Feasibility of sin(2β+γ) Measurement From Time Distribution of
B0 DKS Decay
Vivek SharmaUniversity of California
San Diego
2
sin(2β+γ) From TD analysis of B0/B0→ D(*)0K(*)0 Decays
• CPV due to Interference between decay and mixing as in B D(∗)π– 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 DK*0 with K∗0→K+π−
– Disadvantages:• Color suppressed decays, Br (B ->DKS) ≈λ2 Br(B ->ψKS)
– Smaller decay rates (x 100) than B D(∗)π• Possible competing effects from Doubly-Cabibbo-suppressed D0 decays
• “ Overall requires x3 less B sample to measure sin2(2β+γ) than B Dπ “ – Kayser & London, PRD 61, 116103, 2000
* i i iub cs BrV V e A e eδ γ δ−=*
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 VrV 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
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
4.5 ±1.9 ±0.5B0 D∗0K0
6.2 ±1.2 ±0.4Β0 D0K0
BF (10-5)Mode
124 million BB
N=64 ± 11
N=11 ± 4
D Sidebands
Can measure sin(2β+γ) with some precisionwith D(*)0 Ks in 500 fb−1assuming r ~ 0.4 (?)
Cannot distinguishB0 from B0
Hidden strangenesswith KS in final state
Preliminary
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 D0K*0
• Vcb contribution: – B0 → D0bar K*0
D0bar → K+ π−,π−π0,3πK*0 → K+ π−
– Same sign kaons
• Vub contribution: – B0 → D0 K*0
D0 → K− π+,π+π0,3πK∗0 → K+ π−
– 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
d
s
uB0
D0
K*0
Aλ2
λ
b
d
u
d
s
cB0
D0
K*0
Aλ3(ρ+iη)eiγ
7
What We don’t Know: Limit on rB from Self-Tagging B0→ D0K*0
< 4.1 @ 90% CLB0 D0K∗0
6.2 ±1.4 ±0.6B0 D0K∗0
BF (10-5)Mode
Need large Vub driven amplitude for measurement of γ !
0.8 @90% C.L. ; more sensitive analysis on way<Br
124 million BB
No Signal inVub mediatedDecay
N=45 ± 9
Charge correlation toseparate B0 decay from B0
Vcb transition
Vub driven
0 0 *0
0
*0
KK
B D KD X
K π+−
+−
→→
→
0 0 *0
0
*0 K
BXK
D KD
K π++
+−
→→
→
Preliminary
B0 D0 K*0 ; K*0 K+π-
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
9
Toy Study of B DKSSensitivity to sin(2β+γ)
(Shahram Rahatlou @ CKM Angles Workshop 2003)
10
Time-Dependent Decay Distributions
• Similar to B D*π 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
Bτ
β γ δ
β
δτ
γ
γ δτ
β
−Γ Δ+
−Γ Δ
−Γ+
−
−
Δ−
+ +
⎛ ⎞−Δ = + Δ Δ Δ Δ⎜ ⎟+ +⎝ ⎠
⎛ ⎞−Δ = −
−
Δ Δ Δ Δ⎜ ⎟+ +⎝ ⎠
−Δ = − Δ
+ −
+ −
+
++Δ
+
−
( )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
Kτ
β γ δ+−Γ Δ
−
⎛ ⎞Δ Δ⎜ ⎟
⎝ ⎠
⎛ ⎞−Δ = + Δ Δ + Δ Δ⎜ ⎟+ +⎝
+⎠
+
( ) ( )( )2 22 1sin 2 1 1 12
S SS Sβ γ + − −+⎡ ⎤+ = + ± − −⎢ ⎥⎣ ⎦
One solution: sin2(2β+γ)
The other one: cos2Δ
S+
S-
fit for rB and sin(2β+γ−δ) and sin(2β+γ+δ)
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
β=23°±3°, γ=59°±19° → 2β+γ=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 δ = 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
0.0840.58219.4%Kaon 2
0.0580.36819.9%Other
0.0220.80117%Kaon 1
0.0280.93310.3%Lepton
Dilu. Diff.DilutionEfficiencyCategory
12
Summary of Signal efficiencies and yields circa 2003
• K∗0→Ksπ0:
– Expected events: N(K+π−) x 0.5 (BF) x 0.5 (π0 eff) x 0.75 (Ks eff) ~ 50 events– But more background from π0
• D0→Ksππ: done but not included for technical reason. Fewer events than D0→Kπ mode • D0→KK, ππ: Branching fraction ~ 10 smaller than BF(Kπ)
• B0→ D**0 K(∗)0: similar to B0→ D*0 K(∗)0 but reduced by intermediate branching fraction
74242525Reco0.040.020.08Efficiency
20936431124326ProducedD*0K*0(K+pi-)52161719Reco
0.050.030.12Efficiency1047322562163ProducedD*0Ks240798081Reco
0.080.040.15Efficiency338210401816527ProducedD0K*0(K+pi-)167515461Reco
0.100.060.23Efficiency1691520908263ProducedD0Ks
TotalK3piKpipi0Kpi
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, 2β+γ = 1.88, δ=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
μ: -0.002±0.006σ: 0.013±0.006
σrB
14
First ToyFit Attempt for 500 fb-1 sample: fit 3 parameters rB, sin(2β+γ±δ)
• 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
3.4%2.2%2.6%2β+γ=1.88
3.6%2.4%3.0%2β+γ=0.90
3.0%2.4%3.8%2β+γ=2.80
δ=2.4δ=0.8δ=0.0Frac. Failed Fits
2β+γ=1.88δ=0.8
2β+γ=1.88δ=0.0
15
Plan B Sensitivity for sin(2β+γ±δ) with rB=0.4 (fixed)
• All fits successful!– Problems with MINOS errors in some fits
• Under investigation
0.600.690.642β+γ=1.88
0.650.700.632β+γ=0.90
0.560.630.652β+γ=2.80
δ=2.4δ=0.8δ=0.0Residue sin(2β+γ+δ) RMS
0.610.620.642β+γ=1.88
0.660.640.652β+γ=0.90
0.590.610.602β+γ=2.80
δ=2.4δ=0.8δ=0.0Residue sin(2β+γ−δ) RMS
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(2β+γ±δ) probably not be feasible
with current method with ≈ 500 fb-1 samples (too few data)– With 500 fb-1, expected uncertainty on sin(2β+γ±δ) ~ 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(2β+γ±δ) – All simultaneous fits successful
• Uncertainty on rB: ~ 0.04-0.05• Uncertainty on sin(2β+γ): ~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
18
Getting to rB “ By Hook or By Crook” ! : Exercise@CKM2005 by Viola Sordini
19
Viola Sordini et alsi
n(2β
+γ) R
elat
ive
Erro
r
20
Bottom Line: B DKS
• Like with most pursuits of γ, strength of the b u amplitude is key• So far no observation, only limits on rB from B0→D(*)0K*0 modes, rB <0.39 (Belle)• Playing with measured B -> DK rates and constraining various contributing amplitudes
suggests rB→DKs=0.26±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(2β+γ) 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 ππ mode not prolific (yield ~4x smaller than D Kπ 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 γ !
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