Flavour Physics & CP Violation
Lecture 3 of 4
Tim Gershon
University of Warwick
CERN Summer Student Lecture Programme
5th August 2013
Tim Gershon
Flavour & CPV
1
Contents
●
Part 1
–
●
Part 2
–
●
What do we know from previous experiments?
Part 3
–
●
What is flavour physics & why is it interesting?
What do we hope to learn from current
experiments?
Part 4
–
The future of flavour physics
Tim Gershon
Flavour & CPV
2
Partial summary
sin 2 

∣ md / ms∣
∣V ub /V cb∣
Adding a few other constraints we find
ρ = 0.132±0.020
η = 0.358±0.012
Consistent with Standard Model fit
●
some “tensions”
Still plenty of room for new physics
Tim Gershon
Flavour & CPV
3
0
0
Rt side from B –B mixing
∣ ∣
∗
World average based on
many measurements
Rt =
V td V tb
V cd V
∗
cb
&
P(Δt) = (1±cos(ΔmΔt))e-|Δt|/2τ
Δmd = (0.511 ± 0.005 ± 0.006) ps-1
PRD 71, 072003 (2005)
Tim Gershon
Flavour & CPV
∣V td /V ts∣ =
Δms = (17.768 ± 0.023 ± 0.006) ps-1
NJP 15 (2013) 053021
0.211±0.001±0.005
experimental theoretical
uncertainty uncertainty
4
Ru side from semileptonic decays
Ru =
●
∣ ∣
V ud V ∗ub
V cd V ∗cb
Approaches:
–
exclusive semileptonic B decays, eg. B0 → π- e+ ν
●
require knowledge of form factors
–
–
can be calculated in lattice QCD at kinematical limit
inclusive semileptonic B decays, eg. B → Xu e+ ν
●
●
clean theory, based on Operator Product Expansion
experimentally challenging:
Tim Gershon
Flavour & CPV
●
need to reject b→c background
●
cuts re-introduce theoretical uncertainties
5
|Vub| from exclusive semileptonic decays
Current best measurements use B0 → π– l+ ν
BaBar experiment
PRD 83 (2011) 052011
PRD 83 (2011) 032007
Belle experiment
PRD 83 (2011) 071101(R)
B0 →π–lν
0.35
−3
V
=
3.09
±
0.08
±
0.12
×10
∣ ub∣
−0.29
Tim Gershon
Flavour & CPV
lattice uncertainty
−3
V
=
3.43
±
0.33×10
∣ ub∣
6
|Vub| from inclusive semileptonic decays
●
Main difficulty to measure inclusive B → Xu l+ ν
–
●
Approaches
–
●
background from B → Xc l+ ν
cut on El (lepton endpoint), q2 (lν invariant mass squared),
M(Xu), or some combination thereof
Example: endpoint analysis
–
non BB background subtracted
Tim Gershon
Flavour & CPV
Xc l+ ν background subtracted
7
|Vub| average
●
Averages on |Vub| from both exclusive and inclusive
approaches
–
exclusive:
|Vub| = (3.23 ± 0.31) x 10–3
–
inclusive:
|Vub| = (4.41 ± 0.22) x 10–3
–
slight tension between these results
–
in both cases theoretical errors are dominant
●
–
but some “theory” errors can be improved with more data
PDG2012 does naïve average rescaling due to
inconsistency to obtain |Vub| = (4.15 ± 0.49) x 10–3
Tim Gershon
Flavour & CPV
8
Partial summary
sin 2 

∣ md / ms∣
∣V ub /V cb∣
Adding a few other constraints we find
ρ = 0.132±0.020
η = 0.358±0.012
Consistent with Standard Model fit
●
some “tensions”
Still plenty of room for new physics
Tim Gershon
Flavour & CPV
9
Flavour physics at hadron colliders
Tim Gershon
Flavour & CPV
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Flavour physics at hadron colliders
Tim Gershon
Flavour & CPV
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Geometry
●
●
–
In high energy collisions, bb pairs produced
predominantly in forward or backward
directions
LHCb is a forward spectrometer
The LHCb Detector
JINST 3 (2008) S08005
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Flavour & CPV
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VELO
Material imaged used beam gas collisions
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Flavour & CPV
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RICH
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Flavour & CPV
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LHCb integrated luminosity
Tim Gershon
Flavour & CPV
Instantaneous luminosity (2012) ~ 4 1032/cm2/s
LHCb design luminosity: 2 1032/cm2/s
15
Note “luminosity levelling”
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Flavour & CPV
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Heavy flavour production @ LHCb
“Prompt charm production in pp
collisions at √s = 7 TeV”
Nucl. Phys. B 871 (2013) 1
“Measurement of J/ψ production in
pp collisions at √s = 7 TeV”
Eur. Phys. J. C 71 (2011) 1645
–
"Measurement of σ(pp→bbX) at √s = 7 TeV in the forward region"
Physics Letters B 694 (2010) 209
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Flavour & CPV
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What does ∫Ldt = 1/fb mean?
