4 region. These measurements, driven by the J/ψ benchmark in the
final state, will provide basic information about the Bc production at 7 TeV,
which are propedeutic for any more refined experimental investigation such
as the Bc → Bs X. Some of the most interesting exclusive decay studies are:
• Bs → µ+ µ− , as in the SM flavor-changing neutral current decays are
forbidden at tree level and can only proceed through higher-order loop
diagrams. By having a small error on the theoretical expectations, this
mode is very attractive as a SM test bench and is potentially sensitive
to physics beyond the SM. In the minimal supersymmetric extension of
the SM (MSSM) the branching fraction for this decay can be increased
by up to four orders of magnitude at large tanβ. Lower bounds on
tanβ can be obtained from branching ratio measurements relative to
this channel. CMS published upper limit is B(Bs → µ+ µ− ) < 1.9×10−8
[12], with improvements made in the recent period [18];
• Bs → J/ψ φ ,where the interference between Bs decays to J/ψ φ with
or without mixing gives rise to a CP violating phase φs [16].
2.2
The Bc meson
The Bc meson is the ground state of b̄c system. It is the only quark-antiquark
bound system composed of heavy quarks with different flavors, and thus
flavor asymmetric with open charm and beauty. This peculiarity makes it an
extremely interesting candidate for the study of the heavy-quark dynamics
compared to symmetric heavy quarkonium (bb, cc) states. The production
mechanism for this state is essentially different respect to the quarkonia; while
the bb pair can be created in the parton processes qq (gg → bb), to produce bc
two heavy q q̄ pairs have to be created in a single collision. Hadron colliders
are thus the ideal place for the study of Bc meson, due to the fact that
gluon fusion processes are predominant at the energy of LHC. Indeed, the
first observation of approximately 20 Bc events in the semileptonic channel
Bc± → J/ψl± ν came from the CDF Collaboration.
The variation of bound state conditions for the heavy quarks in various
systems makes possible to study processes where both the strong interactions
CHAPTER 2. PHYSICS AT CMS
22
and the electroweak decays take place. With the study of such processes, it is
possible to shed some light on the CP-violating parameters in the heavy quark
sector and to enlarge the quantitative understanding of QCD dynamics, as
well as to progress in the study of the most important parameters of the
electroweak theory.
The theoretical framework for the long-lived doubly heavy-quark hadrons
is provided by the understanding of QCD dynamics, based on the Operator Product Expansion (OPE), QCD sum rules (SR), non-relativistic QCD
(NRQCD) [19] and potential models (PMs) built on single heavy quark
physics [21]. The small ratio of confinement scale to the heavy quark mass
ΛQCD /mQ allows to describe strong interactions with heavy quarks with two
main tools: the OPE, related to the small virtuality of heavy quark in the
bound state, and the perturbative calculation of Wilson coefficients. Applying OPE on the heavy quark Lagrangian, effective theories are constructed
(HQET). A further simplification is provided by a nonrelativistic description of the process, suggested by the large mass of the heavy quarks. The
low velocity of motion compared with the mass makes non relativistic QCD
(NRQCD) a reliable tool for the study of doubly heavy meson such as the
Bc . This leads to analogies in respect to some heavy quarkonia systems, like
the suppression of light quark-antiquark and quark-gluon sea and the non
relativistic motion of b and c quarks. Under these conditions, the expansion
parameters for the Lagrangian are the relative velocity v of quarks and the
ratio ΛQCD /mQ . This double expansion generalizes the HQET approach to
the NRQCD. In addition, for the direct production of the Bc and other bc
mesons, the 1/mQ parameter is the appropriate quantity for the operator.
The most accurate predictions of the masses of Bc (including excited
states) are obtained in the framework of nonrelativistic potential models in
[15], where the mass of the 1S-level in the bc system is predicted to be
mBc = 6.25 ± 0.03 GeV /c2
with rather high accuracy.
At the moment there are only three modes experimentally seen: Bc± →
J/ψl± ν, Bc± → J/ψπ ± and Bc± → J/ψπ ± π ± π ∓ .
2.2.1
Bc production
The Bc production can be summarized as a three-stepped process:
CHAPTER 2. PHYSICS AT CMS
23
• the concurrent production of the b and c quarks, according to perturbative QCD calculations
• the binding of the quarks, in the framework on potential models
• the decay of excited state to the ground state, via hadronic or electromagnetic transition
The inclusive differential cross section represents the sum of the direct production cross section for the Bc and its excited states and can be written as
[15]:
dσ[p1 + p2 → Bc + X] =
XZ
dx1 dx2 fip1 (x1 , µ)fjp2 (x2 , µ)[dσ(ij → Bc + X)]
ij
(2.1)
where fi are the parton distribution functions and the sum is performed
over the partons i and j in the initial state hadrons. The NRQCD parametrization of the parton-parton cross section is:
dσ[ij → Bc + X] =
X
dσ[ij → bc(n) + X]hOH (n)i
(2.2)
n
It contains the short-distance cross section term dσ(ij → bc(n) + X) to
create the bc in the color and angular-momentum state n, calculated as a
pertubative expansion in αs for gluon fusion and annihilation processes, and
the non perturbative matrix element hOH (n)i, which encodes the probability
for a bc in the state n to bind to form the Bc meson. Such term scales by
the relative velocity v of the charm quark.
As pointed out before, two pairs of heavy quark must be produced in
a single collision: the lowest order process is therefore proportional to α4
instead of α2 (the case of qq). This explains the smaller Bc production cross
section with respect to particles from the Υ and Ψ families: for each Bc event,
one thousand events of other B mesons are expected. As αs depends on the
energy scale of the process, the α4 factor is responsible for large uncertainties
in the theoretical predictions: there is a large ambiguity in the choice of the
scale, since the short distance process involves several scales; experimental
measures will shed light on this. The hadronic hard scattering processes of
the LHC are the best environment possible nowadays for the Bc production,
because gluon fusion process is predominant and the high luminosity will
boost statistics.
CHAPTER 2. PHYSICS AT CMS
2.2.2
24
Bc decay
The first study of the Bc meson decay is dated 1986, with the work of Bjorken
[17] on the the decays of hadrons with heavy quarks. His calculations of
branching fractions and total widths are surprisingly similar to the modern
predictions. An accurate lifetime measurement is important to test the Bc
decay model while experimental studies of Branching Ratios (BR) and form
factors will give a better understanding of the hadronic matrix elements implicated in the process, determined by non-perturbative QCD effects. These
improvements will affect the determination of electroweak parameters, such
as the quark masses and the mixing angles in the CKM matrix, that represent constraints on the physics beyond the Standard Model in the quark
sector.
The processes responsible for the Bc meson decay can be split into three
types:
• the c quark decay with the spectator b quark
• the b quark decay with the spectator c quark
• the annihilation channel Bc± → l± νl (cs, us), l = e, µ, τ .
The Pauli Interference (PI) with the charm quark from the initial state
is separated in the process b → ccs, where cs comes from the W + decay.
The total width is the sum over the partial widths
Γ(Bc → X) = Γ(b → X) + Γ(c → X) + Γ(ann)
(2.3)
Due to the three different possible decay channels, the Bc meson has
an expected lifetime that is roughly one third shorter than other B mesons.
Depending on the theoretical framework chosen, the various branching ratios
are calculated and listed in Table 2.1.
In contrast to what occur in OPE, where the basic uncertainty is given
by the variation of heavy quark masses, in SR calculation these parameters
are fixed by the two-point sum rules for bottomonia and charmonia. The
accurancy for the total width of Bc is determined by the choice of scale for the
hadronic weak lagrangian in decays of charmed quark. Another framework,
used in calculations on non-annihilation channels, is the exclusive approach
(see Table 2.1). Here, to obtain the total width, it is necessary to sum up
widths of different decay modes calculated in the potential models (PM). The
CHAPTER 2. PHYSICS AT CMS
Bc decay mode
b → bl+ ν
b → cud
Σb → c
c → sl+ ν
c → sud
Σc → s
Bc+ → τ + ντ
Bc+ → cs
OPE %
PM %
3.9 ± 1.0
3.7 ± 0.9
16.2 ± 4.1 16.7 ± 4.7
25.0 ± 6.2 25.0 ± 6.2
8.5 ± 2.1 10.1 ± 2.5
47.3 ± 11.8 45.4 ± 11.1
64.3 ± 16.1 65.6 ± 16.4
2.9 ± 0.7
2.0 ± 0.5
7.2 ± 1.8
7.2 ± 1.8
25
SR %
2.9 ± 0.3
13.1 ± 1.3
19.6 ± 1.9
9.0 ± 0.9
54.0 ± 5.4
72.0 ± 7.2
1.8 ± 0.2
6.6 ± 0.7
Table 2.1: Amplitudes of the Bc decay modes calculated in the three frameworks
differences between the results are very thin: the main contibution to the Bc
lifetime is represented by c quark decays (∼ 70%) whereas the b decays and
annihilation contibute with about 20% and 10% respectively.
The calculations of the total Bc width in the inclusive OPE approach
and the exclusive PM approach give consistent values, taking into account
the largest uncertainty represented by the quark masses (especially the c
quark). The final result is [25]
τ (Bc )OP E = 0.55 ± 0.15 ps
Sum rules calculations lead instead to a theoric lifetime value of:
τ (Bc )SR = 0.48 ± 0.05 ps
which is consistent with the value of the Bc lifetime measured by the CDF
Collaboration in the semileptonic channel Bc± → J/ψl± X [6]
τ (Bc ) = 0.46+0.18
−0.16 ± 0.03 ps
2.2.3
Experimental measurements
Due to its small cross section and higher mass, compared to other B mesons,
the Bc meson is a rather elusive particle and its experimental detection is
quite recent respect to its first theorical assumption.
