Abi Soffer

Colorado State University

Super B Workshop, UH, Jan 19, 2004

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

D Dalitz Plot, D00

CLEO, hep-ex/0305048 9 fb1

m2(0) GeV2 m2(0) GeV2

rD = 0.65 ± 0.05D = 4º ± 5º

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

Sensitivity with CPES Only

CP-even

BelleCP-odd

ambiguity

M. Rama

• BR already measured:

BaBar

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(*) Analyses (full reconstruction)Belle, hep-ex/0308048, 140 fb

BaBar, hep-ex/0309017, 82 fb

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

Backup slides

Fraction of allowed range of excluded by this exp.

0 0.5 1

A.S., PRD 60, 054032

Belle Dalitz fit

Sensitivity with CPES + K*K

CP modes

K*+K

Combined

True

True

0.5 ab