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CP Violation Reach at Very High Luminosity B Factories

CP Violation Reach at Very High Luminosity B Factories. Abi Soffer Snowmass 2001. Outline: Ambiguities B  DK B  D* - p + , etc. B  D* - a 0 + , etc. (“designer mesons”) Conclusions. Ambiguities. Measurements of g usually involve the decay rate

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CP Violation Reach at Very High Luminosity B Factories

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  1. CP Violation Reach at Very High Luminosity B Factories Abi Soffer Snowmass 2001 • Outline: • Ambiguities • B  DK • B  D*-p+, etc. • B  D*-a0+, etc. (“designer mesons”) • Conclusions

  2. Ambiguities • Measurements of g usually involve the decay rate • G = |A + Bei(dg)|2 = A2 + B2 + 2AB cos(d  g) • Compare cos(d+g) and cos(d-g) • These are invariant under 3 symmetry operations (lacking a-priori knowledge of phases):

  3. Ssign -180 -90 0 90 180 Result Allowed range g • Sexchange = d  g • Different modes have different d, resolving the ambiguity • Otherwise,d may be small in B decays (doesn’t resolve, but helps) • Ssign = d  -d, g  -g • Gives non-SM value of g Proposed solution: Proposed solution:

  4. Sp Result g Allowed range 180 Sp -180 -180 -90 -90 0 0 90 90 Effective error Ssign Result Allowed range 180 g • Sp = d  d - p, g  g + p (A.S., PRD 60, 54032) • Gives non-SM value of g • Sp Ssign can put g back in allowed range, reducing resolution Proposed solution: No good solution w/o additional info

  5. Resolving the 8-fold Ambiguity gd-g-dg+pd+p-(g+p)-(d+p) • A-priori knowledge that d~0and |d| << p (sin(d)~0 not enough)resolves ambiguities • Measurements that depend on more amplitudes may,in principle, partly resolve ambiguities. • Different modes with different values of d. • Amplitudes with several strong phases might break Sexchange, sp orssign. • 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 d 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

  6. Sensitivity of g Measurement in BDK ~ Factorization: e ~ 0.09 • The small amplitude can’t be measured directly (D. Atwood, I. Dunietz, A. Soni, PRL 78, 3257) • Decay rate asymmetry needed • Similar magnitudes, large dD large CP asymmetry, good chance of resolving Sexchange dD= CP conserving D decay phase • Interference through CP-eigenstate decays of D0(M. Gronau, D. Wyler, PLB 265, 172) • Decay rate asymmetry not needed for measuring g • Interference between amplitudes of very different magnitudes • Variations: D*0 K+, D0 K*+, D0 K*0 , D0(*) K** (resonance phase enhancement), allowed modes only

  7. Combining the Methods • Get the benefits of both methods, increase sensitivity (A.S., PRD 60, 54032): • x = {e, g, dB, dD} • am = Br(B+ K+ (K-p+, etc.)) • a(x ) = theoretical expectation for am • bm = Br(B+ K+ (CP)) • b(x ) = theoretical expectation for bm ~

  8. Sensitivity Estimates • 600 fb-1, symmetric B factory • B+  D(*)0 K(*)+, B0  D(*)0 K*0 (1-mode equivalent ~1900 fb-1) • D0  Kp, Kpp0, K3p, 9 CP eigenstates • Full CLEO-II MC to estimate backgrounds, effect of SVT & PID on bgd and efficiency put in by hand • Cuts on DE, mES, masses, D0 Dalitz, PID, Vtx • am= (B+ K+ (K-p+)) has large K+ K-background, 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 g, dB, dD, taking e = 0.09 • 0 -130 events in amchannels • 700 -1000 events in bmchannels • Use minuit to solve fore, g, dB, dD • Full ambiguity – no external input regarding dB, dD _ ~ ~

  9. c2 with 600 fb-1 sg~5o • Small dD 8-fold ambiguity • Larger dD resolves Sexchange(in principle) • g ~ 90oSsign & Spoverlap. NOTE: Sexchangestill hurts • Accidental ambiguity at e = 1.25 times true value. These are quite common. c2 ~

  10. ... c2 with 600 fb-1 • Small dD 8-fold ambiguity • Larger dD resolves Sexchange(in principle) • g ~ 90oSsign & Spoverlap. NOTE: Sexchangestill hurts • Accidental ambiguity at e = 1.25 times true value. These are quite common. ~

  11. ... c2 with 600 fb-1 • Small dD 8-fold ambiguity • Larger dD resolves Sexchange(in principle) • g ~ 90oSsign & Spoverlap. NOTE: Sexchangestill hurts • Accidental ambiguity at e = 1.25 times true value. These are quite common. ~