The current measurements are limited to few decay modes involving the
J/ψ meson, since this charmonium is clearly detected in experiments due to
5
TABLE II: Branching ratios of exclusive Bc+ decays at the fixed choice of factors: ac1 = 1.20 and ac2 = −0.317 in the non-leptonic
decays of c quark, and ab1 = 1.14 and ab2 = −0.20 in the non-leptonic decays of b̄ quark. The lifetime of Bc is appropriately
normalized by
τ [Bc ] ≈ 0.45 ps.
numbers in AT
square
brackets present the marginal values obtained in some potential
models
CHAPTER
2. The
PHYSICS
CMS
26
in order to show possible range of variation.
Bc+
Bc+
Bc+
Bc+
Bc+
Bc+
Bc+
Bc+
Bc+
Bc+
Bc+
Bc+
Bc+
Bc+
Bc+
Bc+
Bc+
Bc+
Bc+
Bc+
Bc+
Bc+
Mode
BR, %
Mode
BR, %
Mode
→ ηc e+ ν
0.75 [0.5] Bc+ → J/ψK +
0.011 [0.007] Bc+ → Bs0 K +
→ ηc τ + ν
0.23 [0.2] Bc → J/ψK ∗+
0.022 [0.016] Bc+ → Bs∗0 K +
0
→ ηc! e+ ν
0.020 [0.05] Bc+ → D+ D
0.0053 [0.0018] Bc+ → Bs0 K ∗+
∗0
→ ηc! τ + ν 0.0016
[-] Bc+ → D+ D
0.0075 [0.002] Bc+ → Bs∗0 K ∗+
0
+
+
∗+
→ J/ψe ν
1.9
[1] Bc → D D
0.0049 [0.0009] Bc+ → B 0 π +
∗0
+
+
∗+
→ J/ψτ ν
0.48 [0.35] Bc → D D
0.033 [0.003] Bc+ → B 0 ρ+
0
! +
+
+
→ψe ν
0.094 [0.2] Bc → Ds D
0.00048 [0.0001] Bc+ → B ∗0 π +
∗0
! +
+
+
→ψτ ν
0.008
[-] Bc → Ds D
0.00071 [0.00012] Bc+ → B ∗0 ρ+
0
0 +
+
∗+
→D e ν
0.004 [0.02] Bc → Ds D 0.00045 [0.00005] Bc+ → B 0 K +
∗0
0 +
→D τ ν
0.002 [0.08] Bc+ → Ds∗+ D
0.0026 [0.0002] Bc+ → B 0 K ∗+
∗0 +
+
+
→ D e ν 0.018 [0.004] Bc → ηc Ds
0.28
[0.07] Bc+ → B ∗0 K +
∗0 +
+
∗+
→ D τ ν 0.008 [0.016] Bc → ηc Ds
0.27
[0.07] Bc+ → B ∗0 K ∗+
0 +
+
+
→ Bs e ν
4.03
[1] Bc → J/ψDs
0.17
[0.05] Bc+ → B + K 0
∗0 +
+
∗+
→ Bs e ν
5.06 [1.2] Bc → J/ψDs
0.67
[0.5] Bc+ → B + K ∗0
0 +
+
+
→B e ν
0.34 [0.08] Bc → ηc D
0.015
[0.04] Bc+ → B ∗+ K 0
∗0 +
+
∗+
→B e ν
0.58 [0.15] Bc → ηc D
0.010 [0.002] Bc+ → B ∗+ K ∗0
+
+
+
→ ηc π
0.20 [0.12] Bc → J/ψD
0.009 [0.002] Bc+ → B + π 0
+
+
∗+
→ ηc ρ
0.42 [0.3] Bc → J/ψD
0.028 [0.014] Bc+ → B + ρ0
+
+
0 +
→ J/ψπ
0.13 [0.08] Bc → Bs π
16.4
[1.6] Bc+ → B ∗+ π 0
+
+
0 +
→ J/ψρ
0.40 [0.2] Bc → Bs ρ
7.2
[2.4] Bc+ → B ∗+ ρ0
+
+
∗0 +
→ ηc K
0.013 [0.008] Bc → Bs π
6.5
[1.3] Bc+ → τ + ντ
∗+
+
∗0 +
→ ηc K
0.020 [0.018] Bc → Bs ρ
20.2
[11] Bc+ → cs̄
BR, %
1.06
[0.2]
0.37 [0.13]
–
–
1.06
[0.1]
0.96
[0.2]
0.95 [0.08]
2.57
[0.6]
0.07 [0.01]
0.015 [0.012]]
0.055 [0.006]
0.058 [0.04]
1.98 [0.18]
0.43 [0.09]
1.60 [0.06]
1.67
[0.6]
0.037 [0.004]
0.034 [0.01]
0.033 [0.003]
0.09 [0.03]
1.6
4.9
Figure 2.1: Prediction for exclusive decays of the Bc meson.
so that in the absolute value of width it can be compared with the estimate of spectator decay [7],
!
+
−15
!
−
Γ[Bespecially
≈ 20
c → c̄c cs̄] sr
the pure leptonic decays,
J/ψ
→· 10µ+ µGeV,
and J/ψ → e+ e− .
!
three channels that have
provided
a direct
are:
Γ[Bc+
→ c̄c cs̄]!spect.
≈ 90mass
· 10−15measurements
GeV,
The
Bc → J/ψ(→
µ )l1/4.5.
ν This result is in agreement with the estimate in OPE [7], where a
and we find the•suppression
factor ofµabout
strong dependence of negative term caused by the Pauli interference on the normalization scale of non-leptonic weak
lagrangian was •
emphasized,
so that at
Bc± → J/ψ(→
µ+moderate
µ− )π ± scales one gets approximately the same suppression factor, too.
To the moment we certainly state that the accurate direct measurement of Bc lifetime can provide us with the
information on both±the masses of charmed
± ±beauty
• B → J/ψ(→ µ+ µ− )πand
π π ∓ quarks and the normalization point of non-leptonic weak
lagrangian in the Bc cdecays (the a1 and a2 factors). The experimental study of semileptonic decays and the extraction
of ratios for the form factors can test the spin symmetry derived in the NRQCD and HQET approaches and decrease
The first observation
was reported
the CDF
collaboration
1998,
the theoretical uncertainties
in the corresponding
theoretical by
evaluation
of quark
parameters asin
well
as the hadronic
matrix elements,
determined
by the nonperturbative
the reconstruction
quark confinement.channel
The measurement
via the
semileptonic
channel [7]. effects
Beingcaused
not abyfull
of branching
fractions of
forneutrino
the semileptonic
non-leptonic
modesCarlo
and their
ratios can on
inform
on the values of
(because
missingandenergy),
a Monte
corrections
a visible
factorization parameters, which depend again on the normalization of non-leptonic
weak
lagrangian.
The charmed
spectrum
M (Jψl) between 3.35 and 11 GeV/c2 has to be accounted for
quark counting
in the Bwith
c decays is related to the overall contribution of b quark decays as well as with the suppression
of b̄ → cc̄s̄ transition
because
the destructive The
interference,
which value for
depends
on reconstructed
the nonperturbative
the choice
of Bof
mass measured
these
Bcparameters
c candidates.
(roughly estimated,
the
leptonic
constant)
and
non-leptonic
weak
lagrangian.
2
events is M(Bc )=6.40±0.39(stat)±0.13(syst) GeV/c . CDF also measured
Thus, the progress in measuring
the Bc lifetime and decays could enforce the theoretical understanding of what
the inmean
proper
decay
lenght
really happens
the heavy
quark
decays
at all. cτ , Monte Carlo corrected, obtaining a lifetime
±
+ −
±
CHAPTER 2. PHYSICS AT CMS
27
Figure 2.2: First evidence of the Bc meson in the decay channel Bc± → J/ψπ ±
by the CDF Collaboration.
of τ = 0.46+0.18
−0.16 (stat)±0.03(syst) ps [6]. The D0 collaboration measured the
Bc lifetime in the same channel, using about 1.3 f b−1 harvested between 2002
and 2006 [13],obtaining the value τ = 0.448+0.038
−0.036 (stat)±0.032(syst) ps.
±
The fully reconstructed decay Bc → J/ψπ ± has been investigated later,
due to its lower rate, by CDF [8] and D0. The CDF fit of the invariant mass
distributions (Fig 2.2) results in the Bc mass values of M (Bc ) = 6285.7 ±
5.3(stat) ± 1.2(syst) M eV /c2 [1].
The first observation of the Bc meson decaying into J/ψπ + π − π + was
reported by LHCb at EPS Conference in July 2011 [5] and is shown in Figure
2.3. LHCb also observed the Bc → J/ψπ decay and measured 163.1±15.7
events in a data sample of 0.3 fb−1 .
CHAPTER 2. PHYSICS AT CMS
28
(a) Bc± → J/ψπ ± signal
(b) Bc± → J/ψπ + π − π + signal
Figure 2.3: Observation of the Bc meson in the decay channels Bc± → J/ψπ ±
and Bc± → J/ψπ + π − π + by the LHCb Collaboration.
Chapter 3
Event Selection
In this work, the analysis of the Bc± → J/ψπ ± and Bc± → J/ψπ ± π ± π ∓ channels performed on the 2011 data of CMS is reported. The Bc± → J/ψµ± ν
channel has been studied most in the past because of its higher Branching Ratio (BR). The only available Bc lifetime measurement has been performed at
the Tevatron on this semileptonic mode; however, because of the undetected
neutrino, some MC corrections are required. In contrast, the Bc± → J/ψπ ±
and Bc± → J/ψπ ± π ± π ∓ channels are kinematically closed and less affected
by the MC corrections and the related systematics. The topology of the
decay channel Bc± → J/ψπ ± is sketched in Figure 3.1. The decay channel B ± → J/ψK ± , topologically equivalent to Bc± → J/ψπ ± , is studied as it
serves as normalization channel for BR measurements and, being statistically
richer, allows various consistency checks. The analysis strategy adopted for
the reconstruction of the decay is carried out in different steps:
• the reconstruction is driven by the triggered candidate J/ψ;
• the J/ψ meson is then combined with one or three tracks in order to
form a valid vertex;
• several additional cuts are applied to isolate the Bc signal with respect
to the large background.
