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Frontiers of Fundamental Physics 14
CP violation effects in multibody B decays
Jeremy Dalseno
on behalf of the LHCb collaboration
J.Dalseno [at] bristol.ac.uk
18 July 2014
CP violation effects in multibodyB decays 1
Outline1. Motivation
2. LHCb Detector
3. B± → K±K+K− and B± → K±π+π− (penguin dominated)
4. B± → π±K+K− and B± → π±π+π− (tree dominated)
5. B± → K±pp and B± → π±pp
6. Summary
Dalitz plot contains all kinematic and dynamic information of decay
Amplitude analysis one of the most powerful techniques
Extract amplitude-level information rather than amplitude-squared
information
Interference between intermediate states allows measurement of
relative magnitudes and phases
CP violation effects in multibodyB decays 2
MotivationCharmlessB → 3h decay channels provide a rich environment for physics observables
Unknown heavy particle in the loop could carry a new CP violating phase
b
u
s
q
qu
-W
gxbV *xsV
x
x = u, c, t
b
u
s
q
qu
?
g
Tree sensitive to γ = φ3 ≡ − arg
(
VudV ∗
ub
VcdV ∗
cb
)
b
u
s
uu
u
-W
γ ∝ ubVβ
α
γ
*ubVudV
*cbVcdV
*tbVtdV
CP violation effects in multibodyB decays 3
Motivation
In chargedB decays, presence of multiple amplitudes may lead to direct CP violation
A(B → f) =∑
i |Ai|ei(δi+φi)
A(B → f) =∑
i |Ai|ei(δi−φi)
Strong phase (δ) invariant underCP , while weak phase (φ) changes sign underCP
ACP (B → f) ≡|A|2 − |A|2
|A|2 + |A|2∝
∑
i,j
sin(δi − δj) sin(φi − φj)
3 conditions required for direct CP violation
At least 2 amplitudes
Non-zero strong phase difference, δi − δj 6= 0
Non-zero weak phase difference, φi − φj 6= 0
Source of weak phase differences come from different CKM phases of each amplitude
CP violation effects in multibodyB decays 4
Motivation
Direct CP violation more complicated in B → 3h decay channels compared to 2-body decays
There are at least 4 possible sources of strong phase
1. Short-distance contributions (quark level)
BSS mechanism, PRL 43 242 (1979)
Penguin diagram (b) contains 3 quark generations in loop
If gluon in penguin is timelike (on-shell)
Momentum transfer q2 > 4m2i where i = u, c
Particle rescattering (c) generates a phase difference
Tree contribution (a) carries different strong phase
CP violation in 2-body processes caused by this effect
eg. B0 → K+π−
CP violation effects in multibodyB decays 5
MotivationRemaining sources unique to multibody decays
Long-distance contributions (qq level)
2. Breit-Wigner phase
Represents intermediate resonance states
FBWR (s) =
1
m2R − s− imRΓR(s)
Phase varies across the Dalitz plot
3. Relative CP -even phase in the isobar model
A(B → f) =∑
i |Ai|ei(δi+φi)
A(B → f) =∑
i |Ai|ei(δi−φi)
Related to final state interactions between different resonances
CP violation effects in multibodyB decays 6
MotivationEach source of strong phase leaves a unique signature in the Dalitz plot
Illustrate with series of examples
ConsiderB± → K±π+π− with only 2 isobars
B± → K±ρ0 and non-resonant (NR) component
ρ lineshape a Breit-Wigner, FBWρ
ρ0 is a vector resonance, so angular distribution follows cos θ
0ρ +π-π
+K
θ
A+ = aρ+e
iδρ+FBW
ρ cos θ + aNR+ eiδNR
+ FNR
A− = aρ−e
iδρ−FBW
ρ cos θ + aNR− eiδNR
− FNR
ACP ∝ |A−|2 − |A+|
2
∝ [(aρ−)2 − (aρ
+)2]|FBWρ |2 cos2 θ + ...
−2(m2ρ − s)|FBW
ρ |2|FNR|2 cos θ...
