Possibilties and problems for
b → c Dalitz plot analyses at LHCb
Tim Gershon
University of Warwick, UK
2 March 2010
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0 → J/ψ h+ h0−
Bd,s
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0 → D h+ h0−
Bd,s
Tim Gershon
b → c DP analyses @ LHCb
Inaugural meeting of Les NABIS, 02/03/2010
1/13
Possible physics interests
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0 → J/ψ h+ h0−
Bd,s
I
I
I
I
0 → D h+ h0−
Bd,s
I
I
I
Tim Gershon
0
Bd.s
→ J/ψ π + π −
7→ measure 2β in b → cc̄d decay, measure φs in B → PV
b → cc̄s decay, probe π + π − system
0
Bd,s
→ J/ψ K ± π ∓
7→ search for BSM DCPV, search for Z + (4430) state, probe
K + π − system
Bs0 → J/ψ K + K −
7→ measure φs , probe K + K − system
0
Bd,s
→ D π+ π−
7→ measure 2β in b → cc̄d decay, probe π + π − system
0
Bd,s
→ D K ± π∓
7→ measure γ
0
Bd,s
→ D K +K −
7→ measure γ
b → c DP analyses @ LHCb
Inaugural meeting of Les NABIS, 02/03/2010
2/13
Bs0 → J/ψ K + K −
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Measurement of φs from Bs0 → J/ψ φ one of LHCb’s highest
priorities
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Current status of CDF and D0:
Tim Gershon
b → c DP analyses @ LHCb
Inaugural meeting of Les NABIS, 02/03/2010
3/13
LHCb prospects for Bs0 → J/ψ K + K −
,*2]
*+##+"
*+
J"
Tim Gershon
b → c DP analyses @ LHCb
Inaugural meeting of Les NABIS, 02/03/2010
4/13
A possible complication
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Tim Gershon
Analyses to date have neglected possible contributions from
K + K − S-wave under the φ peak
7→ such terms can cause a dilution of the CP violation
not essential for first measurements but needed for precision
b → c DP analyses @ LHCb
Inaugural meeting of Les NABIS, 02/03/2010
5/13
A possible complication – resolved
S-wave contribution can be included model-independently
Y. Xie et al., JHEP 0909:074,2009 (arXiv:0908.3627 [hep-ph])
7→ improves determination of φs (add sensitivity to cos(φs ))
similar approach to determination of cos(2β) in
Bd0 → J/ψ K π BaBar PRD71:032005,2005 (hep-ex/0411016)
(Rad)
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3
2
δ S-δ 0
1
0
-1
-2
-3
1000
I
Tim Gershon
1010
1020
1030
1040
K +K invariant mass
1050
(MeV)
Improved theoretical description of KK S-wave very useful for
comparison
b → c DP analyses @ LHCb
Inaugural meeting of Les NABIS, 02/03/2010
6/13
The Z + (4430)
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Charged charmonium-like state seen by Belle in
Bd0 → ψ 0 K + π − PRL100:142001,2008 (arXiv:0708.1790 [hep-ex])
Events/0.01 GeV
30
20
10
0
3.8
Tim Gershon
b → c DP analyses @ LHCb
4.05
4.3
+ ι
M(π ψ ) (GeV)
4.55
4.8
Inaugural meeting of Les NABIS, 02/03/2010
7/13
The Z + (4430)
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Not seen by BaBar in either Bd0 → J/ψ K + π − or ψ 0 K + π −
PRD79:112001,2009 (arXiv:0811.0564 [hep-ex])
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Detailed understanding of reflections from K + π − structures
necessary – improved theoretical description very helpful
-
(a) B → J/ψπ K
All Kπ- Events
-,0
1000
0,+
500
Events/10 MeV/c2
-
(d) B → ψ(2S)π K
All Kπ- Events
-,0
400
0,+
200
0
0
(b)
400
*
*
(e)
K (892) + K (1430)
*
*
K (892) + K (1430)
2
2
300
500
200
100
0
(c)
200
200
*
K veto
(f)
*
K veto
100
100
0
0
3.5
4
4.5
2
mJ/ψπ- (GeV/c )
Tim Gershon
b → c DP analyses @ LHCb
3.8
4
4.2
4.4
4.6
4.8
mψ(2S)π- (GeV/c2)
Inaugural meeting of Les NABIS, 02/03/2010
8/13
Bd0 → J/ψ K + K − and Bs0 → J/ψ π + π −
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Tree-level diagrams contain annihilation topologies – highly
suppressed
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Potential to study final state interactions / rescattering