For each event there will be the possibilty that multiple candidates fulfill the
basics requests on the quality of the track and on vertex reconstruction. The
one with the highest pT is retained and subjected to additinal topological
selection criteria in the analysis.
29
CHAPTER 3. EVENT SELECTION
30
~B
reco P
c
✓
P~⇡
P~µ
SV
P~µ+
P~Bc
L
PV
PV
Figure 3.1: Bc± → J/ψπ ± decay scheme. The Bc± → J/ψπ ± π ± π ∓ is similar,
except for the number of π.

The same strategy is adopted for both the channels, although each one is
tuned with different cut values in order to maximize the signal yield and its
isolation from the background.
3.1
Datasets and JSON Files
The study reported in this thesis in based on a sub-sample of the data
recorded by the CMS detector in 2011, with a centre of mass energy of
7 T eV .
The LHC delivered about 5.73 f b−1 of data to CMS, of which CMS
recorded about 5.22 f b−1 (Fig.3.2). It must be pointed out that not all the
collisions of the LHC lead to good events: a JSON file (Java Script Object
Notation) certificates which luminosity sections in which runs are considered
good and should be processed. Information on the machine conditions and
tunings, detector calibration, geometry and alignements is contained in the
Global Tag.
The dataset used for the analysis are:
• /MuOnia/Run2011A-PromptReco-v4/AOD
• /MuOnia/Run2011A-PromptReco-v5/AOD
CHAPTER 3. EVENT SELECTION
31
• /MuOnia/Run2011A-PromptReco-v6/AOD
• /MuOnia/Run2011B-PromptReco-v1/AOD
The associated Global Tag are:
GR P V 22
and the JSON file is:
Cert 160404−180252 7T eV P romptReco Collisions11 JSON M uonP hys.txt
The various datasets correspond to different luminosity periods and different
machine conditions, which affect the data taking. The trigger and reconstruction efficiency of the experiments is also affected, as pointed out in Figure
3.3 and Table 3.1.
Figure 3.2: Integrated luminosity vs time delivered to (red), and recorded by
CMS (blue) during stable beams at 7 T eV centre of mass energy.
CHAPTER 3. EVENT SELECTION
32
Ntrk
0.0045
1e33
0.004
2e33
3e33
0.0035
5e33
0.003
0.0025
0.002
0.0015
0.001
0.0005
0
0
100
200
300
400
500
600
700
800
Event Track Size
(a) Track size
Nprim
0.18
1e33
0.16
2e33
3e33
0.14
5e33
0.12
0.1
0.08
0.06
0.04
0.02
0
0
5
10
15
20
25
30
Primary Vertex Size
(b) Primary Vertex Collection size
Figure 3.3: Event track size (3.3a) and Primary Vertex Collection size (3.3b)
for different luminosity periods.
CHAPTER 3. EVENT SELECTION
Dataset
PromptReco
PromptReco
PromptReco
PromptReco
2011A v4
2011A v5
2011A v6
2011B
PV (mean)
5.4
6.4
10.1
11.1
33
Track Size (mean)
216
248
372
399
Table 3.1: Mean number of primary vertex and track size per event for the
2011 data, divided per dataset.
3.2
Triggers
The Trigger system has been described in the section 1.3. As pointed out, in
CMS the trigger plays a fundamental role: the physics analyses are strictly
related to which events the various triggers accept. It is anyway useful to
recall that the HLT contains various trigger paths, each corresponding to a
dedicated selection. A path consists of several steps (software modules), if
an intermediate filter decision on a trigger path is negative, the rest of the
path is not executed (skipped) and the specific trigger rejects the event.
A trigger table contains the names of the paths avalaible for the reconstruction of events. It changes because of technical reasons and variations in
the luminosity delivered by the LHC. Dealing with various versions of HLT
trigger table complicates the study, since the triggered object is selected with
different criteria, affecting from the beginning the efficiency of the whole analyses. In the worst cases, the trigger becomes prescaled (a prescale factor is
applied to its algorithm and its rate is lowered) or is discarded, in order to
free band width in favor of the discovery potential at high pT , for triggers
designed for the leading edge CMS analyses.
For the Heavy Flavor analyses like this one, at relatively low pT , dedicated
dimon triggers were introduced to identify the J/ψ meson from B-decays.
The instantaneous luminosity varied during the year and so did the trigger
tables. Table 3.2 summarizes the various trigger tables implemented in the
periods of analysis.
3.2.1
Analysis Triggers
The analysis is driven by the J/ψ meson decaying into two muons, with a
branching ratio of (5.93 ± 0.06) × 10−2 .
Triggers based on dimuon identification are therefore taken into account.
CHAPTER 3. EVENT SELECTION
Luminosity cm−2 s−1
1 − 1.44 × 1033
2 × 1033
3 × 1033
5 × 1033
34
Trigger tables
Run2011/1.e33/v1.1/HLT/V1 to ../v1.2/HLT/V3
Run2011/2e33/v1.1/HLT/V1 to ../v1.2/HLT/V7
Run2011/3e33/v1.1/HLT/V1 to ../v5.0/HLT/V1
Run2011/5e33/v1.4/HLT/V3 to ../v2.2/HLT/V4
Table 3.2: Instantaneous luminosities and trigger menus used in this analysis.
Events per 10 MeV
Dedicated triggers for the detatched J/ψ → µ+ µ− are very useful for the aim
of this work and are present with slight variations in the whole data under
study (Tab 3.3).
Figure 3.4 shows the mass spectrum for the dimuon vertices reconstructed
by the various triggers, spanning a range from 1 to more than 100 GeV. All
the main physical resonances are well identified, although some of them are
prescaled (the ones not coloured in the plot).
106
2011 Run, L = 1.1 fb-1 J/ψ
CMS s = 7 TeV
5
10
ψ'
Bs
Υ
4
10
ω φ
trigger paths
ψ'
J/ψ
Bs → µ+µΥ
low p double muon
T
high p double muon
T
3
10
Z
102
10
1
10-1
1
10
102
dimuon mass [GeV]
Figure 3.4: Dimuon mass spectrum in 2011 data collected by early July,
corresponding to an integrated luminosity of 1.1 f b−1 . The superimposition
of various dimuon trigger paths is performed, with different colors for the
non prescaled triggers.
CHAPTER 3. EVENT SELECTION
Dataset
PromptReco 2011A v4
PromptReco 2011A v5
PromptReco 2011A v6
PromptReco 2011B
Trigger Path
HLT DiMuon7 Jpsi Displaced v1
HLT DiMuon7 Jpsi Displaced v3
HLT DoubleMu3p5 Jpsi Displaced v2
HLT DoubleMu3p5 Jpsi Displaced v2
HLT DoubleMu4 Jpsi Displaced v1
HLT DoubleMu4 Jpsi Displaced v1
HLT DoubleMu4 Jpsi Displaced v4
HLT DoubleMu4 Jpsi Displaced v5
35
L cm−2 s−1
1 × 1033
1.44 × 1033
2 × 1033
2 × 1033
3 × 1033
3 × 1033
3 × 1033
5 × 1033
Lumi pb−1
954
411.875
673.143
2644
Table 3.3: Datasets and Triggers used in this analysis. For each period, the
corresponding integrated luminosity is reported.
These triggers select events where the two muons have:
• a minimum traverse momentum (single or paired);
• opposite charge;
• a maximum Distance of Closest Approach (DCA), which calculate their
minimum spatial distance;
• a threshold in Confidence Level (CL) of the dimuon vertex, i.e. the
J/ψ candidate.
The following cuts are also applied to establish whether the J/ψ is coming
from the interaction point (prompt J/ψ) or is a decay product of a resonance:
• cosα > 0.9, where α is the angle, in the transverse plane, between
the dimuon momentum and the separation between the dimuon vertex
calculated and the beamspot.
• Lxy /σ > 3 , where Lxy is the transverse detachment between the
dimuon vertex and the beamspot and σ is the relative uncertainty.
• pµµ
T > 6.9 GeV.
The detachment in Lxy /σ is crucial to discard the prompt J/ψ [11].
Numerical values of the requirements for HLT DiMuon7 Jpsi Displaced
and HLT DoubleMu4 Jpsi Displaced are given in Table 3.4.
The offline analysis aims at reconstructing locally the J/ψ which has
fired the trigger. To do this, two opposite charged muons from the Muon
CHAPTER 3. EVENT SELECTION
36
Cuts:
DiMuon7 Jpsi Displaced DoubleMu4 Jpsi Displaced
single PT µ min
0
4
pair PT µ min
6.9
6.9
J/ψ mass window
2.9 - 3.3
2.9 - 3.3
J/ψ vertex CL
0.005
0.15
J/ψ detachment
3
3
J/ψ coseno
0.9
0.9
DCA
0.05
0.05
ηµ max
2.4
2.2
L1 seed
L1 DoubleMu0
L1 DoubleMu0 HighQ
Table
3.4:
List
of
the
main
thresholds
required
HLT DiMuon7 Jpsi Displaced and HLT DoubleMu4 Jpsi Displaced.
by
Collection are selected. Both global and tracker muons are considered, with
arbitration (see section 1.3) perfomed to the latter. The same trigger cuts
are then implemented, with further requirements on the muon track quality,
listed in Table 3.5.
Valid Hits nr
Valid Pixel Hits nr
Normalized χ2
>6
>2
< 10
Table 3.5: Supplementary requirements on muon track quality.
3.2.2
Trigger Match
The Trigger Matching tool allows to check whether the offline J/ψ candidates
correspond to those triggered, giving an important feedback on reliability of
the offline reconstruction strategy and on the various trigger
efficiencies.
q
2
The matching algorithm defines the quantity ∆R = ∆η + ∆φ2 , where
∆η and ∆φ are the differences in η and φ coordinates between the offline
muons and the ones that formed the J/ψ triggered. The Trigger Matching
condition is satisfied if ∆R < 0.5, otherwise the event is rejected.
