CP Violation Reach at Very High Luminosity B Factories

Abi Soffer

Snowmass 2001

Outline:

• Ambiguities

• B DK

• B D* etc.

• B D*a0 etc. (“designer mesons”)

• Conclusions

Ambiguities

• Measurements of usually involve the decay rateei

cos(

• Compare cos(and cos(

• These are invariant under 3 symmetry operations (lacking a-priori knowledge of phases):

• Sexchange = – Different modes have different , resolving the ambiguity– Otherwise, may be small in B decays (doesn’t resolve, but helps)

• Ssign = – Gives non-SM value of

0 9090180 180

Allowed range

Result

Ssign

Proposed solution:

Proposed solution:

• S = (A.S., PRD 60, 54032)

– Gives non-SM value of

• SSsign can put back in allowed range, reducing resolution

0 9090180 180

Allowed range

Result

S

0 9090180 180

Allowed range

Result

Ssign

S

Effective error

Proposed solution:

No good solution w/o

additional info

Resolving the 8-fold Ambiguity

• A-priori knowledge that and || (sin()~0 not enough)resolves ambiguities

• Measurements that depend on more amplitudes may, in principle, partly resolve ambiguities.– Different modes with different values of – Amplitudes with several strong phases might break Sexchange , sorssign

• Even then, resolution may be impossible in practice, due to limited sensitivity: Ambiguities are always a statistical strain.

• If you also measure small magnitudes in addition to phases, parameters can conspire to give additional accidental ambiguities due to ~multiple solutions

• No case (to my knowledge) in which can be measured independently– Some strong phases may be measured, but not enough to resolve ambiguities

• Note that ambiguities are method-dependent, not machine-dependent

Sensitivity of Measurement in BDK• Interference through CP-eigenstate decays of D0 (M. Gronau, D. Wyler, PLB 265, 172)

Decay rate asymmetry not needed for measuring Interference between amplitudes of very different magnitudes

– Variations: D*0 K+, D0 K*+, D0 K*0 , D0(*) K** (resonance phase enhancement), allowed modes only

Factorization: ~

• The small amplitude can’t be measured directly (D. Atwood, I. Dunietz, A. Soni, PRL 78, 3257)

Decay rate asymmetry needed Similar magnitudes, large D large CP asymmetry, good chance of resolving

SexchangeD CP conserving

D decay phase

Combining the Methods

• Get the benefits of both methods, increase sensitivity (A.S., PRD 60, 54032):

• {, , B, D}

• amBr(B+ K+ (K+, etc.))

– a() theoretical expectation for am

• bmBr(B+ K+ (CP))

– b() theoretical expectation for bm

~

2222

2 )()()()(

m

m

m

m

m

m

m

m

b

bb

a

aa

b

bb

a

aa

Sensitivity Estimates

• 600 fb-1, symmetric B factory– B+ D(*)0 K(*)+, B0 D(*)0 K*0 (1-mode equivalent ~1900 fb-1)

– D0 K, K0, K3, 9 CP eigenstates

• Full CLEO-II MC to estimate backgrounds, effect of SVT & PID on bgd and efficiency put in by hand

• Cuts on E, mES, masses, D0 Dalitz, PID, Vtx

– am (B+ K+ (K+)) has large K+ Kbackground, 80% continuum

– Assume that a likelihood fit doubles S/sqrt(S+B)

• Generate the S+B yields of an average experiment for given values of , B, D, taking

– 0 130 events in am channels

– 700 1000 events in bm channels

• Use minuit to solve for , , B, D

– Full ambiguity – no external input regarding B, D

~

_

~

2 with 600 fb1

• Small D 8-fold ambiguity

• Larger D resolves Sexchange (in principle)

• ~ 90o Ssign & S overlap. NOTE: Sexchange still hurts

• Accidental ambiguity at 1.25 times true value. These are quite common.

~

~5o

2

2 with 600 fb1

• Small D 8-fold ambiguity

• Larger D resolves Sexchange (in principle)

• ~ 90o Ssign & S overlap. NOTE: Sexchange still hurts

• Accidental ambiguity at 1.25 times true value. These are quite common.

~

2 with 600 fb1

• Small D 8-fold ambiguity

• Larger D resolves Sexchange (in principle)

• ~ 90o Ssign & S overlap. NOTE: Sexchange still hurts

• Accidental ambiguity at 1.25 times true value. These are quite common.

~

2 with 600 fb1

• Small D 8-fold ambiguity

• Larger D resolves Sexchange (in principle)

• ~ 90o Ssign & S overlap. NOTE: Sexchange still hurts

• Accidental ambiguity at 1.25 times true value. These are quite common.

