Dalitz analysis of the decay*
B+→π+π-π+
* charged conjugate states implied throughout talk
Richard Kass for the BaBar Collaboration
Outline of Talk
*Introduction
*Analysis technique
*Results
*Summary & Conclusions
Richard Kass
HADRON09 Tallahassee FL
1
B+→π+π-π+ is a charmless
3-body B decay
Why study charmless 3-body B decays?
Interference from both penguin & tree amplitudes can give direct CP violation.
Time-dependent measurements & interferences between intermediate states
can allow measurement of all three CKM angles.
Can search for signs of new physics such as enhanced branching fractions or CP
asymmetries – new physics particles can enter in the loop diagrams
Can improve understanding of the nature of some intermediate resonances, i.e.
hadronic physics.
Richard Kass
HADRON09 Tallahassee FL
2
Dalitz-plot Analysis
Dalitz plot is a representation of e.g. the B→PPP phase space.
In our case P=pseudoscalar=charged pion.
The invariant masses are constrained by
mB2+mi2+mj2+mk2=mij2+mik2+mjk2
Make a 2D scatter plot in mij2 and mjk2
Our case: mij=low mass π+π- combo, mjk=high mass π+π- combo
Structure in the DP gives information on resonance masses, widths and
spins, relative phases, interference etc.
Model each contribution to the DP as a separate amplitude with a
complex coefficient (isobar model).
example
mhi2
Red points show a spin 0 resonance
Green points show spin 1 resonance
Purple points show spin 2 resonance
Each of these has a different
mass, width & composition.
Richard Kass
mlow2
HADRON09 Tallahassee FL
3
Dalitz-plot analysis of
B+→π+π-π+
In principle can extract the CKM angle g from
the interference between B+→ cc0p+ & other
modes such as B+→ r0p+
This mode also provides important information
to improve the DP model in B0→ p+p-p0,
which is used to measure the CKM angle a
BF & ACP measurements used to test
factorisation and other effective theories
Light meson spectroscopy aided by information
from as many different final states as
possible
Richard Kass
HADRON09 Tallahassee FL
4
Previous BaBar Results
PRD 72, 052002 (2005) used 232x106 BB events (~half of this analysis)
Prominent ρ(770) and 3σ evidence for f2(1270)
Richard Kass
HADRON09 Tallahassee FL
5
PEP-II at SLAC
asymmetric e+e− collider: 9 GeV (e-)/3.1 GeV (e+)
PEP-II Peak Luminosity 1.2 x 1034 cm-2s-1
BaBar recorded 424 fb-1 at Y(4S)
4.65 x 108 U(4S)→BB events
Richard Kass
HADRON09 Tallahassee FL
6
BaBar Detector
Electromagnetic
Calorimeter
(EMC)
1.5 T Solenoid
Detector of
Internally
Recflected
Cherenkov
Light (DIRC)
Drift Chamber
(DCH)
Instrumented
Flux Return
(IFR)
Silicon Vertex
Tracker (SVT)
SVT, DCH: charged particle tracking: vertex & mom. resolution, K0s/Λ
EMC: electromagnetic calorimeter: g/e/π0/η
DIRC, IFR, DCH: charged particle ID: π/μ/K/p
Highly efficient trigger for B mesons
Richard Kass
HADRON09 Tallahassee FL
7
Analysis Technique
Threshold kinematics: we know the initial energy (E*beam) of the Y(4S) system
Therefore we know the energy & magnitude of momentum of each B meson
*2
mES  Ebeam
- p*B2
Signal
*
E  E B* - E beam
Event topology
Signal
(spherical)
Background
Background
(jet-structure)
Also, use neural networks + unbinned maximum likelihood fits
Richard Kass
HADRON09 Tallahassee FL
8
Backgrounds
B Mesons
Explicitly veto 2-body states that can mimic B+→π+π-π+
B+→D0π+ with D0→π+π- and/or mis-ID’s D0→π+K-/K+KB+→Ksπ+ with Ks→π+πB+→[J/Ψ, Ψ(2S)]π+ with Ψ→l+l- with mis-ID’s l’s as π’s
Estimate background due to other B meson decays
Number of events estimated from MC and used in ML fit
I) 2-body with extra track: B0→π+π- plus π+ (11 events)
II) 3-body with mis-ID track(s): B+→K+π-π+ (199 events)
III) B0→π+π-π0 with π- substituted for π0 (120 events)
IV) B combinatorial backgrounds (495 events)
Continuum: e+e-→uu, dd, ss, cc
modeled using MC and below-Y(4S) data
Richard Kass
HADRON09 Tallahassee FL
9
Amplitude Formalism-I
The total signal amplitudes for B+ and B- decays are:
2
2
2
2
A  A( mmax
, mmin
)   c j F j ( mmax
, mmin
) The nominal model includes:
j
A  A(m
2
max
,m
2
min
)   c j F j (m
2
max
,m
2
min
ρ(770), ρ(1450), f2(1270),
) f0(1370) + non-resonant
j
The F’s contain the strong force dynamics: Fj=Fj
Fj(m2max, m2min)Rj(m)Xj(p*)Xj(q)Tj(m)
j=spin of resonance,
m=mass of resonance
q=momentum of daughter in rest frame of resonance
p*=momentum of bachelor pion in B rest frame
Xj= Blatt-Weisskopf barrier form factors
Rj(m)= resonance line shapes
ρ’s use Gounaris-Sakurai parameterization, others relativistic BWs
PDG
ML fit
Tj(m)=angular distribution (use Zemach tensor formulism)
The c’s contain the weak force dynamics:
cj=(xj+Δxj)+i(yj+Δyj) & cj=(xj-Δxj)+i(yj-Δyj)
Δxj & Δyj are CP violating components
Richard Kass
HADRON09 Tallahassee FL
10
Amplitude Formalism-II
The fit fraction for an individual amplitude is:
2
2
(
c
F

