Feasibility of sin(2b g) Measurement From Time Distribution of B0 ? DKS Decay

1
Feasibility of sin(2bg) Measurement From Time
Distribution of B0 ? DKS Decay

• Vivek Sharma
• University of California
• San Diego

2
sin(2bg) From TD analysis of B0/B0? D()0K()0
Decays
Strong phase difference

• CPV due to Interference between decay and mixing
  as in B? D()p
• Advantages
• Expect large (40) CPV since two processes of
  similar strength
• Time-dependent measurement with K0 ? KS
• Probe rB in self-tagging final state B?DK0 with
  K0?Kp-
• Disadvantages
• Color suppressed decays, Br (B -gtDKS)???2 Br(B
  -gt?KS)
• Smaller decay rates (x 100) than B ? D()p
• Possible competing effects from
  Doubly-Cabibbo-suppressed D0 decays
• Overall requires x3 less B sample to measure
  sin2(2??) than B ? D? Kayser London, PRD
  61, 116103, 2000

3
B0/ B0? D()0K()0 Decay Rate Measurements By
Belle BaBar (2004)
4
B0/B0? D()0KS Rates What We Know Now (BaBar)
hep-ex/0408052
N64 11
Cannot distinguishB0 from B0 Hidden
strangenesswith KS in final state
D0 Sidebands
124 million BB
N11 4
Preliminary
Mode BF (10-5)
B0 ?D0K0 6.2 1.2 0.4
B0 ?D0K0 4.5 1.9 0.5
Can measure sin(2bg) with some precisionwith
D()0 Ks in 500 fb-1assuming r 0.4 (?)
5
B0/B0? D()0KS Rates What We Know Now (Belle)
hep-ex/0408108
274 million BB
78?14
78?15
6
Isolating Vub and V cb Driven amplitudes in B?
D0K0

• Vcb contribution
• B0 ? D0bar K0 D0bar ? K p-,p-p0,3p
  K0 ? K p-
• Same sign kaons
• Vub contribution
• B0 ? D0 K0 D0 ? K- p,pp0,3p
  K0 ? K p-
• Kaons with opposite sign
• Determine rB by measuring the 2 branching
  fractions
• Different sources of background because of charge
  correlation
• Treat them as 2 different decay modes

7
What We dont Know Limit on rB from Self-Tagging
B0? D0K0
Vcb transition
Charge correlation toseparate B0 decay from B0
124 million BB
N45 9
Vub driven
B0 ? D0 K0 K0 ?K?-
Preliminary
Mode BF (10-5)
B0 ? D0K0 6.2 1.4 0.6
B0?D0K0 lt 4.1 _at_ 90 CL
Need large Vub driven amplitude for measurement
of g !
8
What We dont Know Now Limit on rB from
Self-Tagging B0? D0K0
Belle 274 million BB
Br lt 0.5 x 10-5 _at_ 90 CL
Br lt 1.9 x 10-5 90 CL
gt rB lt 0.39 _at_ 90 CL
9
Toy Study of B ?DKSSensitivity to
sin(2??)(Shahram Rahatlou _at_ CKM Angles
Workshop 2003)
10
Time-Dependent Decay Distributions
S
S-
One solution sin2(2bg) The other one cos2D

• Similar to B?Dp time-distribution
• But r expected to be much larger (x 10-20)
• Linear dependency on r can it be measured in the
  fit (?)
• Tag-side DCS effects are small compared to signal
  amplitude
• But there are other potential complications due
  to DCS decays on reco side (20)

fit for rB and sin(2bg-d) and sin(2bgd)
11
Assumptions Used In This Toy Study

• Signal Yield ? 0.3 events / fb-1 ? 160
  reconstructed events (B?D0Ks only for now)
• Yields can be 50 higher (Br. Ratio knowledge,
  better event selection)
• Additional modes can increase signal yield but
  wont be as clean
• No combinatorial or peaking background
• Signal asymmetries expected to be weakly
  correlated with background parameters
• b23?3?, g59?19? ? 2bg105?20? (1.83 rad)
• Use 3 values in toys 0.9, 1.88, and 2.8 rad
• No Knowledge of strong phase
• Use different values d 0.0, 0.8, 2.4 rad
• Realistic BaBar Flavor Tagging circa 03
• 105 tagged events in 500 fb-1
• Vertexing realistic resolution function
• 10 tail and 0.2 outliers with category
  dependent bias
• Parameters fixed in the fit