+2mρΓρ|FBWρ |2|FNR|2 cos θ...
CP violation effects in multibodyB decays 7
Motivation
ACP ∝ [(aρ−)2 − (aρ
+)2]|FBWρ |2 cos2 θ + ...
−2(m2ρ − s)|FBW
ρ |2|FNR|2 cos θ...
+2mρΓρ|FBWρ |2|FNR|2 cos θ...
Only depends on ρ resonance, maximum difference at ρ pole, quadratic in helicity
(GeV) low-π+πm0 0.5 1 1.5 2 2.5
+ -
B-
B
-400
-300
-200
-100
0
> 0θcos
(GeV) low-π+πm0 0.5 1 1.5 2 2.5
+ -
B-
B
-600
-500
-400
-300
-200
-100
0
< 0θcos
MC
0ρ +π-π
+K
θ
0ρ +π-π
+K
θ
Only short-distance effects can create aρ+ 6= aρ
−
CP violation effects in multibodyB decays 8
Motivation
ACP ∝ [(aρ−)2 − (aρ
+)2]|FBWρ |2 cos2 θ + ...
−2(m2ρ − s)|FBW
ρ |2|FNR|2 cos θ...
+2mρΓρ|FBWρ |2|FNR|2 cos θ...
Interference term from real part of Breit-Wigner, zero at ρ pole, linear in helicity
(GeV) low-π+πm0 0.5 1 1.5 2 2.5
+ -
B-
B
-400
-200
0
200
400
> 0θcos
(GeV) low-π+πm0 0.5 1 1.5 2 2.5
+ -
B-
B
-600
-400
-200
0
200
400
600
800
< 0θcos
MC
0ρ +π-π
+K
θ
0ρ +π-π
+K
θ
Caused by long distance effects from final state interactions
CP violation effects in multibodyB decays 9
Motivation
ACP ∝ [(aρ−)2 − (aρ
+)2]|FBWρ |2 cos2 θ + ...
−2(m2ρ − s)|FBW
ρ |2|FNR|2 cos θ...
+2mρΓρ|FBWρ |2|FNR|2 cos θ...
Interference term from imaginary part of Breit-Wigner, maximum at ρ pole, linear in helicity
(GeV) low-π+πm0 0.5 1 1.5 2 2.5
+ -
B-
B
-400
-300
-200
-100
0
> 0θcos
(GeV) low-π+πm0 0.5 1 1.5 2 2.5
+ -
B-
B
0
100
200
300
400
500
600
700
< 0θcos MC
0ρ +π-π
+K
θ
0ρ +π-π
+K
θ
Caused by long distance effects from Breit-Wigner phase and final state interactions
CP violation effects in multibodyB decays 10
Motivation
Last source of strong phase
4. Final state KK ↔ ππ rescattering
Can occur between decay channels with the same flavour quantum numbers
eg. B± → K±K+K− and B± → K±π+π−
CPT conservation constrains hadron rescattering
For given quantum numbers, sum of partial widths equal for charge-conjugate decays
KK ↔ ππ rescattering generates a strong phase
Look into rescattering region
If rescattering phase in one decay channel generates direct CP violation in this region,
Rescattering phase should generate opposite sign direct CP violation in partner decay channel
CP violation effects in multibodyB decays 11
LHCb Detectorpp collisions
b quark tends to foward/backward direction
Data set: 1 fb−1 @ 7 TeV and 2 fb−1 @ 8 TeV
Forward spectrometer
Vertex Locater (VeLo)Precision tracking
Tracker Turicensis (TT)Tracking, p measurement
Ring Imaging Cherenkov (RICH)Particle identification
Electromagnetic Calorimeter (ECAL)e, γ ID
Hadronic Calorimeter (HCL)Hadronic showers
Muon Detector
Magnet polarity reversal
CP violation effects in multibodyB decays 12
B± → K±h+h−, π±h+h−
B− → K−π+π− B+ → K+π+π− B− → K−K+K− B+ → K+K+K−
NSig = 181069 ± 404 (stat) NSig = 109240 ± 354 (stat)
]2c [GeV/−π+π−Km
5.1 5.2 5.3 5.4 5.5×