c
F
)
dm
dm
J J
max
min
 J J
2
2
FFJ 
2
2
(
A

A
)
dm
dm
max
min

2
2
note: sum of fit fractions can be <1 or >1 due to interference
The CP asymmetry for a contributing resonance is:
ACP , J 
2
2
2
2
( cJ - cJ )
( cJ  cJ )
The nominal model includes ρ(770), ρ(1450), f2(1270),
f0(1370) + non-resonant BUT additional resonance added too,
e.g. f0(980).
Richard Kass
HADRON09 Tallahassee FL
11
Maximum Likelihood Fit
Event yields are extracted using an unbinned
extended maximum likelihood fit.
Ne
L  e - N 
j
k
our fit has
2
2
N k Pkj ( mmax
, mmin
, m ES , E , qB ) 20 free
parameters
N=∑NK with Nk= event yield for category k.
signal, qq, B meson backgrounds (number fixed from MC)
Ne= total number of events in data sample
qB= charge of the B meson
Pk=PDF for category k: P=P(mES)xP(∆E)xP(Dalitz)
The signal reconstruction efficiencies are
determined as a function of location in Dalitz plot
(m2max, m2min) for B+ and B- separately using MC.
Procedure is extensively tested with Monte Carlo
toy MCs and embedded MCs
Richard Kass
HADRON09 Tallahassee FL
12
Fit to Data
We calculate a chisq between a model & data:
Number of events in a bin vs predicted number PRD 79, 072006 (2009)
The best model is the one with the lowest chisq/dof
4335 B± candidates yields 1219±50 signal events
__
ML fit
signal
__
ML fit
qq
qq
__
ML fit
signal
__
ML fit
“sPlots”
NIM A 555 (2005) 356
Richard Kass
HADRON09 Tallahassee FL
13
Systematic Errors
Many sources of systematic errors considered
allow BB backgrounds to float
vary the PDF parameters
compare with data/MC control samples: B-→ D0π-, D0→K-π+
tracking efficiency & particle ID
modeling of Neural Network
Dalitz plot model (composition of model & values of masses, widths, etc)
Richard Kass
HADRON09 Tallahassee FL
14
Branching Fraction Results
“Best Fit Solution”
The decay is dominated by B+→ ρ(770)0π+ and 3π non-resonant
The χc0, χc2, & f0(980) components not statistically significant
stat syst model
PDG: (16.2±1.5)x10-6
determined from ML fit
f0(1370) mass=1400±50 MeV/c2
f0(1370) width=300±80 MeV
Richard Kass
HADRON09 Tallahassee FL
15
CP Asymmetry Results
“Best Fit Solution”
All CP asymmetries are consistent with zero.
Large variation in the ACP’s between best & 2nd best fit:
best
Richard Kass
2nd best
HADRON09 Tallahassee FL
χ2best/dof =82/84
χ22nd/dof= 86/84
16
B+→π+π-π+ Conclusions
●This analysis uses the full BaBar data set
Published: PRD 79, 072006 (2009)
●Decay is dominated by ρ(770)π & 3π non-resonant
No evidence for χc0, χc2, & f0(980)
BFs in good agreement with PDG & theories
Li and Yang, PRD 73, 114027 (2006), Chiang and Zhou, J. HEP. 03 (2009) 055.
●All CP asymmetries consistent with zero
Lack of χc0 & χc2 implies this mode is not useful for
CKM angle γ measurement with present data samples.
●These results will help other analyses
Reduce model related errors in determination of CKM
angle α from time dependent Dalitz analysis of B0→π+π-π0
Richard Kass
HADRON09 Tallahassee FL
17
Extra slides
Richard Kass
HADRON09 Tallahassee FL
18
BaBar K/p ID
D*+ → D0p+
D0→ K+ p-
BaBar DIRC
Richard Kass
HADRON09 Tallahassee FL
19
Dalitz Plot, Data
Background subtracted Dalitz plot
exclude charm and charmonia regions
D0
Richard Kass
J/Ψ & Ψ(2S)
HADRON09 Tallahassee FL
20
Best & 2nd Best Fit Results
Richard Kass
HADRON09 Tallahassee FL
21
Model Parameterization
Blatt-Weisskopf Barrier Form Factors:
rBW=4.0±1.0 (GeV/c)-1
Breit-Wigner line shape:
q0=q(m0)
Zemach Tensors:
Gounaris-Sakurai parameterization
Non-resonant:
αnr=0.28±0.06(GeV/c2)-2
Richard Kass
HADRON09 Tallahassee FL
22
Predictions
Li and Yang, PRD 73, 114027 (2006).
Chiang and Zhou, J High Energy Phys. 03 (2009) 055.
Scheme A2
Scheme B2
Richard Kass
HADRON09 Tallahassee FL
23