●
Measured cross-section, in LHCb acceptance
–
σ(pp→bbX) = (75.3 ± 5.4 ± 13.0) μb
●
PLB 694 (2010) 209
–
So, number of bb pairs produced in 1/fb ( 2011 sample)
1015 x 75.3 10–6 ~ 1011
●
Compare to combined data sample of e+e– “B
–
9
factories” BaBar and Belle of ~ 10 BB pairs
for any channel where the (trigger, reconstruction, stripping, offline)
efficiency is not too small, LHCb has world's largest data sample
●
–
p.s.: for charm, σ(pp→ccX)
= (6.10 ± 0.93) mb
LHCb-CONF-2010-013
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Flavour & CPV
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Why wasn't the ηb discovered at a
hadronic experiment?
●
–
The ηb meson – the groundstate (pseudoscalar) bb
meson, was discovered by BaBar in 2008
–
●
●
PRL 101 (2008) 071801
–
The Υ(1S) – the vector bb state – was discovered at
FNAL in 1977
PRL 39 (1977) 252
–
●
e+e– → γ + undetected ηb
fixed target experiment: p on Be; Υ(1S)→μ+μ–
Hadron collisions produce all types of b hadrons
So why couldn't the ηb be discovered, e.g., at the
Tevatron?
Tim Gershon
Flavour & CPV
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The all important trigger
JINST 8 (2013) P04022
Challenge is
● to efficiently select most
interesting B decays
● while maintaining
manageable data rates
Main backgrounds
● “minimum bias” inelastic
pp scattering
● other charm and beauty
decays
Handles
● high p signals (muons)
T
●
displaced vertices
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Flavour & CPV
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CP violation searches in
0
0
D and Bs systems
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Flavour & CPV
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The other Unitarity Triangles
●
High statistics available at LHCb will allow sensitivity
to smaller CP violating effects
–
CP violating phase in Bs oscillations (O(λ4))
●
–
CP violating phase in D0 oscillations (O(λ5))
●
●
●
Bs oscillations (Δms) measured 2006 (CDF)
D0 oscillations (xD = ΔmD/ΓD & yD = ΔΓD/2ΓD) measured 2007
(Babar, Belle, later CDF)
First definitive (5σ) observation 2011 (LHCb)
Observations of CP violation in both K0 and B0 systems
won Nobel prizes!
Tim Gershon
Flavour & CPV
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Time-dependent CP Violation
Formalism
●
Generic (but shown for Bs) decays to CP eigenstates
Tim Gershon
Flavour & CPV
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Time-dependent CP Violation
Formalism
●
Generic (but shown for Bs) decays to CP eigenstates
CP violating asymmetries
2
A
dir
CP
= C CP =
Tim Gershon
Flavour & CPV
1−∣ CP∣
2
1∣ CP∣
A =
CP conserving parameter
2 ℜ CP 
2
1∣ CP∣
dir 2
CP
A
2
mix
CP
= SCP =
 A   A     A
mix 2
CP
2 ℑ CP 
2
1∣CP∣
 =1
24
Time-dependent CP Violation
Formalism
●
●
Generic (but shown for Bs) decays to CP eigenstates
Untagged analyses still sensitive to some interesting
physics
Tim Gershon
Flavour & CPV
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Time-dependent CP Violation
Formalism
●
Generic (but shown for Bs) decays to CP eigenstates
0
0
0
●
In some channels, expect no direct CP violation
●
and/or no CP violation in mixing
Tim Gershon
Flavour & CPV
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Time-dependent CP Violation
Formalism
●
Generic (but shown for Bs) decays to CP eigenstates
1
0
1
0
●
In some channels, expect no direct CP violation
●
Bd case: ΔΓ negligible
Tim Gershon
Flavour & CPV
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Time-dependent CP Violation
Formalism
●
Generic (but shown for Bs) decays to CP eigenstates
