1. LHCb Strategies for g from B→DK
Beauty 2006, Oxford UK, September 2006
LHCb Strategies for g from B→DK
ADS with B+→DK+
and B0 →DK*0
Yuehong Xie
University of Edinburgh
for the LHCb Collaboration
Dalitz with B+→DK+
and B0 → DK*0

2. Physics Aim Tree fit Loop fit
It is generally assumed tree processes are dominated by SM contributions
Disagreement between the tree-determined triangle (|Vub| + g from B→DK) and the loop-determined triangle (eK, Dmd, Dms, sin2b, … ) indicates new physics.
They are consistent within current measurement precision.
Have big uncertainty in g used for tree fit. Improvement needed!
Require sensitivity of g from tree ~ 5º to match the precision of indirect determination
LHCb: g from Bs→DsK is clean and unaffected by new physics, but has sensitivity of 14º with 2 fb-1 of data. We will see B→DK is more promising for LHCb.
g (tree)
Tree fit
Loop fit
Beauty 2006, Oxford UK
Yuehong Xie

3. LHCb detector PID: Detector status: RICH1/RICH2 Talk by Lluis Garrido
SPD/PS
ECAL
HCAL
M1-M5
RICH PID performance
2<p<100 GeV
<e(KK,P)> = 93%
<e(K,P)> = 4.7%
Detector status:
Talk by Lluis Garrido 
Trigger:
Talk by Eduardo Rodrigues
Tracking:
Vertex Locator TT
T1-T3
Magnet
Tracking efficiency
94% for physics tracks
with p>10GeV
Beauty 2006, Oxford UK
Yuehong Xie

4. Data simulation LHCb will start data-taking in 2007.
Full Pythia+Geant4 simulations are used for trigger, reconstruction and event selection studies.
Used event samples include
260m minimum bias events for trigger study,
140m Inclusive bb events for background study,
Dedicated signal events.
Sensitivities are obtained using fast simulations according to efficiencies, resolutions and background level from full simulations.
Beauty 2006, Oxford UK
Yuehong Xie

5. Event selection criteria
Hadron particle identification using RICH
Composite particle invariant masses (B, D, K*, Ks)
Impact parameters and transverse momentum of B and decay products
Vertex c2 of B, D, K*, Ks
Angle between B momentum and flight direction
Event topology
Cuts are optimized to reject most background events from a large inclusive bb sample and retain high signal efficiencies. Final B/S ratios are assessed based on a separate bb sample.
Beauty 2006, Oxford UK
Yuehong Xie

6. B→DK decays B decays (rB  0.1) D0 D0
Three parameters for CKM favoured B→DK and disfavoured B→DK
weak phase difference g = Arg(-(VubV*cs)/(VcbV*us))
strong phase difference dB and
amplitude ratio rB= |A(B→DK )|/|A(B→DK )|
Interference allows to extract g, if same D0 and D0 final states
B decays (rB  0.1) b c
ubar s b
ubar u
cbar s D0 D0
ubar
ubar
B0 decays (both diagrams colour suppressed → rB  0.4) b
dbar c
ubar s D0 b
dbar u
cbar s D0
Beauty 2006, Oxford UK
Yuehong Xie

7. ADS: use Interference DCS favoured
Consider a final state common to D0 and D0, e.g. Kp
DCS
favoured
Define
There are four possible charged B decays
(1)
(2)
(3)
(4)
Interference ~ O(1) for suppressed (2) and (4)
Beauty 2006, Oxford UK
Yuehong Xie

8. ADS tailored for LHCb
D0→Kp: 3 observables from the relative rates of the 4 processes depends on 4 unknowns g, rB, dB, dDKp
rDKp is already well measured
may benefit from cos(dD) measurements in CLEO-c and/or BES III
Need another D0 decay channel to solve for all unknowns
4-body decay D0→Kppp provides 3 observables which depends on 4 unknowns g, rB, dB, dDK3p – only dDK3p new (4-body Dalitz, p.17)
Each CP mode D0→KK/pp provides one more observables with no new unknowns
The ADS method constrains g only if we can see suppressed decays!
Good opportunity for LHCb.
Beauty 2006, Oxford UK
Yuehong Xie