)2 cC
andi
date
s / (
0.01
GeV
/
02468
1012141618
310×
LHCb
]2c [GeV/−π+π+Km5.1 5.2 5.3 5.4 5.5
×
model−π+π± K→ ±B
combinatorial 4-body→B
±)Kγ0ρ’(η → ±B ±π−π+π → ±B
]2c [GeV/−K+K−Km5.1 5.2 5.3 5.4 5.5
×
)2 cC
andi
date
s / (
0.01
GeV
/
0
2
4
6
8
10
12
310×
LHCb
]2c [GeV/−K+K+Km5.1 5.2 5.3 5.4 5.5
×
model−K+K± K→ ±B
combinatorial 4-body→B
±π−K+ K→ ±B−π+π± K→ ±B
]2c [GeV/-π+π-πm5.1 5.2 5.3 5.4 5.5
×
)2 cC
andi
date
s / (
0.01
GeV
/
0
0.5
1
1.5
2
2.5
3
310×
LHCb
]2c [GeV/-π+π+πm5.1 5.2 5.3 5.4 5.5
×
model±π−π+π → ±B
combinatorial 4-body→B
−π+π± K→ ±B
]2c [GeV/-π+K-Km5.1 5.2 5.3 5.4 5.5
×
)2 cC
andi
date
s / (
0.01
GeV
/
0
0.2
0.4
0.6
0.8
1310×
LHCb
]2c [GeV/-π+K+Km5.1 5.2 5.3 5.4 5.5
×
model±π−K+ K→ ±B
combinatorial 4-body→ SB
4-body→B −K+K± K→ ±B−π+π± K→ ±B
Prelim
inary
LHCb-
PAPER-2
014-
044
Penguin
Tree
B− → π−π+π− B+ → π+π+π− B− → π−K+K− B+ → π+K+K−
NSig = 24907 ± 222 (stat) NSig = 6161 ± 172 (stat)
CP violation effects in multibodyB decays 13
B± → K±h+h−, π±h+h−
Global direct CP asymmetry
ARawCP =
NB− −NB+
NB− +NB+
Correct for B± production asymmetry and unpaired hadron (eg. B± → K±π+π−) detection
asymmetry
ACP = ARawCP −AP −Ah
D
AP and AKD from B± → J/ψ[µ+µ−]K±, PRL 108 201601 (2012)
AπD from promptD+ studies, PLB 713 186 (2012)
ACP (B± → K±π+π−) = +0.025 ± 0.004 (stat) ± 0.004 (syst) ± 0.007 (J/ψK±) (2.8σ)
ACP (B± → K±K+K−) = −0.036 ± 0.004 (stat) ± 0.002 (syst) ± 0.007 (J/ψK±) (4.3σ)
ACP (B± → π±π+π−) = +0.058 ± 0.008 (stat) ± 0.009 (syst) ± 0.007 (J/ψK±) (4.2σ)
ACP (B± → π±K+K−) = −0.123 ± 0.017 (stat) ± 0.012 (syst) ± 0.007 (J/ψK±) (5.6σ)
Prelim
inary
LHCb-
PAPER-2
014-
044
CP violation effects in multibodyB decays 14
B± → K±h+h−, π±h+h−
Dalitz plot background subtracted and effiency corrected with ∼ (NB+ +NB−) in each bin
B±→ K±π+π− B±
→ K±K+K−
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
]4c/2 [GeV -π+π2m
0 5 10 15 20
]4 c/2 [G
eV - π+
K2m
0
5
10
15
20
25
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
LHCb (a)
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
]4c/2 [GeVlow-
K+K2m
0 2 4 6 8 10 12 14
]4 c/2 [
GeV
high
-K+
K2m
0
5
10
15
20
25
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
LHCb (b)
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
]4c/2 [GeVlow-π+π2m
0 2 4 6 8 10 12 14
]4 c/2 [G
eVhi
gh- π+ π2
m
0
5
10
15
20
25
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
LHCb (c)
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
]4c/2 [GeV-π+K2m
0 5 10 15 20 25
]4 c/2 [G
eV-
K+K2
m
0
5
10
15
20
25
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
LHCb (d)Prelim
inary
LHCb-
PAPER-2
014-
044
Penguin
Tree
B±→ π±π+π− B±
→ π±K+K−
CP violation effects in multibodyB decays 15
CP Asymmetry by InterferenceProject onto mππ of B± → π±π+π−
]2c[GeV/ low−π+πm0.5 1 1.5
)2Y
ield
/(0.
