Post on 19-Dec-2015
Outline
• NP-independent (incomplete list, hopefully representative)
– sin2 in BD0K (GW, ADS)
– Recent developments• BD0
(CP)K
• BD0(non-CP)K, D0K
• Untagged B0
– sin(2+) • B0D(*(*))(*)
• B0DK• D0K0
• Comparison to NP-sensitive results• Penguins
• Mixing
• Cautious predictions for ~10 ab1
NP
r ei() + ei D
B+
b
u
u
u
cs K+
D0
B+bu
cu
su
D0
K+
K
K 1
Amplitude
bu
bc
sin2 with BD(flavor+CP)K
Atwood, Dunietz, Soni, PRL 78, 3257 (ADS)
cos D measurable @ charm factory
A.S., hep-ex/9801018 Gronau, Grossman, Rosner, PLB508, 37, 2001 Atwood, Soni, hep-ph/0304085
(1 r ei())CPES (CP eigenstate)
r ei()
Initial a2/a1 ~ 0.25: r ~ 0.1
B0 D0 0, etc., suggest r ~ 0.2
Gronau, Wyler, PLB 265, 172 (GW)
ei D
Sensitivity
A.S., PRD 60, 054032
• L~600 fb1, r = 0.1
• BD(*)K(*)
• DK(n)+, CPES
True
3
3
2
58o
58o
S:
S± : S:
Resolved by large D
New Developments
• More modes & methods – more statistics• New methods reduce ambiguity to 2-fold• More experimental experience
Each of these methods satisfies the NIMSBHO principle:Not Inherently More Sensitive But Helps Overall
(despite possible claims to the contrary…)
Don’t Measure BR r2
Jang, Ko, PRD 58, 111Gronau, Rosner, PLB 439, 171
Determine r ( Vub /Vcb color suppression) indirectly, from
Color-suppressed bc modes
NIMSBHO
r
SCS non-CP D Decay Modes
B+
b
u
u
u
cs K+
D0
B+bu
cu
su
D0
K+
K
(1+r rD ei(D))
1
Amplitude
bu
bc
KK...
KK... (rD+r ei(D))
• No need to measure BR’s r2, sensitive at O(r)• BR measurable now • S resolved – ambiguity only 4-fold
rD = = 0.7 for K*K, measure with
D*-tagged D0’sD = arg
Grossman, Ligeti, A.S. PRD 67, 071301
K
NIMSBHO
D Dalitz Plot
BaBar, hep-ex/0207089 22 fb1
m2(K0+) GeV2
m2 (
K
+)
GeV
2
D0K0K D0K0K
There is also the K+K0 mode
B+
b
u
u
u
cs K+
D0
B+bu
cu
su
D0
K+
K
CP even (K+K...)
1
(1 + r ei())
Amplitude
bu
bc
Special Case: CP Modes
Gronau, hep-ph/0211282
CP odd (Ks0...) (1 r ei())
• No need to measure BR’s r2, sensitive at O(r2)• 8-fold ambiguity (when used standalone)
K
NIMSBHO
BD(multi-body)KGiri, Grossman, A.S., Zupan, PRD68, 054018, 2003
Expand to multi-body decay:
Model-independent analysis: bin the D Dalitz plot
Bf K1 + rD2 r2 + 2 r rD cos(B + D – )
|A(D f)||A(D f)|
Arg(D f) Arg(D f)
|A(D f)|2|A(D f)|2 |A(D f) A(D f)| cos [or sin] Dibin
ibin
ibin
For a unique D final state f (such as a 2-body D decay):
(From fit or charm factory: ci, si2)
bin i Bfi KTi + Ti r2 + 2 r [cos(B – ) ci + sin(B – ) si ]
(From D*+D0+) (From D*D0)
Application to Cabibbo-Allowed D Decays
NIMSBHO
Divide the DKsDalitz plot into n bins (n 4)
• 2n observables: (B+)i & (B)i in each bin
• n + 3 unknowns: ci, si, r, B,
m2(Ks) GeV2
m2 (
Ks )
GeV
2
ci
ci
si
si
Resolves S. Resonances resolve S± (essentially no model dependence)
Belle
• Cabibbo-allowed: high statistics• Dalitz plot suppression
• Best interference is around DCS decays
• This formalism is also needed for DK0 and K (ADS/GW)
Assume Breit-Wigner Resonances in D Decay
B B
Belle, hep-ex/0308043, 140 fbfb
More model dependence, smaller statistical error
Errors with 140 fb
r = 0.33 ± 0.10 = 95° ± 23° ± 13° ± 10° = 162° ± 23° ± 12° ± 24°
