Feasibility of sin Measurement From Time Distribution of
B0 DKS Decay
Vivek SharmaUniversity of California
San Diego
2
sin(2+) From TD analysis of B0/B0 D(*)0K(*)0 Decays
• CPV due to Interference between decay and mixing as in B D– Advantages:
• Expect large (40%) CPV since two processes of similar strength • Time-dependent measurement with K KS
• Probe rB in self-tagging final state BDK*0 with KK
– Disadvantages:• Color suppressed decays, Br (B ->DKS)2 Br(B ->KS)
– Smaller decay rates (x 100) than B D• 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
* i i iub cs BrV V e A e e *
cb usV V A
0 0 (*)0
0 0 (*)0
*
* ~ 0.4
B
ub csB
cb us
A B D Kr
A B D K
V Vr
V V
Strong phasedifference
b c
d d
u
s
0(*)D
0(*)K
*cbV
usV0B
b
c
d
u
s
ubV
*csV0B
b
0B
d
d
0(*)K
0(*)D
4
B0/B0 DKS Rates : What We Know Now (BaBar)
hep-ex/0408052
Mode BF (10-5)
DK 6.2 ±1.2 ±0.4
B DK 4.5 ±1.9 ±0.5
124 million BB
N=64 ± 11
N=11 ± 4
D Sidebands
Can measure sin() with some precisionwith D(*)Ks in 500 fbassuming r ~ 0.4 (?)
Cannot distinguishB from B
Hidden strangenesswith KS in final state
Preliminary
6
Isolating Vub and V cb Driven amplitudes in B D0K*0
• Vcb contribution: – B0 D0bar K*0
D0bar K , K*0 K
– Same sign kaons
• Vub contribution: – B0 D0 K*0
D K , K K
– 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
b
d
c
ds
uB0
D0
K*0
A2
b
d
u
ds
cB0
D0
K*0
A3(+i)ei
7
What We don’t Know: Limit on rB from Self-Tagging B0 D0K*0
Mode BF (10-5)
B DK 6.2 ±1.4 ±0.6
BDK < 4.1 @ 90% CL
Need large Vub driven amplitude for measurement of !
0.8 @90% C.L. ; more sensitive analysis on wayBr
124 million BB
No Signal inVub mediatedDecay
N=45 ± 9
Charge correlation toseparate B decay from B
Vcb transition
Vub driven
0 0 *0
0
*0
KK
B D KD X
K
0 0 *0
0
*0 K
BXK
D KD
K
Preliminary
B0 D0 K*0 ; K*0 K+-
8
What We don’t Know Now: Limit on rB from Self-Tagging B0 D0K*0
Belle 274 million BB
rB < 0.39 @ 90% CL
Br < 1.9 x 10-5 90% CLBr < 0.5 x 10-5 @ 90% CL
10
Time-Dependent Decay Distributions
• Similar to BD* 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%)
0
0
2
2 2
2
2 2
20
2 2
1 2( , ; ) 1 cos sin8 1 1
1 2( , ; ) 1 cos sin8 1
sin 21
1 2( , ; ) 1 cos sin8
sin
1
2
s1
in 2
t
t
t
e r rf tag X t m t m tr r
e r rf tag X t m t m tr r
e r rf tag X t m tr
B
K
K
KB
r
B
2
20
2
1 2( , ; ) 1 cos sin8 1
s1
in 2t
m t
e r rf tag X t m t m tr
Br
K
2 22 1sin 2 1 1 12
S SS S
One solution: sin2()
The other one: cos
S+
S-
fit for rB and sin() and sin()
11
Assumptions Used In This Toy Study• Signal Yield: 0.3 events / fb-1 160 reconstructed events (BD0Ks 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 =23±3, =59±19 2=105±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 = 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
• KKs:
– Expected events: N(K+) x 0.5 (BF) x 0.5 ( eff) x 0.75 (Ks eff) ~ 50 events– But more background from
• DKs: done but not included for technical reason. Fewer events than D0K mode • DKK, : Branching fraction ~ 10 smaller than BF(K)
• BD**K: similar to BD*K but reduced by intermediate branching fraction
Kpi Kpipi0 K3pi TotalD0Ks Produced 263 908 520 1691 Efficiency 0.23 0.06 0.10 Reco 61 54 51 167D0K*0(K+pi-) Produced 527 1816 1040 3382 Efficiency 0.15 0.04 0.08 Reco 81 80 79 240D*0Ks Produced 163 562 322 1047 Efficiency 0.12 0.03 0.05 Reco 19 17 16 52D*0K*0(K+pi-) 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 D*0
reco. efficiencyof 50%
13
Fit Validation with 50 ab-1: rB
• Validate fit with 500 experiments of 50 ab-1
– rB(gen) = 0.4, 2 = 1.88, =0.0
rB(fit) – rB(gen) rB(fit) uncertainty rB(fit) uncertainty vs. rB(fit)
No bias in the fitted values for any parameter
Slightly better errors for larger rB
Mean: 0.014RMS: 0.001
: -0.002±0.006: 0.013±0.006
rB
14
First ToyFit Attempt for 500 fb-1 sample: fit 3 parameters rB, sin(±)
• 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
3.0% 2.4% 3.6%
2.6% 2.2% 3.4%
3.8% 2.4% 3.0%
15
Plan B Sensitivity for sin(±) with rB=0.4 (fixed)
• All fits successful!– Problems with MINOS errors in some fits
• Under investigation
Residue sin() RMS =0.0 =0.8 =2.4
=0.90 0.63 0.70 0.65
=1.88 0.64 0.69 0.60
=2.80 0.65 0.63 0.56
Residue sin() RMS =0.0 =0.8 =2.4
=0.90 0.65 0.64 0.66
=1.88 0.64 0.62 0.61
=2.80 0.60 0.61 0.59
Not perfect Gaussian shape
Bad errors mostlyfor the positive error
Probably hitting non-physicalregion in LL
16
Summary of Preliminary Toy Study
• Sensitivity with 0.5 ab-1?– Simultaneous determination of rB, and sin(±) probably not be feasible
with current method with 500 fb-1 samples (too few data)– With 500 fb-1, expected uncertainty on sin(±) ~ 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(±) – All simultaneous fits successful
• Uncertainty on rB: ~ 0.04-0.05• Uncertainty on sin(): ~0.15-0.20• The errors now scale with luminosity
17
Getting to rB “By Hook or By Crook” ! : Exercise@CKM2005 by Viola Sordini etal
Learning Today From Data on B DK Family of Decays
20
Bottom Line: B DKS
• Like with most pursuits of , strength of the bu amplitude is key• So far no observation, only limits on rB from B0D(*)0K*0 modes, rB <0.39 (Belle)• Playing with measured B -> DK rates and constraining various contributing amplitudes
suggests rBDKs=0.260.16. Is this approach theoretically kosher?• ToyMC based time-dependent CPV studies indicate that with 500 fb-1 samples, mild
information only on sin() provided rB obtained from elsewhere• More B modes need to be added
– Self tagging decay B D**0 KS decays (poor Br. for self tagging modes)– B DKs, D Ks mode not prolific (yield ~4x smaller than DK mode)
• Precise measurements require > ab-1 data samples• Can LHCb do such modes (Large Ks decay lengths)• There are no shortcuts in clean measurements of !