A check has been carried out on the dataset 2011A PromptReco v4, showing that the cases where the reconstructed J/ψ is different from the triggered
one are in the order of 10−4 .
CHAPTER 3. EVENT SELECTION
37
Figure 3.5 shows the numbers of the J/ψ triggered in each event; in most
of the cases only one J/ψ pass the trigger, and is correctly identified by the
trigger match.
jpsiCounter_coseno
1
Entries 2903880
Mean
1.5
RMS
0.0207
10-1
10-2
10-3
10-4
10-5
10-6
1
2
3
4
5
6
7
Number of J/ ψ candidates
Figure 3.5: Number of Jpsi triggered per event in 2011A PromptReco v4
dataset, semilogarithmic view.
3.3
Track Combination
Once the J/ψ meson is correctly reconstructed, a third track from the Track
Collection is selected: it has not to be identified as a muon track and must
satisfy quality cuts analogous to those applied to the muon pair (Tab 3.6).
An additional cut imposes a minimum transerse momentum threshold for
the accepted third track of 0.9 GeV /c, rejecting the very low pT tracks.
The three tracks vertex is reconstructed using the Kalman Vertex Fitter
and the vertex CL has to be greater than 0.001.
CMS does not have a particle identification detector to distinguish a pion
track from a kaon one. It is thus only possible to assign a priori the π mass to
the selected track in the Bc analysis and the K mass for the B ± normalization
channel. In the Bc± → J/ψπ ± π ± π ∓ analysis, three tracks are selected instead
CHAPTER 3. EVENT SELECTION
38
of one, each subjected to the same quality cuts mentioned before. In case of
multiple candidates per event, the one with highest pT is chosen (Fig. 3.6).
Valid Hits nr
Valid Pixel Hits nr
χ2 /ndof
pT (GeV)
|η|
>6
>2
<3
> 0.9
< 2.4
Table 3.6: Third track quality requirements.
Mean
RMS
×10
3
2200
5.089
5.372
2000
1800
1600
1400
1200
1000
800
600
400
200
0
0
5
10
15
20
25
30
35
40
number of Bc candidates per event
Figure 3.6: Distribution of Bc candidates for a Bc± → J/ψπ ± event.
The invariant mass distributions of the highest pT candidate per event for
B and Bc are presented in Fig.3.7. The B ± peak is clearly visible without
any additional cut in the region between 5.1 and 5.4 GeV /c2 . On the other
hand, the Bc invariant mass shows no evidence for the signal in the expected
mass region (between 6 and 6.5 GeV /c2 ). The peak in the region between
5 and 5.5 GeV/c2 of the Bc± → J/ψπ ± channel is due to the Cabibbosuppressed decay B ± → J/ψπ ± , overwhelmed by the ”reflection” caused by
the decay of a B ± whose K is misidentified as a π. In the Bc± → J/ψπ ± π ± π ∓
plot (3.7c) a similar effect is visible; in this case the misidentified K could
come from the decay B ± → J/ψπ ± π ± K ∓ . The reflected peak in this five
bodies state is less sharp because of the higher combinatorial background
produced in the analysis.
±
CHAPTER 3. EVENT SELECTION
3.4
39
Signal optimization
Further studies are performed on the selected Bc events, aiming at improving
the yield and the Signal toNoise ratio of the selection [20]. The main cuts,
analyzed in order to achieve this goal and obtain a stable and isolated signal,
are:
• Secondary vertex CL
Although a minimum threshold of the secondary vertex is already required, a tighter cut can improve the selection as it increases the goodness of the fit. It is more likely for the background events to have a
lower CL, since the vertex isn’t a real particle decay.
• J/ψ and tracks η.
A narrow |η| window allows to improve the track resolution, since more
precise momentum measurements are performed by the detector.
• Bc and track pT
Applying a minimum threshold in transverse momentum helps in rejecting the softer particles, often responsible for background effects.
• pointing back angle
The pointing back angle θ is defined as the angle between the vector
connecting the primary and the secondary vertex and the reconstructed
l·Bc
is defined, in ”analcandidate momentum. The quantity cosθ = |l|·|B
c|
ogy” with the J/ψ trigger request.
• L/σL
−
L is the decay length, obtained as the projection of the vector →
s,
pointing from the primary to the secondary vertex, onto the momen→
− ·−
p→
B
tum (L = s−
). The primary vertex is chosen as the one with the
→
pB
highest track pT from the Vertex Collection and is recalculated eventually excluding the tracks belonging to the secondary vertex. σL is the
resolution on L, for discarding those candidates whose proper decay
length is not well reconstructed.
The combinations of these cuts for the extraction of good signals in Bc± →
J/ψπ ± and Bc± → J/ψπ ± π ± π ∓ channels are performed and disussed in later
sections.
CHAPTER 3. EVENT SELECTION
40
HBcK
Entries 5971680
Mean
4.625
0.6002
RMS
80000
70000
60000
50000
40000
30000
20000
10000
0
4
4.5
5
5.5
6
6.5
7
2
GeV/c
(a) Channel B ± → J/ψK ±
BcPi
50000
HBcPi
Entries 5971680
Mean
4.683
0.6325
RMS
40000
30000
20000
10000
04
4.5
5
5.5
6
6.5
7
GeV/c2
(b) Channel Bc± → J/ψπ ±
22000
20000
EachBcMass
Entries
3413227
Mean
5.038
0.7668
RMS
18000
16000
14000
12000
10000
8000
6000
4000
4
4.5
5
5.5
6
6.5
7
GeV/c2
(c) Channel Bc± → J/ψπ ± π ± π ∓
Figure 3.7: Invariant mass distributions of B ± (3.7a) and Bc (3.7b and 3.7c)
candidates, after candidate selection.
Chapter 4
Monte Carlo studies
The knowledge of the reconstruction efficiencies is a necessary condition for
any branching ratio measurement, and only Monte Carlo studies are able to
provide this information.
The Bc production rate is ∼ 10−3 with respect to the bb production.
Therefore, in PYTHIA, only one Bc is produced out of ∼ 106 p-p interactions.
To enhance the event generation efficiency a dedicated generator is necessary:
BCVEGPY is a hadronic production program for B c mesons, based on a
complete calculation approach [22][23]. The Bc production is computed at
the lowest order α4 in terms of the dominant subprocess of perturbative
QCD (pQCD) gg → Bc (Bc∗ ) + c + b. The generation is interfaced with
PYTHIA and the CMSSW analysis framework in two steps. BCVEGPY
generates ”parton” configurations in Les Houches Accord format (file LHE),
a standard file format proposed to store process and event information. The
files are then input to PYTHIA6 for the hadronization.
Since the general samples do not implement the Bc production, private
samples have been produced locally. The production conditions are a collision
energy of 7 TeV and a luminosity of L = 2×1033 , representing an intermediate
point for the machine conditions in the whole 2011 data. The sample for the
B ± → J/ψK ± channel is produced completely in PYTHIA6 (Tune Z2).
A total of 385000 Bc± → J/ψπ ± , 180000 B ± → J/ψK ± and 385000
Bc± → J/ψπ ± π ± π ∓ events are produced and tested.
41
CHAPTER 4. MONTE CARLO STUDIES
4.1
42
Testing the generator
Some studies are carried out in order to test the reliability of the Bc production model at 7 TeV:
• the comparison between the pure signal MC and sideband-subtracted
data.
Agreement in the distributions of the main kinematical and topological variables is a necessary condition to suggest that data are well
reproduced by the local MC.
• the comparison between the MC and data sidebands.
The study of these distibutions is useful for refining cuts on variables
that present different trends for the signal and the background, offering
a more effective background selection preserving the signal.
4.1.1
MC signal - Data signal
In this section is presented a series of studies on the distibution of the main
variables of the event. The pure signal events coming from the Bc → J/ψπ ±
Monte Carlo are compared with data after the subtraction of the background.
The results are shown in Figures 4.2 and 4.3.
A ±2σ region is taken within the Bc mass value and two sideband of
2σ each are chosen at the two sides as representatives of pure background
regions (see Fig.4.1). The assumption is that the sideband regions represent
the background under the signal and, consequently, their subtraction will
result in a clean signal distribution.
The tune of the cuts is driven by statistic considerations, as the trigger rejects most of the event generated and it is not trivial to perform the
reconstruction with a sufficient set of events.
The correspondant studies with the three pions channel suffer from the efficiency drop of the trigger so that not enough events are collected to perform
a statistically significant test.
The analysis presents an overall agreement between the distributions
shapes, both for kinematical and topological variables. In particular, the
pT of data and MC appear to be very similar (plot 4.2a), suggesting that the
generator and the trigger are able to reproduce data.
CHAPTER 4. MONTE CARLO STUDIES
43
BcPi
300
HBcPi
Entries 3039905
Mean
6.172
RMS
0.4134
250
200
150
100
50
0
5.6
5.8
6
6.2
6.4
6.6
6.8
7
2
GeV/c
Figure 4.1: Invariant mass distribution for the Bc candidates, showing signal
region (orange) and sidebands (grey).
4.1.2
MC signal - Data background
Several complementary issues could emerge from the study of the MC with
respect to the data background events coming from the sidebands. The focus
of these analyses is the search for substantial differencies in the two distributions, in order to develop more effective strategies and a better set of cuts for
the signal over background isolation. The plots reported in Figures 4.4 and
4.5 attest that no additional signatures, which could be exploited to better
discriminate signal against background, manifest. However, the pT distribution (Fig.4.4a) suggests that the signal is lying at slightly higher pT values
than the background. A mimimum threshold for the candidate transverse
momentum will cut events more likely coming from the background rather
than signal. Regarding the η instead (see plot 4.4b), the sidebands data seem
to cover wider pseudorapidity windows with respect to the MC, which slightly
prefers more central regions. Narrowing the maximum |η| could favour the
signal isolation and also improve resolutions.