05 G
eV/c
0
200
400
600
800 LHCb +B−
B
]2c[GeV/ low−π+πm0.5 1 1.5
+ -
B-
B
-200-100
0100200300 LHCb
]2c[GeV/ low−π+πm0.5 1 1.5
)2Y
ield
/(0.
05 G
eV/c
0
0.5
1
1.5310×
LHCb +B−
B
]2c[GeV/ low−π+πm0.5 1 1.5
+ -
B-
B
-1000
100200300 LHCbPre
limina
ry
LHCb-
PAPER-2
014-
044
0 ρ+ π
- π
+K
θ0 ρ
+ π- π
+K
θ
Sign-flip and zero around ρ0 pole, CP asymmetry may be dominated by real part of Breit-Wigner
CP violation effects in multibodyB decays 16
CP Asymmetry by Rescatteringππ ↔ KK rescattering region: 1.0 − 1.5 GeV/c2
B± → K±π+π− B± → K±K+K−
]2c [GeV/−π+π−Km
5.1 5.2 5.3 5.4 5.5×
)2 cC
andi
date
s / (
0.01
GeV
/
00.20.40.60.8
11.21.41.61.8
310×
LHCb
]2c [GeV/−π+π+Km5.1 5.2 5.3 5.4 5.5
×
model−π+π± K→ ±B
combinatorial 4-body→B
±)Kγ0ρ’(η → ±B ±π−π+π → ±B
]2c [GeV/−K+K−Km5.1 5.2 5.3 5.4 5.5
×
)2 cC
andi
date
s / (
0.01
GeV
/
00.20.40.60.8
11.21.41.61.8
22.22.4
310×
LHCb
]2c [GeV/−K+K+Km5.1 5.2 5.3 5.4 5.5
×
model−K+K± K→ ±B
combinatorial 4-body→B
±π−K+ K→ ±B−π+π± K→ ±B
Prelim
inary
LHCb-
PAPER-2
014-
044
ACP (B±→ K±π+π−) = +0.121 ± 0.012 (stat) ± 0.017 (syst) ± 0.007 (J/ψK±)
ACP (B±→ K±K+K−) = −0.211 ± 0.011 (stat) ± 0.004 (syst) ± 0.007 (J/ψK±)
Clear opposite sign CP asymmetry in KK/ππ - related channels
KK ↔ ππ rescattering would require this by CPT conservation
CP violation effects in multibodyB decays 17
B± → K±pp and B± → π±ppAnother new preliminary result based on full data set
B± → K±pp penguin dominated
B± → π±pp tree dominated
Similar physics to non-baryonic 3-body charmless decays
pp ↔ h+h− rescattering expected to be smaller than
KK ↔ ππ rescattering
CP asymmetry could be less pronounced
Threshold enhancement in low mpp typical in B → ppX
decays
Need to better understand dynamics of these decays
Previous publication based on 1 fb−1
No evidence of CP violation
PRD 88 052015 (2013)
u uud
p
du p
b
+B
d,su
u
+π,+K
W
u uud
p
du pb
+B
d,s
u
u
+π,+KW
CP violation effects in multibodyB decays 18
Signal Yield
B± → K±pp
NSig = 18721 ± 142 (stat)
]2 [GeV/c±Kppm5.1 5.2 5.3 5.4 5.5
)2C
and
idat
es /
(0.0
1 G
eV/c
0
500
1000
1500
2000
2500
3000
3500
4000
4500
LHCb
Blue: Signal
Red: Combinatorial
B± → π±pp
NSig = 1988 ± 74 (stat)
]2 [GeV/c±πppm5.1 5.2 5.3 5.4 5.5
)2C
and
idat
es /
(0.0
1 G
eV/c
0
100
200
300
400
500
600
700
LHCb
Green: Partially reconstrcuted
Purple: Cross-feed
Prelim
inary
LHCb-
PAPER-2
014-
034
CP violation effects in multibodyB decays 19
Dalitz PlotBackground subtracted and efficiency corrected using calibrated MC
B± → K±pp
]4/c2 [GeV2ppm
5 10 15 20
]4/c2
[G