9. Example: B+→(Kp)DK+, rB=0.077
Favoured modes
Background from D0p decays dominates
(BR ~13 × D0K)
Use RICH information to separate D0K and D0p
Use dedicated sample of D0p decays
→ Expect ~17k bkgrd events/year from D0p
Use bb sample to assess combinatorial background
→ Expect ~0.7k bkgrd events/year
Suppressed modes
bb sample indicates that the combinatorial contribution dominates :
→ Expect ~0.7k background events/year
D0p: 17k*RDpBELLE ~ 60 events/year
Efficiency / %
e(KK ,) = 93%
e(pK ,) = 4.7%
~28k/year B+→ (K+p-)DK+ B/S ~ 0.6
~28k/year B- → (K-p+)DK B/S ~ 0.6
Momentum / GeV
MC B±→D0(Kp)p± events
687 / 580k pass all cuts except B mass
387 / 580k inside 3s B mass cut
~530/year B+→ (K-p+)DK+ B/S ~ 1.5
~180/year B- → (K+p-)DK- B/S ~ 4.3
(depending on rB )
B± mass /MeV
Beauty 2006, Oxford UK
Yuehong Xie

10. Performance with B+→DK+
Take g = 60º, rB = 0.077
dB = 130º
rDKp = rDK3p = 0.06
-25º< δDK < 25º and
-180º< δDK3p <180º
Combine Kp with
K3p similar yields and background level as Kp
KK and pp modes
w/o bkgrd
δDKp, δDK3p
estimated bkgrd
δDKp, δDK3p
~4.3k B+→ D0(hh)K B/S ~ ~3.3k B- → D0(hh)K B/S ~ 1
(Highlighted are RMS quoted for non-Gaussian distribution of fit results due to close ambiguous solutions, will disappear as statistics increase. Global analysis using all modes will also help.)
s(g) ~ 5º -15º in a year, depending on rB, δDK and δDK3
Beauty 2006, Oxford UK
Yuehong Xie

11. ADS with D*K Attractive feature Potential However
D*→D0p0 (BR~2/3) – has strong phase δB
D*→D0g (BR~1/3) – strong phase δB+p
→ if can distinguish the two decays → powerful additional constraint !
Potential
Including D*K without background improves precision to s(g) = 2º - 5º
However
Reconstruction efficiency is small for soft g while background is enormous
Non-trivial to separate D0p0 and D0g
Fit DK mass shape to get p0 and g components ignoring neutrals
all favoured modes can reach 10k/year or more with B/S ~ O(1)
Suppressed modes still problematic: under study
Idea to use the event topology to reconstruct momentum of p0/g is being investigated
B±→D*(D0g)K±
bb sample
Background dominating:
1 bb event here represents 5k/year!
D0K mass
B±→D*(D0p0)K±
B±→D*(D0g)K±
Charged reconstruction
Beauty 2006, Oxford UK
Yuehong Xie

12. ADS with B0→DK*0
The same method can be applied to B0 →D0K* with D0→Kp and KK, (historically treated with “GLW” method)
rB ~ 0.4, big interference in CP modes (rDCP=1)
Mode
Yields
S/B
favoured B0  (K+-)D K*0 + c.c.
3400
> 3.3
disfavoured B0  (K-+)D K*0 + c.c.
500
> 0.6
B0  (K+K-/p+p-)D K*0 + C.C.
600
> 0.7
() ~ 7º-10 in a year (2 fb-1) (55 <  < 105, rB~0.4, -20 < dB < 20)
Beauty 2006, Oxford UK
Yuehong Xie

13. Dalitz: B+→(Ksp+p-)DK+
Three body decay D0→Ksp+p- fully parameterized with two parameters m+2=m2(Ksp+) and m-2=m2(Ksp-)
Use pre-determined model to describe D0 decay amplitudes as a function of (m+2, m-2)
Total B decay amplitude as sum of contributions via D0 and D0
N: number of resonances
aj, aj: amplitude and phase parameters from B factories
Aj: model-dependent parameterization of
matrix element
Interference has sensitivity to g
G(m-2,m+2) = |f(m-2,m+2)|2 + rB2 |f(m+2,m-2)|2
+ 2 rB Re [ f(m-2,m+2)f*(m+2,m-2)ei (-g+dB) ]
Beauty 2006, Oxford UK
Yuehong Xie

14. Comparison to BELLE data
Naïve model amplitude Isobar amp. + non-res Belle data with model fit
Beauty 2006, Oxford UK
Yuehong Xie

15. Performance of B+→(Ksp+p-)DK+
for rB = 0.077
LHCb generator studies m-
5k events/year assuming “good” Ks efficiency at HLT, combinatorial B/S < 0.7, D(Kspp)p B/S in (0.11, 12) at 95% C.L.
Need large D(Kspp)p sample to clarify
Model parameters from B and charm factories
s(g) ~ 8º + model uncertainty, w/o b.g. and detector effect in fit
Two-fold ambiguity (g, dB), (g-p, dB-p)
r(770)
K* and DCS K* m+
Statistical precision depends on rB, e.g., s(g)~4º for rB=0.15
Current Ks problem in HLT:
Only 25% of Ks decay inside active region of VELO, giving 1.5k events/year. Online reconstruction of the pion tracks from other Ks requires special treatment and is challenging due to HLT time limit. Great efforts are being made to speed up the online reconstruction of no-VELO tracks. Depending on how this will be accomplished, annual yield can vary between 1.5k - 5k, leading to d(g)~8º-16º for rB =
Beauty 2006, Oxford UK
Yuehong Xie