CHAPTER 4. MONTE CARLO STUDIES
44
Bc pt - pt sideband
0.2
HDiffPt_Bc
Entries
335
Mean
22.43
Data
0.15
MC
HDiffPt_Bc
0.1
Entries
56
Mean
21.87
0.05
0
-0.05
0
5
10
15
20
25
30
35
40
45
GeV/c
(a) Transverse momentum
Bc eta - eta sideband
0.12
Data
0.1
MC
HDiffEta_Bc
0.08
HDiffEta_Bc
Entries
Entries
335
56
Mean-0.0306
0.1252
Mean
0.06
0.04
0.02
0
-0.02
-2
-1
0
1
2
η
(b) η
Figure 4.2: Comparison between MC (red) and data Bc signal (black) for
some variables.
CHAPTER 4. MONTE CARLO STUDIES
45
Bc CL SV - sideband
0.1
Data
HDiffCLs_Bc
Entries
Mean
0.08
HDiffCLs_Bc
56
0.5834
Entries
MC
Mean
335
0.5233
0.06
0.04
0.02
0
-0.02
-0.04
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
(a) Secondary vertex CL
Bc L/Sigma - L/Sigma sideband
0.2
Data
MC
0.15
HDiffLS_Bc
HDiffLS_Bc
Entries
Mean
335
Entries
56
18.26
0.1
Mean
15.77
0.05
0
0
10
20
30
40
50
(b) L/σ
Figure 4.3: Comparison between MC (red) and data Bc signal (black) for
some variables.
CHAPTER 4. MONTE CARLO STUDIES
46
Bc sideband pt
0.18
Data sideband
0.16
MC
HPt_Bc_BKG
Entries
Mean
100
20.13
0.14
0.12
HDiffPt_Bc
Entries
56
Mean 21.87
0.1
0.08
0.06
0.04
0.02
0
0
5
10
15
20
25
30
35
40
45
GeV/c
(a) Transverse momentum
Eta sideband
0.05
Data sideband
MC
0.04
0.03
0.02
0.01
HDiffEta_Bc
HEta_Bc_BKG
Entries
Mean
100
Entries
0.0272
Mean
0
-2
-1
0
1
2
56
-0.0306
η
(b) η
Figure 4.4: Distributions of the main variables for the MC (red) and the
background data from the sidebands (black).
CHAPTER 4. MONTE CARLO STUDIES
47
CL SV sideband
HCLs_Bc_BKG
Entries
100
Mean
0.4754
0.06
Data sideband
HDiffCLs_Bc
Entries
MC
56
Mean 0.5834
0.05
0.04
0.03
0.02
0.01
0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
(a) Secondary vertex CL
L/Sigma sideband
0.16
Data sideband
0.14
MC
0.12
HLS_Bc_BKG
Entries
100
Mean
13.44
0.1
0.08
Entries
Mean
56
15.77
0.06
0.04
0.02
0
0
10
20
30
40
50
(b) L/σ
Figure 4.5: Distributions of the main variables for the MC (red) and the
background data from the sidebands (black).
CHAPTER 4. MONTE CARLO STUDIES
4.1.3
48
Additional MC studies
The study of the distributions of primary vertices and track size for the MC
and the data can bring to light differencies in the overall event topology. A
mean value of 6.1 for the number primary vertex and 210 for the track size
are found, proving a substantial agreement with the data observations (recall
Tab.3.1).
The J/ψ pT distribution of the generated events slightly differs between
the Bc± → J/ψπ ± and the Bc± → J/ψπ ± π ± π ∓ productions (Fig 4.6). In
particular, the spectrum of the J/ψ in the first channel is shifted to higher
values with respect to the latter. This effect could be explained by the
different number of bodies in the final state, resulting in a lower Q-value
for the three pions decay. Less energy is thus avalaible for the J/ψ and its
momentum would be consequently lower.
It is worth noticing that the trigger transverse momentum threshold is at
7 GeV , therefore a great part of the generated J/ψ mesons does not survive
this cut. Only 6% of the generated J/ψ matches this trigger requirement for
π/K analysis; for the three pions case the situation is worse, with only a 3%
of accepted events.
In the context of topological analyses, the correct identification of the
vertices positions plays a crucial role. The choice between the multiple primary vertices of interactions emerging from each collision depends on the
criteria of arbitration assumed. The event production vertex is inferred from
the CMS Offline Primary Vertex Collection. In the high pile-up conditions,
when multiple Primary Vertices (PV) are reconstructed, the choice of the
event vertex is not trivial. In this analysis the production vertex is chosen as
the primary vertex whose associated track collection has the higest pT sum,
while the decay vertex (i.e. the secondary vertex) is reconstructed offline. To
verify that the arbitration does not bias the analysis, a test with the MC is
mandatory. The wrong choice of PV would affect the L evaluation and all the
correlated variables. The lifetime measurement would be strongly influenced
by the selection. A typical bias check is the pull distribution, in which is
calculated the quantity
→
−
−
x RECO − →
x GEN
σ
where the three spatial coordinate distance between the true primary vertex
(obtained by generation) and the one chosen in the reconstruction is divided
by the position error of the latter. If no biases are introuduced, the typical
CHAPTER 4. MONTE CARLO STUDIES
49
Pt Jpsi
Mean 3.262
RMS
9000
2.144
8000
7000
6000
5000
4000
3000
2000
1000
0
0
2
4
6
8
10
12
14
16
18
20
pT(J/ ψ ) GeV/c
(a) Bc± → J/ψπ ± channel
Mean 2.606
RMS 1.794
7000
6000
5000
4000
3000
2000
1000
0
0
2
4
6
8
10
12
14
16
18
20
p (Jψ) GeV/c
T
(b)
Bc±
± ± ∓
→ J/ψπ π π
channel
Figure 4.6: Transverse momentum distributions of the generated J/ψ for
Bc± → J/ψπ ± (4.6a) and Bc± → J/ψπ ± π ± π ∓ channels (4.6b).
expected function is a Gaussian with mean µgaus = 0 and associated error
σgaus = 1. Pull distributions in the three dimensions are produced for the
Bc± → J/ψπ ± channel and fitted with Gaussian (µ = 0, σ = 1) in Figure 4.7.
The results of the fit guarantee that the choice of the primary vertex with
respect to the pT criterion does not bias the analysis.
Although the limited statitic forbids to perform a robust analysis for the
Bc± → J/ψπ ± π ± π ∓ channel, pull distributions have been studied as well and
do not show any dramatic biases (Fig. 4.8).
CHAPTER 4. MONTE CARLO STUDIES
XRECO PV - X GEN PV / σRECO
50
Entries
556
RMS
50
1.227
χ2 / ndf
30.25 / 29
37.43 ± 2.21
Constant
40
Mean
30
-0.003874 ± 0.049920
1.112 ± 0.046
Sigma
20
10
0
-10
-8
-6
-4
-2
0
2
4
6
8
10
(a) x coordinate
Y RECO PV - Y GEN PV/ σRECO
Entries
Mean
RMS
556
0.03681
1.244
38.69 / 34
45
χ 2 / ndf
40
Constant
41.24 ± 2.39
Mean
0.02192 ± 0.04441
Sigma
0.9934 ± 0.0373
35
30
25
20
15
10
5
0
-10
-8
-6
-4
-2
0
2
4
6
8
10
(b) y coordinate
ZRECP PV - Z GEN PV/ σRECO
Entries
556
RMS
45
1.183
χ 2 / ndf
40
Constant
35
Mean
30
Sigma
41.82 / 26
36.4 ± 2.3
-0.08653 ± 0.05067
1.033 ± 0.046
25
20
15
10
5
0
-10
-8
-6
-4
-2
0
2
4
6
8
10
(c) z coordinate
Figure 4.7: The Bc± → J/ψπ ± pull distributions in the three spatial dimensions are showed. The choice of the PV does not bias the analysisis.
CHAPTER 4. MONTE CARLO STUDIES
51
Pull: (XPRIMBP-XPRIM)/Error
Entries
13
Mean -0.08563
RMS
0.9368
3
2.5
2
1.5
1
0.5
0
-10
-8
-6
-4
-2
0
2
4
6
8
10
(a) x coordinate
Pull: (YPRIMBP-YPRIM)/Error
Entries
13
Mean
0.2875
RMS
1.249
2
1.8
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
0
-10
-8
-6
-4
-2
0
2
4
6
8
10
(b) y coordinate
Pull: (ZPRIMBP-ZPRIM)/Error
Entries
13
Mean
0.6093
RMS
1.107
2
1.8
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
0
-10
-8
-6
-4
-2
0
2
4
6
8
10
(c) z coordinate
Figure 4.8: The Bc± → J/ψπ ± π ± π ∓ pull distributions in the three spatial
dimensions are showed.
Chapter 5
Bc± → J/ψπ ± and
Bc± → J/ψπ ±π ±π ∓ analysis
While the pre-selection cuts allow for the B ± → J/ψK ± peak to be resolved
clearly, no evidence of Bc signal emerges from the Bc invariant mass distribution (see plots 3.7). The strategy adopted for the Bc signal extraction is
driven by the selection criteria exposed in section 3.4.
Starting from a reasonable baseline selection, various cuts are separately
evolved to tighter values and the response of the signal is checked in terms of
variations in the peak yield and Signal to Noise (StoN) ratio. Such approach,
supported by the Monte Carlo considerations, leads to the discrimination of
the most favourable selections for the optimization of the signal.