1
1
yΓt
xΓt
1
1
yΓt
xΓt
●
In some channels, expect no direct CP violation
●
Bd case: ΔΓ negligible
●
D0 case: both x = Δm/Γ and y=ΔΓ/2Γ small
Tim Gershon
Flavour & CPV
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Charm mixing and CP violation
HFAG world average Including results from BABAR, Belle, CDF, CLEO(c), FOCUS, LHCb
Inconsistent with no mixing point (0,0)
Tim Gershon
Flavour & CPV
Consistent with no CP violation point (1,0)
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Φs = –2βs
●
●
Most attractive channel
Bs0→J/ψφ
VV final state
three helicity amplitudes
→ mixture of CP-even and CP-odd
disentangled using angular & time-dependent distributions
→ additional sensitivity
many correlated variables
→ complicated analysis
●
LHCb also uses Bs→J/ψf0 (f0→π+π–)
–
–
CP eigenstate; simpler analysis
fewer events; requires input from J/ψφ analysis (Γs, ΔΓs)
Tim Gershon
Flavour & CPV
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0
CP violation in Bs → J/ψφ & J/ψππ
PRD 87 (2013) 112010
Tim Gershon
Flavour Physics
& CPV
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0
CP violation in Bs → J/ψφ & J/ψππ
Tim Gershon
Flavour Physics
& CPV
Significant further improvement warranted
for precise test of the SM prediction
32
Direct CP violation
Tim Gershon
Flavour & CPV
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Categories of CP violation
●
Consider decay of
neutral particle to a CP
eigenstate
qA
CP =
pA
q
∣ ∣≠1
p
A
∣ ∣≠1
A
 
qA
ℑ
≠0
pA
Tim Gershon
Flavour & CPV
CP violation in mixing
CP violation in decay (direct CPV)
CP violation in interference
between mixing and decay
34
Direct CP violation
●
●
–
Condition for DCPV: |A/A|≠1
–
Need A and A to consist of (at least) two parts
–
●
with different weak (φ) and strong (δ) phases
Often realised by “tree” and “penguin” diagrams
i   T −T 
i   P −P 
i  T T 
i   P P 
A = ∣T ∣e
∣P∣e
A = ∣T ∣e
∣P∣ e
2
2
2 ∣T∣∣P∣ sin T − P  sin T − P 
∣ A∣ −∣ A∣
ACP =
=
2
2
2
2
∣ A∣ ∣ A∣
∣T∣ ∣P∣ 2 ∣T∣∣ P∣cos T − P cos T − P 
Example: B→Kπ
(weak phase difference is γ)
Tim Gershon
Flavour & CPV
35
The famous penguin story
Tim Gershon
Flavour & CPV
36
The famous penguin story
Tim Gershon
Flavour & CPV
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Direct CP asymmetries in charmless hadronic B decays
Tim Gershon
Flavour & CPV
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Direct CP violation in B→Kπ
●
Direct CP violation in B→Kπ sensitive to γ
too many hadronic parameters ⇒ need theory input
NB. interesting deviation from naïve expectation
Belle Nature 452 (2008) 332
” A (K–π+) = –0.082 ± 0.006
e
l
CP
zz
u
– 0
p
A
(K
π ) = +0.040 ± 0.021
π
CP
“K
HFAG averages
Could be a sign of new physics …
… but first need to rule out possibility of
larger than expected QCD corrections
Tim Gershon
Flavour & CPV
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How to rule out large QCD corrections?
●
Measure more Bu,d→Kπ decays & relate by isospin
●
Perform similar analysis on B→K*π &/or B→Kρ
●
Measure Bs→KK decays & relate by U-spin
PRL 110 (2013) 221601
consistent with SM expectation
Tim Gershon
Flavour & CPV
40
Importance of γ from B→DK
●
γ plays a unique role in flavour physics
the only CP violating parameter that can be measured
through tree decays (*)
(*)
●
more-or-less
A benchmark Standard Model reference point
●
∝ V cb V
doubly important after New Physics is observed
∗
us
Tim Gershon
Flavour & CPV
∗
∝ V ub V cs
Variants use different B or D decays
–
require a final state common to both D0 and D0
41
Why is B→DK so nice?