16. Acceptance studies
Selection tuned to maximise signal-to-background ratio
Flat phase space MC generated
Overall acceptance not flat as a result of trigger and offline selection % m- % m- m+ m+
Acceptance evaluation with isobar model in progress – as expected similar acceptance function is indicated. Can be checked with B→Dp data.
Beauty 2006, Oxford UK
Yuehong Xie

17. Dalitz: B+  (KsK+K-)D K+
Same method works for D0  KsK+K- decay
BR reduced by factor of 6
BR(D0  K0K+K-) =(1.03±0.10)%
But less background because of two more particle identification constraints from RICH
Dalitz model has fewer resonances (, a0) but complex threshold effects (Babar hep-ex/ )
Work on event selection and sensitivity ongoing
Beauty 2006, Oxford UK
Yuehong Xie

18. “Dalitz”: four-body D decay
The idea for 3-body D0 decays can be extended to 4-body D0 decays. Need 5 parameters to describe D0 decays: not really a Dalitz plot.
B+→(ppKK)DK+
for g=60º, dB=130º, rB=0.08
~ 1.5k events in a year
Preliminary number d(g) ~ 15º w/o b.g. and detector effect
B+→(pppK) DK+
The same channel as used in ADS, but to take into account strong phase dependence on Dalitz space
rB~rD big interference
Sensitivity under study
Beauty 2006, Oxford UK
Yuehong Xie

19. Dalitz: B0  (KSp+p-)D K*0
Branching ratio reduced by factor 10 compared with B+ mode
Same method as in B+
Annual yield < 600 events
Big interference (rB~0.4)
Will complement the “GLW” modes D0→Kp, KK and pp
Also suffers KS HLT problem
PDG ‘04
Beauty 2006, Oxford UK
Yuehong Xie

20. Summary of performances: 2 fb-1
B mode
D mode
d(g)
B+→ DK+
Kp + KK/pp + K3p
5º - 15º
B+ → DK+
Kspp
8º ~ 16º
KKpp
~ 15º
B0 → DK*0
Kp + KK
7º - 10º
Under study
no b.g.,
detector effect
More modes are being investigated.
Combined precision should not be far away from 5º
Beauty 2006, Oxford UK
Yuehong Xie

21. Sources of systematics
As we approach statistical error of 10º, understanding and controlling systematical uncertainty becomes more and more important for LHCb
Dalitz model dependence
Improve D decay model by work of B and Charm factories (LHCb for 4-body)
Other contributions to K* region in B→DK*
To be studied
Dalitz acceptance not flat
Currently obtained using Mont Carlo simulation, should be calibrated with data
Production asymmetry and detection charge asymmetry to be studied
D0-D0 mixing and CP violation
CP-conserving D0 mixing is a very small effect and can be neglected
New physics with big CP violation in D0 mixing may change the value of g extracted from B→DK. Not really a systematic error but a new physics effect.
D0 mixing and CP violation can be probed in LHCb. See Raluca Muresan’s talk Friday.
g = 92º ± 41º ± 11º ± 12º (Babar) g = 58º ± 18º ± 3º ± 9º (Belle)
Beauty 2006, Oxford UK
Yuehong Xie

22. Conclusions
LHCb will be able to extract g from B→DK to the required 5º precision to match the indirect determination with ~2 fb-1
Comparison of g from B→DK and indirect determination will become a stringent test of the SM
Together with improvement on |Vub| the measured g from B→DK will enable to construct a reference Unitarity Triangle needed for new physics search
A lot of work to do before data-taking
Beauty 2006, Oxford UK
Yuehong Xie

23. Offline track finding strategy
T track
Upstream track
VELO
seeds
Long track (forward)
Long track (matched)
VELO track
T seeds
Downstream track
Multiple pass track finding:
Velo seeds
T seeds
Long tracks  highest quality for physics
Downstream tracks  needed for efficient KS finding
Upstream tracks  lower p, worse p resolution, useful for RICH1 pattern recognition
Beauty 2006, Oxford UK
Yuehong Xie

24. CKM global fit
Beauty 2006, Oxford UK
Yuehong Xie