5.1
Bc± → J/ψπ ± signal
A good set of topological selections, which leads to a good signal yield and
to a signal to noise ratio of ∼ 0.3, for the Bc± → J/ψπ ± channel is:
• Secondary vertex CL > 10 %
• cosθ > 0.85
• |η(J/ψ)| < 1.6
• L/σ > 3
• |η(π/K)| < 1.6
52
CHAPTER 5. BC± → J/ψπ ± AND BC± → J/ψπ ± π ± π ∓ ANALYSIS
53
• pT (Bc ) > 8 GeV
• pT (µ) > 4 GeV
The signals of B ± → J/ψK ± and Bc± → J/ψπ ± with these selections
are shown in Figure 5.1. A yield of 495±71 events with a signal to noise
ratio of 0.33 is obtained for the Bc . As expected, many more B ± events are
reconstructed, leading to a yield of 164541±533 with a signal to noise ratio
of 6.9.
(a) B ± → J/ψK ± channel
(b) Bc± → J/ψπ ± channel
Figure 5.1: Invariant mass distributions for B ± → J/ψK ± (5.1a) and Bc± →
J/ψπ ± (5.1b) channels. The peak is fitted with a Gaussian over a polynomial
background.
CHAPTER 5. BC± → J/ψπ ± AND BC± → J/ψπ ± π ± π ∓ ANALYSIS
54
The behaviors of the Bc± → J/ψπ ± yield (a) and StoN ratio (b) when the
various variables are evolved are presented in plots from Figure 5.2 to 5.5.
When the evolution is performed on a variable, the others are kept fixed at
correspondant baseline values.
The cosine evolutions (Fig 5.2a and 5.2b) show a constant increase in the
StoN ratio, without substantial yield loss; at the last steps, which correspond
to cosines greater than 0.9997, the peak is reconstructed with StoN ≥ 1
without compromising the yield much. The pointing back angle turns out to
be a useful criterion of selection for topology studies also in its offline three
dimensional generalization (remember that cosθxy is already implemented in
the J/ψ trigger).
Regarding the secondary vertex confidence level, a better vertex reconstruction (up to 0.20 in CL) boost the StoN till ∼ 0.5 (5.3a), achieving an
increase of a factor of 4 in spite of an almost constant yield (5.3b).
The behavior of the extracted signal as a function of η needs a more
precise explanation, as it can appear misleading. The plot 5.4a suggests a
linear correlation between pseudorapidity and yield until the latter reach a
plateau at about |η| ∼ 1.5. On the other hand, such increase comes along
with a reduction in StoN ratio. The physical explanations lies in the fact
that integrating over |η| adds both signal and background events and so, the
more signal events are extracted (increasing the yield), the more background
is added. The StoN properly estimates how many background events are
reconstructed for each signal event. From a certain point (|η| ∼ 1.5 in this
case), no more signal events are retained and all the new contribution comes
from the background: the yield reachs a value of ∼ 450 while the StoN drop
to ∼ 0.15. The pseudorapidity is therefore a powerful tool for the extraction
of with out a strong signature, such as the Bc .
Finally, the L/σ evolutions (Fig 5.5a and 5.5b) show that a more severe
detachment causes a yield loss (remember that the Bc has a shorter lifetime
than most of other B-mesons) but is efficient in the background reduction as
the combinatory is more likely to be short lived.
Yield
CHAPTER 5. BC± → J/ψπ ± AND BC± → J/ψπ ± π ± π ∓ ANALYSIS
600
500
400
300
200
100
0
0
10
20
30
40
50
60
70
80
cosθ evolution (cut number)
S/N
(a) Yield evolution of cosθ, from 0.9599 to 0.9999
2.5
2
1.5
1
0.5
0
0
10
20
30
40
50
60
70
80
cosθ evolution (cut number)
(b) StoN evolution of cosθ, from 0.9599 to 0.9999
Figure 5.2: Yield and signal to noise evolutions for Bc± → J/ψπ ±
55
Yield
CHAPTER 5. BC± → J/ψπ ± AND BC± → J/ψπ ± π ± π ∓ ANALYSIS
600
500
400
300
200
100
0
0
2
4
6
8
10
12
14
16
18
20
Secondary vertex CL evolution (cut number)
S/N
(a) Yield evolution of CL, from 0.01 to 0.20
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0
2
4
6
8
10
12
14
16
18
20
Secondary vertex CL evolution (cut number)
(b) StoN evolution of CL, from 0.01 to 0.20
Figure 5.3: Yield and signal to noise evolutions for Bc± → J/ψπ ±
56
Yield
CHAPTER 5. BC± → J/ψπ ± AND BC± → J/ψπ ± π ± π ∓ ANALYSIS
600
500
400
300
200
100
0
0
2
4
6
8
10
12
14
16
18
ηπ evolution (cut number)
S/N
(a) Yield evolution of pion |η|, from 0.7 to 2.4
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0
2
4
6
8
10
12
14
16
18
ηπ evolution (cut number)
(b) StoN evolution of pion |η|, from 0.7 to 2.4
Figure 5.4: Yield and signal to noise evolutions for Bc± → J/ψπ ±
57
Yield
CHAPTER 5. BC± → J/ψπ ± AND BC± → J/ψπ ± π ± π ∓ ANALYSIS
600
500
400
300
200
100
0
0
2
4
6
8
10
12
14
L/σ evolution (cut number)
S/N
(a) Yield evolution of L/σ, from 0 to 14
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0
2
4
6
8
10
12
14
L/σ evolution (cut number)
(b) StoN evolution of L/σ, from 0 to 14
Figure 5.5: Yield and signal to noise evolutions for Bc± → J/ψπ ±
58
CHAPTER 5. BC± → J/ψπ ± AND BC± → J/ψπ ± π ± π ∓ ANALYSIS
59
From the evolution studies, some cuts are identified giving a S/B ratio
≥ 1. For instance, a signal yield of a 187 ± 32 events is achieved, with a
S/B=1.33, when the cosθ > 0.9994 cut is applied over the baseline cuts. The
corresponding invariant mass distribution is shown in Fig.5.6.
Figure 5.6: Invariant mass distribution for Bc± → J/ψπ ± . The cut cosθ >
0.9994 is tightened with respect to the baseline cuts.
5.2
Bc± → J/ψπ ±π ±π ∓ signal
The same signal optimization strategy is performed on the the Bc± → J/ψπ ± π ± π ∓
channel. However, some requests for the baseline selections must be hardened with respect to the Bc± → J/ψπ ± channel, since it is more difficult
to reconstruct higher multiplicity final states while keeping the background
under control. No evidence of signal is found with the baseline selection of
the Bc± → J/ψπ ± analysis (Fig.5.7). The secondary vertex confidence level,
for instance, is raised to 0.15, since the evolution plots for the Bc± → J/ψπ ±
suggest an improvement in StoN without consistent drawbacks. The cut on
|ηπ | is spread to the two new tracks, while the |ηJ/ψ | and the minimun candidate pT are mantained invariated. The major improvements comes from the
CHAPTER 5. BC± → J/ψπ ± AND BC± → J/ψπ ± π ± π ∓ ANALYSIS
60
topological cuts like the pointing back angle and the L/σ detachment, which
play a striking role for the background reduction. The baseline selection for
Bc± → J/ψπ ± π ± π ∓ channel is:
• Secondary vertex CL > 15 %
• cosθ > 0.99
• |η(J/ψ)| < 1.6
• L/σ > 8
• |η(π)| < 1.6
• pT (Bc ) > 8 GeV
• pT (µ) > 4 GeV
The signal obtained with this selection is presented in Figure 5.8: a yield of
193±47 is obtained, with a StoN ratio of 0.33.
Figure 5.7: Invariant mass distribution for Bc± → J/ψπ ± π ± π ∓ with Bc± →
J/ψπ ± baseline cuts. The region between the red lines is where the Bc signal
is expected.
The evolutions of the variables are shown in plots from 5.9 to 5.12. From
the cosine evolution (Fig. 5.9a and 5.9b) it can be inferred that when
CHAPTER 5. BC± → J/ψπ ± AND BC± → J/ψπ ± π ± π ∓ ANALYSIS
61
a cosθ ∼ 0.9994 is reached, the StoN ratio approaches 1 without a dramatic loss in the yield. The cut of CL > 0.15 is necessary to isolate the
Bc± → J/ψπ ± π ± π ∓ signal. Spanning of the cut up to 0.25 does not show any
significant improvement to reduce the background (Fig. 5.10a and 5.10b). In
the η evolution figures, the number of events are shown when integrated in
an increasing region from 0.5 to 1.6. It is clear from the plot that, when region wider than |η| > 1.3 are considered, more backgroundis integrated than
signal. The L/σ variable is eventually evolved. When L/σ > 16 is reached,
the StoN arrives at ∼ 1. However, since the Bc is a short lived state, a severe
detachment cut reduces the yield of a form ∼ 3. A value of L/σ > 8 is then
considered also for the final signal selection.
Figure 5.8: Invariant mass distribution for Bc± → J/ψπ ± π ± π ∓ with baseline
cuts.