7→ Bd0 → J/ψ K + K − : (d d̄) → (ss̄)
7→ Bs0 → J/ψ π + π − : (ss̄) → (d d̄)
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One interesting example: Bs0 → J/ψ f0 (980) → J/ψ π + π −
S. Stone and L. Zhang, PRD79:074024,2009 (arXiv:0812.2832
[hep-ph]), arXiv:0909.5442 [hep-ex]
I measure φ in B → PV b → cc̄s decay
s
I new experimental information to constrain S-waves
Tim Gershon
b → c DP analyses @ LHCb
Inaugural meeting of Les NABIS, 02/03/2010
9/13
γ from Bd0 → DK ∗0
I. Dunietz, PLB 270 (1991) 75
I Interfering amplitudes in B 0 → DK ∗0 are of comparable size
−→ large interference effects sensitive to γ
I charge of kaon in K ∗0 → K + π − tags flavour of B
c 0
u D
b
W
0
B
u
b
W
0
s
d
d
B
K*0
c
s
d
d
D0
K*0
T.G., PRD79 (2009) 051301(R)
I Exploit interference with B 0 → D ∗− K +
2
−→ provides reference amplitude in full Dalitz plot analysis
I charge of pion in D ∗− → Dπ − tags flavour of D
2
s
W
B0
Tim Gershon
b → c DP analyses @ LHCb
u
b
c
d
d
K+
*-
D2
Inaugural meeting of Les NABIS, 02/03/2010
10/13
γ from Bd0 → DK ∗0
T.G. and M. Williams, PRD80 (2009) 092002
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Toy Monte Carlo studies for proof-of-principle
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Extension of method to include all D → h+ h0− decays:
D → K π (fav), D → K π (sup), D → KK , ππ (CP)
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Comparison of γ sensitivity to quasi-two-body (Q2B) analysis
Compared to the Q2B analysis, the DP analysis provides:
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at least 50% better sensitivity to γ
(depends on value of δB as well as DK π Dalitz plot structure)
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resolution of ambiguous solutions
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much reduced dependence of the sensitivity on δB
Tim Gershon
b → c DP analyses @ LHCb
Inaugural meeting of Les NABIS, 02/03/2010
11/13
Potential problems in B → DK π Dalitz plot analysis
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Dalitz plot analysis will have model uncertainties
7→ initial studies suggest effect on γ is small, but we are
aiming for high precision
Modelling of nonresonant amplitudes
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Possible contributing K π, Dπ and DK resonances
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existence of a “dabba” pole?
Alternative: model-independent approach
T.G. and A. Poluektov, PRD81 (2010) 014025
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I
Tim Gershon
amplitudes for both b → c and b → u transitions
7→ potentially different Dalitz plot structures
double Dalitz plot analysis of B → DK π, D → KS0 π + π −
measure effective hadronic parameters in Dalitz plot bins
b → c DP analyses @ LHCb
Inaugural meeting of Les NABIS, 02/03/2010
12/13
Summary
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Dalitz plot analyses provide exciting physics opportunities for
LHCb
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To exploit fully this potential will need improved theoretical
descriptions
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Tim Gershon
Improve sensitivity to key benchmark measurements
Create new possibilities for discovery
nonresonant amplitudes
structures in ππ, K π, KK , Dπ, DK channels
... and maybe other exotic structures
Unprecedented statistics are coming in the next few years
7→ we need to aim for high precision
b → c DP analyses @ LHCb
Inaugural meeting of Les NABIS, 02/03/2010
13/13
University of Warwick, UK, September 6-10, 2010
http://ckm2010.warwick.ac.uk
Tim Gershon
b → c DP analyses @ LHCb
Inaugural meeting of Les NABIS, 02/03/2010
14/13
The end
Tim Gershon
b → c DP analyses @ LHCb
Inaugural meeting of Les NABIS, 02/03/2010
15/13