Category Efficiency Dilution Dilu. Diff.
Lepton 10.3 0.933 0.028
Kaon 1 17 0.801 0.022
Kaon 2 19.4 0.582 0.084
Other 19.9 0.368 0.058
12
Summary of Signal efficiencies and yields circa
2003
    Kpi Kpipi0 K3pi Total
D0Ks Produced 263 908 520 1691
  Efficiency 0.23 0.06 0.10  
  Reco 61 54 51 167
D0K0(Kpi-) Produced 527 1816 1040 3382
  Efficiency 0.15 0.04 0.08  
  Reco 81 80 79 240
D0Ks Produced 163 562 322 1047
  Efficiency 0.12 0.03 0.05  
  Reco 19 17 16 52
D0K0(Kpi-) Produced 326 1124 643 2093
  Efficiency 0.08 0.02 0.04  
  Reco 25 25 24 74
Yields for 500 fb-1 withBF 4 x 10-5
Assuming D0reco. efficiencyof 50

• K0?Ksp0
• Expected events N(Kp-) x 0.5 (BF) x 0.5 (p0
  eff) x 0.75 (Ks eff) 50 events
• But more background from p0
• D0?Kspp done but not included for technical
  reason. Fewer events than D0?K? mode
• D0?KK, pp Branching fraction 10 smaller than
  BF(Kp)
• B0? D0 K()0 similar to B0? D0 K()0 but
  reduced by intermediate branching fraction

13
Fit Validation with 50 ab-1 rB

• Validate fit with 500 experiments of 50 ab-1
• rB(gen) 0.4, 2bg 1.88, d0.0

Slightly better errors for larger rB
rB(fit) rB(gen)
rB(fit) uncertainty
rB(fit) uncertainty vs. rB(fit)
Mean 0.014 RMS 0.001
m -0.0020.006 s 0.0130.006
?rB
No bias in the fitted values for any parameter
14
First ToyFit Attempt for 500 fb-1 sample fit 3
parameters rB, sin(2bgd)

• Problem with fit convergence
• Small values of rB are problematic
• rB constrained to be positive in the fit
• 10 of fits with rB close to the limit

Frac. Failed Fits d0.0 d0.8 d2.4
2bg0.90 3.0 2.4 3.6
2bg1.88 2.6 2.2 3.4
2bg2.80 3.8 2.4 3.0
2bg1.88d0.8
2bg1.88d0.0
15
Plan B ? Sensitivity for sin(2bgd) with rB0.4
(fixed)

• All fits successful!
• Problems with MINOS errors in some fits
• Under investigation

Not perfect Gaussian shape
Bad errors mostlyfor the positive
errorProbably hitting non-physicalregion in LL
Residue sin(2bgd) RMS d0.0 d0.8 d2.4
2bg0.90 0.63 0.70 0.65
2bg1.88 0.64 0.69 0.60
2bg2.80 0.65 0.63 0.56
Residue sin(2bg-d) RMS d0.0 d0.8 d2.4
2bg0.90 0.65 0.64 0.66
2bg1.88 0.64 0.62 0.61
2bg2.80 0.60 0.61 0.59
16
Summary of Preliminary Toy Study

• Sensitivity with 0.5 ab-1?
• Simultaneous determination of rB, and sin(2bgd)
  probably not be feasible with current method with
  ? 500 fb-1 samples ? (too few data)
• With 500 fb-1, expected uncertainty on
  sin(2bgd) 0.6-0.7 provided rB known from
  elsewhere.
• ignoring DCS effects which at 22 is small
  compared to expected errors and where CLEO-c can
  help ?
• Sensitivity with 5 ab-1?
• No problem measuring rB and sin(2bgd)
• All simultaneous fits successful
• Uncertainty on rB 0.04-0.05
• Uncertainty on sin(2bg) 0.15-0.20
• The errors now scale with luminosity

17
Getting to rB By Hook or By Crook !
Exercise_at_CKM2005 by Viola Sordini etal
Learning Today From Data on B ? DK Family of
Decays
18
Getting to rB By Hook or By Crook !
Exercise_at_CKM2005 by Viola Sordini
19
Viola Sordini et al
sin(2??) Relative Error
20
Bottom Line B ? DKS

• Like with most pursuits of ?, strength of the b?u
  amplitude is key
• So far no observation, only limits on rB from
  B0?D()0K0 modes, rB lt0.39 (Belle)
• Playing with measured B -gt DK rates and
  constraining various contributing amplitudes
  suggests rB?DKs0.26?0.16. Is this approach
  theoretically kosher?
• ToyMC based time-dependent CPV studies indicate
  that with 500 fb-1 samples, mild information only
  on sin(2bg) provided rB obtained from elsewhere
• More B modes need to be added
• Self tagging decay B ? D0 KS decays (poor Br.
  for self tagging modes)
• B ? DKs, D? Ks ?? mode not prolific (yield 4x
  smaller than D?Kp mode)
• Precise measurements require gt ab-1 data samples
• Can LHCb do such modes (Large Ks decay lengths)
• There are no shortcuts in clean measurements of ?
  !