Yield
CHAPTER 5. BC± → J/ψπ ± AND BC± → J/ψπ ± π ± π ∓ ANALYSIS
62
250
200
150
100
50
0
10
20
30
40
50
60
70
80
cosθ evolution (cut number)
S/N
(a) Yield evolution of cosθ, from 0.999 to 0.9999
2
1.8
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
0
10
20
30
40
50
60
70
80
cosθ volution (cut number)
(b) StoN evolution of cosθ, from 0.999 to 0.9999
Figure 5.9: Yield and Signal to Noise evolutions for Bc± → J/ψπ ± π ± π ∓
Yield
CHAPTER 5. BC± → J/ψπ ± AND BC± → J/ψπ ± π ± π ∓ ANALYSIS
63
260
240
220
200
180
160
140
120
100
0
2
4
6
8
10
12
14
16
Secondary vertex CL evolution (cut number)
S/N
(a) Yield evolution of CL, from 0.10 to 0.25
0.6
0.5
0.4
0.3
0.2
0
2
4
6
8
10
12
14
16
Secondary vertex CL evolution (cut number)
(b) StoN evolution of CL, from 0.10 to 0.25
Figure 5.10: Yield and Signal to Noise evolutions for Bc± → J/ψπ ± π ± π ∓
64
Yield
CHAPTER 5. BC± → J/ψπ ± AND BC± → J/ψπ ± π ± π ∓ ANALYSIS
250
200
150
100
50
0
2
4
6
8
10
12
ηπ evolution (cut number)
S/N
(a) Yield evolution of pion |η|, from 0.5 to 1.6
0.7
0.6
0.5
0.4
0.3
0.2
0
2
4
6
8
10
12
ηπ evolution (cut number)
(b) StoN evolution of pion |η|, from 0.5 to 1.6
Figure 5.11: Yield and Signal to Noise evolutions for Bc± → J/ψπ ± π ± π ∓
Yield
CHAPTER 5. BC± → J/ψπ ± AND BC± → J/ψπ ± π ± π ∓ ANALYSIS
65
250
200
150
100
50
0
2
4
6
8
10
L/σ evolution (cut number)
S/N
(a) Yield evolution of L/σ, from 8 to 18
1.4
1.2
1
0.8
0.6
0.4
0.2
0
2
4
6
8
10
L/σ evolution (cut number)
(b) StoN evolution of L/σ, from 8 to 18
Figure 5.12: Yield and Signal to Noise evolutions for Bc± → J/ψπ ± π ± π ∓
CHAPTER 5. BC± → J/ψπ ± AND BC± → J/ψπ ± π ± π ∓ ANALYSIS
66
Driven by considerations obtained from the evolution plots, a signal with
good StoN ratio, of the order ∼ 1.3, is obtained with a harder cut selection,
increasing the cosθ > 0.9995 and narrowing the pseudorapidity window to
|ηπ | < 1.2. The relative signal plot is shown in Figure 5.13.
Figure 5.13: Invariant mass distribution for Bc± → J/ψπ ± π ± π ∓ . More severe
cuts cosθ > 0.9995 and |ηπ | < 1.2 are applied over the baseline selection.
Separated studies on the various datasets have shown that the scaling of
the signal is not proportional to the increase of the statistic. In particular,
the 2011 B dataset contributes mainly with background events. Morover, the
overall event topology varies with time. With the increase of the luminosity,
which grows from the value 1.44 × 1033 of the PromptReco 2011A v4 to
5 × 1033 in the last period of PromptReco 2011B v1, the reconstruction of
the events becomes more challenging and the multiplicity of tracks and vertex
increases. Different trigger conditions play a role too. The efficiency of the
analysis suffers because of these variations, as shown in the plots 5.14a and
5.14b.
CHAPTER 5. BC± → J/ψπ ± AND BC± → J/ψπ ± π ± π ∓ ANALYSIS
67
(a) 2011A v4
(b) 2011B v1
Figure 5.14: Invariant mass distributions of Bc± → J/ψπ ± π ± π ∓ channel for
two datasets, 2011A v4 (upper plot) and 2011B v1 (lower plot). Despite the
lower statistic, the upper plot shows more signal than the lower one.
Chapter 6
Branching Ratio evaluations
6.1
σ(Bc± )×Br(Bc± →J/ψπ ± )
σ(B ± )×Br(B ± →J/ψK ± )
Once a reliable signal extraction is achieved, the ratio
can be evaluated through the relation
σ(Bc± )×Br(Bc± →J/ψπ ± )
σ(B ± )×Br(B ± →J/ψK ± )
σBc± × Br(Bc± → J/ψπ ± ) × Bc±
N (Bc± → J/ψπ ± )
=
N (B ± → J/ψK ± )
σB ± × Br(B ± → J/ψK ± ) × B ±
Differently from CDF, which performed a similar measurement using the
Bc± → J/ψµ± ν semileptonic channel, two hadronic decay channels are compared here. The two channels have three bodies in the final state and similar
signatures. Uncertainties on the production mechanism and many systematics cancel out in the ratio Bc± /B ± , which relates the two channel reconstruction efficiencies.
The non-vanishing effects are taken into account by the different efficiencies, obtained by Monte Carlo calculations. The efficiency values i can be
factorized as
i =
Naccepted
Ntriggered Nreconstructed
×
×
= acceptance + trigger + reco
Ngenerated
Naccepted
Ntriggered
where Naccepted is the number of the generated events that lie in the region
|η| < 2.5, i.e. the detector active region, Ntriggered are the events that pass
the trigger and Nreconstructed the ones that reach the end of the analysis. The
different factors, expressed in percentage, are summarized in Table 6.1. The
68
CHAPTER 6. BRANCHING RATIO EVALUATIONS
acceptance
trigger
reconstruction
69
Bc± →J/ψ π± % B ± →J/ψK ± %
56.63 ± 0.15 51.27 ± 0.21
0.31 ± 0.01
0.86 ± 0.03
21.95 ± 2.01
29.26 ±2.19
Table 6.1: MC efficiencies at L = 2 × 1033 cm−2 s−1 .The efficiency values are
factorized in the three components.
low statistic at the end of the reconstruction is mostly due to the low trigger
efficiency, determined by the tight cuts on the J/ψ dicussed in the previous
section.
The efficiency evaluation through the local MC sample is performed under
two correlated assumptions:
• 2×1033 represents an average luminosity value for the 2011 data taking;
• the efficiency results can be extended to the other luminosity periods.
For a more precise measurement, the signal events should be divided
into the different luminosity periods and corrected by the corresponding efficiencies, generated by different MC. By the way, it must be recalled that the
creation and the testing of the private MC sample tuned for Bc production at
7 TeV has been a great effort for the Milano group. The yields considered for
the measurement correspond to the baseline selections of the Bc± → J/ψ π ±
and B ± → J/ψK ± channels (Fig.5.1).
N (Bc± →J/ψπ ± )×B ±
σ(Bc± )×Br(Bc± →J/ψπ ± )
is equal to
The first estimate of σ(B
± )×Br(B ± →J/ψK ± ) = N (B ± →J/ψK ± )×
±
Bc
497 ± 71
(1.23 ± 0.08) × 10−3
×
= (0.982 ± 0.214)%
164541 ± 533 (3.77 ± 0.57) × 10−4
This measurement is compared with a preliminary number presented by
the LHCb Collaboration at EPS 2011, studying the 7 TeV collisions, namely
(1.4 ± 0.4 ± 0.1)%. The two cross-section × branching ratios from CMS and
LHCb are in good agreement.
Comparison with Tevatron data at 1.8 TeV can be also carried out, with
indirect considerations. CDF performed the measurement
σ(Bc± ) × BR(Bc± → J/ψl± ν)
+0.032
= 0.132+0.041
−0.037 (stat.)±0.031(syst.)−0.020 (lif etime)
±
±
±
σ(B ) × BR(B → J/ψK
CHAPTER 6. BRANCHING RATIO EVALUATIONS
70
Inferring the ratio (Bc± → J/ψl± ν)/(Bc± → J/ψπ ± ) from the theory, the
value of (0.90 ± 0.28)% can be estrapolated, still in agreement with the result
here presentated for the first time in CMS.
In order to renforce the result, the same ratio is calculated in various η
regions. In Table 6.2 are presented the results obtained for |η| < 0.5, 0.5 −
1, 1−1.5 for the baseline cuts and the tight selection, where the cosθ > 0.9994
is requested in addition to the baseline. No evidences for any particular
dependance as a function of |η| are found.
baseline cuts
tight cuts
|η| < 0.5
0.5 < |η| < 1.0 1.0 < |η| < 1.5
(0.98 ±0.29)% (0.82 ±0.28)% (0.06±0.03)%
(1.10 ±0.38)% (0.94 ±0.34)% (0.96 ±0.32)%
Table 6.2: Bc± /B ± ratio calculated for different |η| windows and cut selections.
When all the events are weighted by the efficiency evaluated in the last
period of data taking (with L = 3 − 5 × 1033 ) the ratio is R = 1.32 ± 0.29%.
To proceed with further considerations, a higher MC statistic would be
necessary.
6.2
Br(Bc →J/ψ3π)
Br(Bc →J/ψπ)
The first observation of the channel Bc± → J/ψπ ± π ± π ∓ in CMS allows to
c →J/ψ3π)
measure the BR ratio Br(B
.
Br(Bc →J/ψπ)
Differently from the previous evaluation for B ± /Bc , the cross section
production σBc vanishes in the calculation and the comparison between the
yield lead directly to the BR.
Br(Bc± → J/ψπ ± π ± π ∓ ) × (Bc± →J/ψπ± π± π∓ )
N (Bc± → J/ψπ ± π ± π ∓ )
=
N (Bc± → J/ψπ ± )
Br(Bc± → J/ψπ ± ) × (Bc± →J/ψπ± )
The efficiencies are listed in Table 6.2. The MC assumptions made for the
B /Bc ratio are still valid. To limit possible residual systematics introduced
by the analysis cuts, the Bc± → J/ψπ ± channel is now subjected to the same
severe selection as the Bc± → J/ψπ ± π ± π ∓ .
±
CHAPTER 6. BRANCHING RATIO EVALUATIONS
71
The list of the cuts and the correspondant signal are presented in Figure
6.1.
The tighter cuts reduce the yield and the MC efficiency but improve the
discrimination from the background and a clear isolation of the signal peak.
acceptance
trigger
reconstruction
Bc± →J/ψπ± % Bc± →J/ψπ± π± π∓ %
56.63 ± 0.15
52.57 ± 0.14
0.31 ± 0.01
0.16 ± 0.01
4.1 ± 0.08
2.1 ±0.8
Table 6.3: MC efficiencies at L = 2 × 1033 cm−2 s−1 , with separate efficiency
contributions.
Cut set
sv CL
> 15%
cosθ
> 0.999
|η(J/ψ)|
< 1.6
L/σ
>8
|η(π)|
<1
pT (Bc )
> 8 GeV
pT (µ)
> 4 GeV
Figure 6.1: Cut selection and correspondant Bc± → J/ψπ ± π ± π ∓ signal for
c →J/ψ3π)
the Br(B
branching ratio.