eV2 K
pm
2
4
6
8
10
12
14
16
18
20 )8/c4
Sig
nal
yie
ld /(
0.16
GeV
0
2000
4000
6000
8000
10000
12000LHCb
B± → π±pp
]4/c2 [GeV2ppm
5 10 15 20 25
]4/c2
[G
eV2 pπ
m
0
2
4
6
8
10
12
14
16
18
20 )8/c4
Sig
nal
yie
ld /(
0.20
GeV
0
500
1000
1500
2000
2500
3000
3500
LHCb
6
�������
��
��
��
�������1
Low mpp threshold enhancement
Charmonimum resonances
Definempp < 2.85 GeV/c2 as charmless region
Λ(1520) → pK
Prelim
inary
LHCb-
PAPER-2
014-
034
CP violation effects in multibodyB decays 20
Forward-Backward Asymmetry
AFB =N(cos θ > 0) −N(cos θ < 0)
N(cos θ > 0) +N(cos θ < 0)
Meausure forward-backward asymmetry in bins of mpp
Gives hint on pp waves that might contributepp
+h
θ
B± → K±pp
]2 [GeV/cppm2 2.2 2.4 2.6 2.8
FB
A
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
LHCb
B± → π±pp
]2 [GeV/cppm2 2.2 2.4 2.6 2.8
FB
A
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
LHCb
AppKFB (mpp < 2.85 GeV/c2) = +0.495 ± 0.012 (stat) ± 0.007 (syst)
AppπFB (mpp < 2.85 GeV/c2) = −0.409 ± 0.033 (stat) ± 0.006 (syst)
Large asymmetries indicate dominance of non-resonant pp scattering, J Phys G 34 283 (2007)
Prelim
inary
LHCb-
PAPER-2
014-
034
CP violation effects in multibodyB decays 21
Direct CP Asymmetry
Measure ACP in Dalitz plot bins
Same number of events in each bin
ACP (mpp < 2.85 GeV/c2,m2Kp > 10 GeV2/c4)
= +0.096±0.024 (stat)±0.004 (syst) (4.0σ)
First evidence of CP violation in any B decay
involving baryons
B± → K±pp
]2)2 [(GeV/cpp2m
5 10 15 20
]2 )2 [
(GeV
/cK
p2
m
2
4
6
8
10
12
14
16
18
CP
Raw
A
-0.2
-0.15
-0.1
-0.05
0
0.05
0.1
0.15
0.2
����������*
6
)4/c2 (GeVpp2m
4 6 8
)4/c2
)/(0
.33
GeV
+)-
N(B
-N
(B
-150
-100
-50
0
50
100
150
)4/c2 (GeVpp2m
4 6 8
)4/c2
)/(0
.33
GeV
+)-
N(B
-N
(B
-150
-100
-50
0
50
100
150
Prelim
inary
LHCb-
PAPER-2
014-
034
CP violation effects in multibodyB decays 22
Summary
New preliminary results with the full LHCb data set
B± → K±h+h− and B± → π±h+h−
Evidence of global direct CP violation
Large localised CP asymmetries across the Dalitz plot
Long-distance effects play an important role in generating a strong phase
B± → h±pp
Large forward-backward asymmetries indicate dominance of non-resonant pp scattering
First evidenceCP violation in decays involving baryons
Sign-flip of CP asymmetry probably generated by interference of long-distance pp waves
Look forward to amplitude analyses on all these channels
CP violation effects in multibodyB decays 23
Backup
CP violation effects in multibodyB decays 24
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