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CP Violation Reach at Very High Luminosity B Factories

This paper discusses ambiguities in measuring CP violation parameters in B meson decays at high luminosity B factories, proposing solutions and methods to improve sensitivity. It explores the impact of different decay modes and strong phases on resolving ambiguities, emphasizing the statistical challenges and limitations faced in practical measurements.

gretchen-griffin
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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 ~ 5 - 10% from B  DK • ssin(2b+g) ~ 0.05 from B  D(*)- p+/r+/a1+(corresponding to s2b+g < ~3o).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 ~ 1o from B  D(*)- p+/r+/a1+ (without 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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