Br(Bc →J/ψπ)
CHAPTER 6. BRANCHING RATIO EVALUATIONS
72
The calculation leads to the result
92 ± 19
(7.1 ± 1.4) × 10−5
×
= (3.55 ± 1.79)
102 ± 15 (1.8 ± 0.7) × 10−5
This evaluation suffers from a big uncertainty, mainly due to the efficiency
estimations. Ongoing efforts in the production of larger MC samples will
limit this dominant source of error in the future, aiming at a more precise
measurement. This result can be compared to theoretical predictions and
a recent experimental calculation. The LHCb collaboration has obtained
for the same BR the value of 3.0 ± 0.6 ± 0.4 [14]. From the theoretical
side, predictions of this BR calculated by Rakitin and Koshkarev with a norecoil approximation lead to the value 1.5 [3]. Likhoded and Luchinsky use
three different approaches to predict the form factors and obtained ratios
Br(Bc+ →J/ψπ + π + π − )
=2.0,1.9 and 2.3 respectively [2].
Br(B + →J/ψπ + )
Chapter 7
Bc lifetime
The lifetime of the Bc meson is performed using the reduced proper time
technique[4] in the Bc± → J/ψπ ± channel. This estimate represents the first
lifetime calculation for a fully reconstructed Bc decay mode. This analysis
method has been traditionally used for the determination of the charmed
meson lifetimes, whose values sit in the range of 10−13 s, i.e. the same as the
Bc meson. The reduced proper time t0 is defined as
t0 =
mBc × (L − Nσ )
cp
where L is the distance between the primary and the secondary vertex, mBc
and p are the mass and the momentum of the Bc candidate, c the light speed
and Nσ is number of σL after which the reduced time is considered.
If σL is independent from L, the t0 distribution follows the same exponential distribution of the proper decay time, with the same τ and therefore
same lifetime value. The application of this technique corresponds to the
requirement of a minimum L/σ cut, in analogy with the topology criterion
defined for the signal isolation. Although the efficiency at short proper times
is reduced, the background rejection is enhanced, since background events
are mostly short-lived.
The reduced proper time is evaluated on a event-by-event basis and the
obtained distribution is fitted with a binned maximum likelihood. Such
method allows to infer the signal and background distributions directly from
data and does not require any background parametrization. The signal reduced proper time distribution is made with events taken within ±2σ of the
Bc mass peak, while the backgound distributions are formed by events com73
CHAPTER 7. BC LIFETIME
74
ing from two sidebands chosen at 4σ above and below the Bc mass peak,
each half as wide as the signal region (Fig.7.1). The signal and background
reduced proper time distributions are divided in proper time wide bins, spanning about 6 nominal lifetimes.
BcPi
80
HBcPi
Entries 2141458
Mean
6.053
RMS
0.3331
70
60
50
40
30
20
10
0
5.6
5.8
6
6.2
6.4
6.6
6.8
2
GeV/c
Figure 7.1: Events considered in lifetime measurement: the signal region is
represented in orange, while sidebands are colored in grey.
The number of events for each reduced proper time bin ni is predicted as
the sum of two terms, representing the signal and the background:
0
f (t0i )e−t /τ
bi
ni = (Ns − B) ·
+B·
0 −t0 /τ
Σi f (ti )e
Σi bi
where Ns and B are the total number of events in the signal and background
regions respectively, bi is the observed number of events in a reduced proper
time bin i of the sideband histogram, and f (t0i ) is a correction function obtained from Monte Carlo simulation. B and τ are the free parameters of the
fit. The MC correction function is obtained dividing the simulated reconstructed reduced proper time in each bin by the input decay exponential:
in this way the geometric acceptance, reconstruction efficiency and analysis
cuts are taken into account in the binned fit. The plot 7.2 shows the f (t0i )
correction function.
CHAPTER 7. BC LIFETIME
75
Correction function
14
12
10
8
6
4
2
0
0
0.5
1
1.5
2
2.5
t' (ps)
Figure 7.2: Correction function, obtained by dividing the simulated reconstructed reduced proper time in each bin by the generated proper time distribution.
In Figure 7.3, the results of this technique performed on the 2011 data
samples are shown; the baseline selection cuts of the Bc± → J/ψπ ± π ± π ∓
signal are used for the extraction of the Bc signal.
In the left plot, three t0 distributions are shown:
• the predicted distibution, result of the binned fit, is indicated by the red
histogram;
• the data are indicated with black dots and error bars;
• the background distibution is superimposed, incicated by the teal histogram.
In the right plot a pure exponential function with the fitted lifetime
value is superimposed to the background subtracted, efficiency corrected reduced proper time distribution. From the fit, the value τ = 0.453+0.042
−0.038 ps
is obtained. This result is in agreement with the PDG value of τP DG =
0.45 ± 0.04 ps, based on the CDF and D0 meaurements in the semileptonic
channel Bc± → J/ψµ± ν. Further improvements will be performed with new
MC samples that will lead to a better determination of the correction functions, and with the new statistic expected for the 2012 data harvesting.
CHAPTER 7. BC LIFETIME
Bc reduced proper time
102
76
Bc Signal corrected proper time
Bc reduced proper time
Background proper time
Bc Signal corrected proper time
Bc corrected proper time
10
10
1
1
0
0.2 0.4 0.6 0.8
1
1.2 1.4 1.6 1.8 2
t' (ps)
0
0.2 0.4 0.6 0.8
1
1.2 1.4 1.6 1.8 2
t' (ps)
Figure 7.3: On the left, the reduced proper time distribution for observed
events (dots) is shown. The red histogram represents the predicted events
and the teal histogram the background events superimposed. On the right,
an exponential curve with the fitted lifetime (pink line) is superimposed to
background subtracted and MC corrected reduced proper time distribution
(dots).
Conclusions
The last year has been very exciting for the high energy physic. The LHC
delivered to the CMS experiment more than 5 f b−1 of luminosuty, exceeding
by far the expectations. The various CMS analyses received thus a great
boost, entering the region in which hints of New Physics could begin to
show up. CMS refined not only the Higgs searches, but also those involving
Supersymmetry and Exotica (new physics beyond the Standard Model).
The harvesting of such high statistic made also possible the study of rare
processes in the B sector, such as Bs → µ+ µ− (with the CMS result B(Bs →
µ+ µ− ) < 7.7 × 10−9 at 95% CL). In addition, the elusive Bc particle has been
detected in the fully reconstructed (Bc± → J/ψπ ± and Bc± → J/ψπ ± π ± π ∓
channels. A clear signal yield of 495 ± 71 Bc has been obtained for the
Bc± → J/ψπ ± decay mode and of 193±47 for the channel Bc± → J/ψπ ± π ± π ∓ .
The signal Bc± → J/ψπ ± π ± π ∓ reported in this work is the first evidence of
this decay in CMS. These Bc signals have led to preliminary measurements
of production cross sections at 7 T eV , branching ratios and Bc lifetime.
σ(Bc )×(Br(Bc →J/ψπ ± )
The ratio σ(B
+ )×(Br(B ± →J/ψK ± ) is estimated as (0.982 ± 0.214)%, in agreement with the preliminary value from LHCb.
± ± ∓
c →J/ψπ π π )
ratio lead to a result of 3.55±1.79.
The measurement of Br(B
Br(Bc →J/ψπ ± )
Although preliminary, this measurement is compatible with theoretical predictions and with the only other experimental value calculated by LHCb. The
main uncertainties affecting these values come from the still limited Monte
Carlo samples avalaible and will be reduced thanks to a new production in
progress.
The lifetime measurement of 0.453+0.042
−0.038 ps is performed for the fully reconstructed channel Bc± → J/ψπ ± ; it is consistent with the PDG average
τP DG = 0.45 ± 0.04 ps. The studies of the Bc meson discussed represent a
first effort in CMS to better understand this still unknown doubly flavored
state.
77
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Ringraziamenti
Eccoci al momento dei ringraziamenti, la pagina più letta di tutta la tesi.
Desidero innanzitutto ringraziare il prof. Moroni: senza le sue celebri
lezioni chissà se avrei bussato alla sua porta in cerca di una tesi. Sono felice
di averlo fatto, perchè ho avuto modo di lavorare con un gruppo fantastico,
composto da persone brillanti e nello stesso tempo attente al mio lavoro ed
alla mia crescita.
Grazie a Sandra, che mi ha seguito ad ogni passo, contagiandomi con la
sua passione e rifornendomi di stimoli sempre nuovi; a Paolo, onnipresente
ed ottimista, a Dario, che ha cercato (invano?) di mettere un po’ di ordine
nei miei codici e nella mia testa, e a Daniele, che non si è mai tirato indietro
a qualsiasi mia domanda.
Grazie a Riccardo e a Sara, a cui in questi ultimi mesi ho negato la
tranquillità di uno studio silenzioso e che hanno partecipato con me ad una
lunga serie di giorni definitivi.
Ringrazio tutti i miei amici: quelli dell’università, con cui ogni pranzo
non si sa mai che discorso esce, quelli storici che ormai il venerdı̀ è fisso (ora
ritornerò stabilmente promesso!), quelli con cui mi diverto il fine settimana,
quelli con cui fingo di dare quattro calci al pallone, e chi più ne ha più nel
metta.. Se in questo momento stai leggendo questa pagina, sei sicuramente
fra questi quindi grazie!
Un ringraziamento enorme va ai miei genitori, perchè si sa..sono anche
farina del loro sacco! E come tale mi hanno sempre sostenuto, dandomi i
mezzi per realizzare ciò che io sono e voglio, senza imposizioni sulle scelte
veramente importanti. Penso che sia questa in fondo la cosa più grande e
spero che in questo giorno importante siano fieri di me.
E poi ci sei tu, tesoro, che mi hai accompagnato in tutta questa avventura,
e solo io so veramente quanto è stato bello averti al mio fianco...ed ora, un
capitolo della mia vita si chiude ed uno nuovo se ne apre, insieme.
80