  12. ... c2 with 600 fb-1 • Small dD 8-fold ambiguity • Larger dD resolves Sexchange(in principle) • g ~ 90oSsign & Spoverlap. NOTE: Sexchangestill hurts • Accidental ambiguity at e = 1.25 times true value. These are quite common. ~

  13. Quantifying Sensitivity, 600 fb-1 -180o < dB, dD <180o • Due to ambiguities, the error s(g) is not very meaningful • Instead, ask what fraction of SM-allowed region of g (40o-100o) is excluded by this experiment at the c2 > 10 level, given values of g, dB, dD sin(dB) < 0.25 Fraction of excluded g range

  14. Resolving in Principle & in Practice • Allowed levels of D0 mixing (xD~0.01) affect g from B ->DK by 5o-10o(J.P. Silva, A.S., PRD61, 112001) • Ssignresolved in principle • In practice, resolving Ssign requires ~36 ab-1 with xD~0.01 • cosdD can be very well measured at t-c factory, reducing uncertainty, but not resolving an ambiguity

  15. c2 with 6 ab-1 c2=10 c2=10 c2=10 c2=10 • Statistical error in measurement of g is 1.5 – 3o • Even with ambiguities, c2<10 region is very small • Different DK modes with moderately different dB efficiently resolve ambiguities

  16. B+B- D*+p- cc uds h+ BABAR 10 fb-1 D(*)- Partial reconstruction Final state sin(2b + g) • h+ = p+ /r+ /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

  17. …sin(2b + g) Measure Dt distributions of Dt (ps) Extract sin(2b + g d)

  18. sin(2b + g d) Sensitivity • BABAR Book estimate (partial reconstruction, D*p only): • s(sin(2b + g)) ~ 2 s(sin(2b)) • Add r, a1, add full reconstruction* – this is a reasonable estimate • ~30 fb-1, sin(2b) = 0.59 0.14 0.05 •  With 600 fb-1, expect s(sin(2b + g)) ~ 0.07 • Toy Monte Carlo study: B  D(*)- p+ full reconstruction (C. Voena) •  With 600 fb-1, expect s(sin(2b + g)) ~ 0.06 • * Note: full & partial reconstruction analyses are statistically almost independent

  19. sin(2b + g) Sensitivity Enhancement • In B  D(*)- p+, measure terms • 1  r2 & r sin(2b+g) • so ssin(2b+g)  1/r2 • Angular analysis in B  D*- r+/a1+, rely only on terms • O(1) & O(r) (D. London, N. Sinha, R. Sinha, hep-ph/0005248) • sostan (2b+g)  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(**)- p+ • Interference due to overlapping D(**)- resonances • Looking into uncertainty in Breit Wigner resonance shapes (Grossman, Pirjol, A.S.)

  20. sin(2b + g) 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+  hp+ • Background estimate for h  gg mode (Br ~ 40%): • In 20 fb–1, BABAR has ~900 signal events in each of B D(*)- r+, with ~180 background (didn’t try too hard to reduce the background) • m(a0+) > m(r+) by ~200 MeV • G(a0+) ~ 1/3 – 2/3 of G(r+), • Assume harder cuts (down to 700 B D(*)- r+ 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 h modes • This mode is interesting, but probably can’t rely on it solely • Use all “designer mesons” states (but need to consider interference)

  21. Ambiguities in sin(d f) • S’exchange = f d - p/2d f + p/2 • S’sign = f -f - pd - d • Sp = f f +pd d + p fd+p/2-f -p/2 -d f+pd+3p/2p-fp/2 -d

  22. Conclusions 600 fb-1 at an e+e- Y(4S) machine is likely to yield • sg ~ 5o- 10o from B  DK • ssin(2b+g) ~ 0.05 from B  D(*)- p+/r+/a1+(corresponding to s2b+g ~5o).NOTE: This is without the proposed sensitivity enhancements • Machine-independent statements for these values of sg& s2b+g: • Large dB: • Sexchange & S’exchange in principle resolved, but significantly limit sensitivity • Spsignificantly limits sensitivity • Small dB: Better sensitivity since ambiguities are far from gtrue: • Sexchangeallows g = 0 • Spallows g = p* • Ambiguities allow 2b+g = p/2* & 2b+g  p  (2b+g) • In any case, Ssign allows g = -gtrue*, S’sign allows 2b+g = - (2b+g)true*, limiting sensitivity • Don’t forget accidental ambiguities • Possible theory advances *Unless theory dictates d  p & can be trusted

  23. …Conclusions With 6 ab-1 at an e+e- Y(4S) machine: • sg ~ 1.5 - 3o from B  DK • s2b+g ~ 1.5o from B  D(*)- p+/r+/a1+ (w/out sensitivity enhancements) • sin(2b+g) 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

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