90% CL:0.15 < r < 0.50
61° < < 142°104° < < 214° Asymmetry in BD
syst has a significant 1/N component
Removing Color Suppression
B+
b
u
u
u
cs K+
D0
B+bu
cu
su
D0
K+
B+bu
cu
s
u
D0
K+
uu
0
B+bu
uu
s
c D0
K+
uu
0
r ~ 0.4 instead of ~ 0.1 or 0.2
bu
bc
Aleksan, Petersen, A.S., PRD 67, 0960XX
Dalitz Plot Suppression
Ds**+
D*0
K*+
bu bc
Expect mostly NR-NR & NR-K* interference
NR
Simulation
Small K(1430) – Ds(2450) overlap Oliver et al, hep-ph/9801363
K(1430)
Ds(2450)
Simulation
Assuming NR/R ~ 0.4 (or equivalent interference), 400 fb1, expect ~ 0.2
Resolves S. Resonances resolve S± (essentially no model dependence)NIMSBHO
1
rf eiD
New: from Untagged B0 DecaysGronau, Grossman, Shumaher, A.S., Zupan
B0
b
d
u
d
cs K0
D0
B0
b
d
c
d
us K0
D0
f
(Bf KS) = X(1+rf2) + 2Yrf cos(D +)
Ar ei()
Untagged rates:
where X A2(1+r2) Y 2A2 r cos B
Depend only on the B decay
For N D decay modes:• N+3 unknowns: D
N, , X, Y• Solvable with N 3 (or a multibody D mode)• For 2 B decay modes, need only N 2
(Bf KS) = X(1+rf2) + 2Yrf cos(D )
Analytic SolutionSpecial case: CP odd and even eignstate and 1 flavor state:
SoddSevenCP KfBKfB 21
SoddSevenCP KfBKfB 21
21 f
SflavSflavflav r
KfBKfB
21 f
SflavSflavflav r
KfBKfB
22
2
2
22
1
2tan
flavCPCPf
f
flav
r
r
Combining with B+ Modes
• Best use of untagged B0 modes is to combine them with results from B+ decays (& tagged B0 decays) with the same D modes:• Every untagged B0 mode adds 2 unknowns (X, Y) and 2
measurements ((Bf KS), (Bf KS))
• D decay parameters & are the same as in the tagged/B+ decays
• Expect significant improvement in overall sensitivity, since:• Sensitivity is dominated by smallest interfering amplitude
• This amplitude has the same magnitude for B+ and untagged B0 (up to KS/K+ reconstruction efficiencies, etc.)
S = sin(2)
b d
h
db
c dduD(*)
duc dhD(*)
t
t
sin(2+) with BD(*)h
rei
~0.02
,,a1Dunietz, hep-ph/9712401
BD* with Partial ReconstructionBaBar, hep-ex/0310037, 76 fb
BD*+
D0
Reconstructed
Not reconstructed
Lepton tag Kaon tag
Lepton tag Kaon tag
00
00
)(
tagtag
tagtag
BB
BB
CP
NN
NN
tA
BD(*) Results
a r (S+ + S) = 2 r sin(2) cos() = magnitude of ACP
c r (S+ – S) = 2 r sin() cos(2)
2 rD* S+D*0.092 0.059 (stat) 0.016 (syst) 0.036 (D*ln)
2 rD* SD*0.033 0.056 (stat) 0.016 (syst) 0.036 (D*ln)
2 rD S+D 0.094 0.053 (stat) 0.013 (syst) 0.036 (D*ln)
2 rD SD0.022 0.054 (stat) 0.013 (syst) 0.036 (D*ln)
Belle S sin(2
aD0.022 0.038 (stat) 0.020 (syst)
aD*0.068 0.038 (stat) 0.020(syst)
cD 0.025 0.068 (stat) 0.033 (syst)
cD*0.031 0.070 (stat) 0.033 (syst)
BaBar (full reconstruction)
aD*(K tag) 0.054 0.035 (stat) 0.017(syst)
S+D*(l tag)0.078 0.052 (stat) 0.021 (syst)
S+D*(l tag) 0.070 0.052 (stat) 0.019 (syst)
Avg. of aD*& (S+D* + S+
D*)/2: 0.063 0.024 (stat) 0.014 (syst)
BaBar (partial reconstruction, D* only)
magnitude of ACP
BD* Systematics (example)
Specific to partial reco. Need to measure in data (big statistical component)
For 10 ab1, need to reduce these systematics by a factor of ~5 – 10
sin(2)D with partial reconstruction lepton tag
Reduction by 2–3 seems very reasonable
Both are currently quite conservative.