~

Quantifying Sensitivity, 600 fb1

• Due to ambiguities, the error is not very meaningful

• Instead, ask what fraction of SM-allowed region of (40o100o) is excluded by this experiment at the 2 > 10 level, given values of , B, D

Fraction of excluded range

180o < B, D < 180o

sin(B) < 0.25

Resolving in Principle & in Practice

• Allowed levels of D0 mixing (xD~0.01) affect from B DK by 5o10o (J.P. Silva, A.S., PRD61, 112001)

• Ssign resolved in principle

• In practice, resolving Ssign requires ~36 ab-1 with xD~0.01

• cos D can be very well measured at -c factory, reducing uncertainty, but not resolving an ambiguity

2 with 6 ab1

• Statistical error in measurement of is 1.5 – 3o

• Even with ambiguities, 2<10 region is very small

• Different DK modes with moderately different B efficiently resolve ambiguities

2=10

2=10

2=10

2=10

sin()

h+

D(*)

Final state

• h+ = + / + / a1+

(R. Aleksan, I. Dunietz, B. Kayser, F. Le Diberder, Nucl. Phys. B361, 141)

• Amplitude ratio r = O(0.01 – 0.04)

• Small asymmetry – increase statistics with partial reconstruction

udscc

B+B

D*+

BABAR 10 fb1

Partial reconstruction

t (ps)

…sin()

Tag B f

B0 D*h+

B0 D*h

B0 D*h+

B0 D*h

Measure t distributions of

Extract sin()

• BABAR Book estimate (partial reconstruction, D* only):

(sin()) ~ 2 (sin())

• Add , a1, add full reconstruction* – this is a reasonable estimate

• ~30 fb1, sin() = 0.59 0.14 0.05

With 600 fb1, expect (sin()) ~ 0.07

• Toy Monte Carlo study: B D(*)+ full reconstruction (C. Voena)

With 600 fb1, expect (sin()) ~ 0.06

* Note: full & partial reconstruction analyses are statistically almost independent

sin() Sensitivity

sin() Sensitivity Enhancement

• In B D(*)+, measure terms1 r2 & r sin

• so sin1/r2

• Angular analysis in B D*+/a1+, rely only on terms

O(1) & O(r) (D. London, N. Sinha, R. Sinha, hep-ph/0005248)

• so tan 1/r

• Large sensitivity enhancement, even with partial amplitude overlap, many fit parameters, etc.– Requires more detailed Monte Carlo study (H. Staengle)

• Same idea can be applied to B D(**)+

– Interference due to overlapping D(**) resonances– Looking into uncertainty in Breit Wigner resonance shapes (Grossman,

Pirjol, A.S.)

sin() from B D(*)a0+

• Mesons with very small decay constants amplitude ratio r = O(1) (M. Diehl, G. Hiller, hep-ph/0105213)

• Estimate Br(B D(*)a0+) ~ (1 – 4) 10–6

– a0+

• Background estimate for mode (Br ~ 40%):– In 20 fb–1, BABAR has ~900 signal events in each of B D(*)+, with

~180 background (didn’t try too hard to reduce the background)• m(a0

+) > m(+) by ~200 MeV

• (a0+) ~ 1/3 – 2/3 of (+),

• Assume harder cuts (down to 700 B D(*)+ events), likelihood analysis

– Assume B D(*)a0+ background can be reduced to 7 events per 20 fb–1,

• In 10 ab–1,

– Some additional sensitivity from hadronic modes

• This mode is interesting, but probably can’t rely on it solely– Use all “designer mesons” states (but need to consider interference)

60

140to

60

35~;

3500

140to

3500

35~

B

S

B

S

Ambiguities in sin( )

• S’exchange = • S’sign = • S =

Conclusions

600 fb1 at an e+e Y(4S) machine is likely to yield• ~ 5 10% from B DK

• sin(2+ ~ 0.05 from B D(*)+/+/a1+ (corresponding to 2+~3o).

NOTE: This is without the proposed sensitivity enhancements

• Machine-independent statements for these values of & 2+– Large :

• Sexchange & S’exchange in principle resolved, but significantly limit sensitivity

• S significantly limits sensitivity

– Small : Better sensitivity since ambiguities are far from true:

• Sexchange allows

• S allows • Ambiguities allow &

– In any case, Ssign allows true, S’sign allows true, limiting sensitivity

– Don’t forget accidental ambiguities– Possible theory advances Unless theory dictates

& can be trusted

…ConclusionsWith 6 ab1 at an e+e Y(4S) machine:

• ~ 1.5 3o from B DK

• 2+ ~ 1o from B D(*)+/+/a1+ (without sensitivity enhancements)

• sin(2+ with “designer modes” still very hard, not needed in light of other good measurements

• Errors small enough to resolve ambiguities very efficiently– Exact situation depends on the actual phase values – no guarantees