●
●
For theorists:
–
theoretically clean: no penguins; factorisation works
–
all parameters can be determined from data
For experimentalists:
–
many different observables (different final states)
–
all parameters can be determined from data
–
γ & δB (weak & strong phase differences), rB (ratio of
amplitudes)
γ
Tim Gershon
Flavour & CPV
γ
42
Evidence for direct CP violation (γ≠0)
Latest results on B→DK : GLW
Tim Gershon
Flavour & CPV
PLB 712 (2012) 203
43
+
+
γ from combination of B →DK modes
BaBar PRD 87 (2013) 052015
Belle CKM2012 preliminary
LHCb-PAPER-2013-020
& LHCb-CONF-2013-006
●
All direct CP violation effects caused by γ in the Standard Model
●
Only those in B→DK type processes involve only tree-level diagrams
●
enable determination of γ with negligible theoretical uncertainty
●
Several different B and D decays can be used
●
Combination includes results from GLW/ADS (D→hh) & GGSZ (D→K Shh)
●
Sensitivity: BaBar & Belle each ~16°; latest LHCb ~12°
Tim Gershon
Flavour & CPV
44
Observed CP violation effects
●
●
Kaon sector
–
|ε| = (2.228 ± 0.011) × 10−3
–
Re(ε′ /ε) = (1.65 ± 0.26) × 10−3
B sector
–
SψK0 = +0.679 ± 0.020
–
Sη′K0 = +0.59 ± 0.07, SφK0 = + 0.74+0.11−0.13, Sf0K0= +0.69+0.10−0.12, SK+K−K0 = +0.68+0.09–0.10
–
Sπ+π− = −0.65 ± 0.07, Cπ+π− = −0.36 ± 0.06, ABs→K∓π± = 0.26 ± 0.04
–
Sψπ0 = −0.93 ± 0.15, SD+D− = −0.98 ± 0.17, SD∗+ D∗− = − 0.77 ± 0.10
–
AK∓π± = −0.082 ± 0.006
–
AD(CP+)K± = +0.19 ± 0.03
–
Phase-space distributions in B+ → KKK, KKπ, Kππ, πππ decays
Tim Gershon
Flavour & CPV
45
Back up
Tim Gershon
Flavour & CPV
46
Measurement of α
●
●
– decays (e.g. B 0→π+π–)
Similar analysis using b → uud
d
probes π–(β+γ) = α
–
– penguin transitions contribute to same final
but b → duu
states ⇒ “penguin pollution”
–
C ≠ 0 ⇔ direct CP violation can occur
–
S ≠ +ηCP sin(2α)
Two approaches
(optimal approach combines both)
–
try to use modes with small penguin contribution
–
correct for penguin effect (isospin analysis)
PRL 65 (1990) 3381
Tim Gershon
Flavour & CPV
47
Experimental Situation
large CP violation
large penguin effect
Tim Gershon
Flavour & CPV
small CP violation
small penguin effect
improved measurements needed!
48
α = (89.0 +4.4–4.2)°
Tim Gershon
Flavour & CPV
Is there any physical significance in the fact that α ≈ 90°?
THESE SOLUTIONS RULED OUT BY OBSERVATION
OF DIRECT CP VIOLATION IN B0→π+π–
Measurement of α
49
+ –
Is there CP violation in D → h h decays?
LHCb PRL 108 (2012) 111602
Measurement of CP asymmetry at pp collider requires knowledge of production and
detection asymmetries; e.g. for D0→f, where D meson flavour is tagged by D*+→D0π+ decay
final state detection asymmetry
vanishes for CP eigenstate
Cancel asymmetries by taking difference of raw asymmetries in two different final states
(Since AD and AP depend on kinematics, must bin or reweight to ensure cancellation)
D0→K+K–
1.4M events
Tim Gershon
Flavour & CPV
D0→π+π–
0.4M events
50
Is there CP violation in the charm system?
(and if so, where does it come from?)
To reduce systematics and (perhaps) enhance
CP violation effect, experiments measure
LHCb arXiv:1303.2614, LHCb-CONF-2013-003
CDF PRL 109 (2012) 111801
Belle ICHEP preliminary
ΔACP related mainly to direct CP violation
(contribution from indirect CPV suppressed by
difference in mean decay time)
ΔaCPdir = (−0.33 ± 0.12)%
Previous evidence for CPV
not confirmed
Need more precise measurements
Tim Gershon
Flavour Physics circa 2013
51
All shifts consistent with being statistical in origin