from sin(2+)Silva, A.S., Wolfenstein, Wu, PRD 67, 036004
True
Mea
sure
d
True
few ab1
So far seems small
Allowed range
Resolving ambiguities is crucial
Sensitivity to r
• Hard to measure r from (1r2)cos(m t), need to take it from BDs+
• Angular analysis with BD*a, exploit interference between the 3 helicity amplitudes to do away with r2 terms
London, Sinha, Sinha, PRL 85, 1807
• The same can be done with BD** • 2 D** resonances & continuum • Resonance mass shapes add to angular information, resolves
ambiguities
Sinha, Sinha, A.S.
r2 r 1• Enough to measure terms r
• Expect significant improvement for this mode
• Perhaps large ’s will resolve ambiguities
• More complicated fit
sin(2+) with Tagged BD(*)Ksh
hc dsu
D(*)duc s
hD(*)d d
KS
d dKS
r ~ 0.4
Aleksan, Petersen, hep-ph/0307371
• Dalitz plot suppression• Ambiguity only 2-fold ( • Expect ~ 0.2 – 0.3 with 400 fb1
NIMSBHO
Tagged B0DK0
Gronau, London, PLB 253, 483Kayser, London, PRD 61, 116013Atwood, Soni, PRD 68, 033009
r ~ 0.36
Data suggest r ~0.6 0.2(109 B’s, sub-BR, tagging, no reco eff. Or bgd.) Belle, PRL 90, 141802
NIMSBHO
with 10 ab1
• Use all methods
– Will measure to ~ 2° (%) (stat) or less!
– Only ambiguity is left• Excluded theoretically?
– The error is so small that ambiguities won’t matter
Compare to from Penguins
• Theoretical uncertainties in precision extraction of • Disagreement with “clean” measurements could be due to NP or EW penguins
• Theoretical understanding will improve by the time the machine is built
B0bd
ud
d / su
+/K+
B0
b
d d
u
ud / s+/K+ b d
Compare to |Vtd| from Mixing
bd / s b
d / s
Straight forward comparison of |Vtd| &
d
s
B
B
s
d
ts
td
m
m
m
m
V
V
2
2
1.4% 0.5% with 0.5 ab1Ronga, CKM ’03
BaBar, PRL 88, 221803
10% 1-2% “soon”Shoji Hashimoto (SLAC, Oct.)P. Lepage
O(%) @ CDF
xs
xs / x
s
New Physics in the “SM-only” Measurements
• “Clean” measurements may not be absolutely clean
• NP has to look like tree-level charged current interactions– Charged Higgs?
• Such NP will presumably have a different effect on loop diagrams & other measurements.
• D0 mixing may affect BDK. – Current limits on D mixing yield an effect at the few-degree level
(Silva, A.S., PRD61, 112001)
– The effect will decrease as D mixing limits tighten, or will be incorporated into the analysis once D mixing is measured
Conclusions
• Many (albeit related) clean ways to measure – Frequent improvements & new ideas
• From foreseeable mixing, theory & lattice precision, the target for precision should be ~1°– May decrease by the time the machine is built, depending on
developments in theory and experiment
• With 10 ab1 we will– Measure to ~ 2° or less (statistical)
– Resolve essentially all ambiguities
– Understanding systematic errors at this level will be crucial
• This is a rough, cautious estimate. B factory data will provide much better estimates in 2-3 years