1. CP Violation Reach at Very High Luminosity B Factories Abi Soffer Snowmass 2001 Outline: Ambiguities B  DK B  D*     etc. B  D*  a 0   etc. (“designer mesons”) Conclusions

2. Ambiguities Measurements of  usually involve the decay rate  e i         cos(  Compare cos(  and cos(  These are invariant under 3 symmetry operations (lacking a-priori knowledge of phases):

3. S exchange =  –Different modes have different , resolving the ambiguity –Otherwise,  may be small in B decays (doesn’t resolve, but helps) S sign =  –Gives non-SM value of  090  90  180 180  Allowed range Result S sign Proposed solution:

4. S  =  (A.S., PRD 60, 54032) – Gives non-SM value of  S  S sign can put  back in allowed range, reducing resolution  090  90  180 180 Allowed range Result SS 090  90  180 180  Allowed range Result S sign SS Effective error Proposed solution: No good solution w/o additional info

5.   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 S exchange, s  or  s sign  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

6. Sensitivity of  Measurement in B  DK Interference through CP-eigenstate decays of D 0 (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 +, D 0 K* +, D 0 K* 0, D 0(*) 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 S exchange  D  CP conserving D decay phase

7. Combining the Methods Get the benefits of both methods, increase sensitivity (A.S., PRD 60, 54032) :  { , ,  B,  D } a m  Br(B +  K + (K   +, etc.)) –a(  )  theoretical expectation for a m b m  Br(B +  K + (CP)) –b(  )  theoretical expectation for b m ~

8. Sensitivity Estimates 600 fb -1, symmetric B factory –B +  D ( * )0 K ( * )+, B 0  D ( * )0 K* 0 (1-mode equivalent ~1900 fb -1 ) –D 0  K , K  0, 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, m ES, masses, D 0 Dalitz, PID, Vtx –a m  (B +  K + (K   + )) 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 ,  B,  D, taking  –0  130 events in a m channels –700  1000 events in b m channels Use minuit to solve for , ,  B,  D –Full ambiguity – no external input regarding  B,  D ~ _ ~

9.  2 with 600 fb  1 Small  D  8-fold ambiguity Larger  D resolves S exchange (in principle)  ~ 90 o   S sign & S  overlap. NOTE: S exchange still hurts Accidental ambiguity at  1.25 times true value. These are quite common. ~   ~5 o 22

10.  2 with 600 fb  1 Small  D  8-fold ambiguity Larger  D resolves S exchange (in principle)  ~ 90 o   S sign & S  overlap. NOTE: S exchange still hurts Accidental ambiguity at  1.25 times true value. These are quite common. ~

11.  2 with 600 fb  1 Small  D  8-fold ambiguity Larger  D resolves S exchange (in principle)  ~ 90 o   S sign & S  overlap. NOTE: S exchange still hurts Accidental ambiguity at  1.25 times true value. These are quite common. ~

12.  2 with 600 fb  1 Small  D  8-fold ambiguity Larger  D resolves S exchange (in principle)  ~ 90 o   S sign & S  overlap. NOTE: S exchange still hurts Accidental ambiguity at  1.25 times true value. These are quite common. ~

13. Quantifying Sensitivity, 600 fb  1 Due to ambiguities, the error  is not very meaningful Instead, ask what fraction of SM-allowed region of  (40 o  100 o ) is excluded by this experiment at the  2 > 10 level, given values of ,  B,  D Fraction of excluded  range  180 o <  B,  D < 180 o sin(  B ) < 0.25

14. Resolving in Principle & in Practice Allowed levels of D 0 mixing (x D ~0.01) affect  from B  DK by 5 o  10 o (J.P. Silva, A.S., PRD61, 112001) S sign resolved in principle In practice, resolving S sign requires ~36 ab -1 with x D ~0.01 cos  D can be very well measured at  -c factory, reducing uncertainty, but not resolving an ambiguity

15.  2 with 6 ab  1 Statistical error in measurement of  is 1.5 – 3 o Even with ambiguities,  2 <10 region is very small Different DK modes with moderately different  B efficiently resolve ambiguities  2 =10

16. sin(  )  h + D(*)D(*) Final state h + =  + /  + / a 1 + (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 uds cc B+BB+B D* +   B A B A R 10 fb  1 Partial reconstruction

17.  t (ps) …sin(  ) Tag Bf B0B0 D*  h + B0B0 D*  h  B0B0 D*  h + B0B0 D*  h  Measure  t distributions of Extract sin(  )

18. B A B A R Book estimate (partial reconstruction, D*  only):  ( sin(  ) ) ~ 2  ( sin(  ) ) Add , a 1, add full reconstruction* – this is a reasonable estimate ~30 fb  1, sin(  ) = 0.59  0.14  0.05  With 600 fb  1, expect  ( sin(  ) ) ~ 0.07 Toy Monte Carlo study: B  D ( * )   + full reconstruction (C. Voena)  With 600 fb  1, expect  ( sin(  ) ) ~ 0.06 * Note: full & partial reconstruction analyses are statistically almost independent sin(    ) Sensitivity

19. sin(  ) Sensitivity Enhancement In B  D ( * )   +, measure terms 1  r 2 & r sin  so  sin   1/r 2 Angular analysis in B  D*   + /a 1 +, 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.)

20. sin(  ) from B  D ( * )  a 0 + Mesons with very small decay constants  amplitude ratio r = O(1) (M. Diehl, G. Hiller, hep-ph/0105213) Estimate Br(B  D ( * )  a 0 + ) ~ (1 – 4)  10 –6 –a 0 +     Background estimate for   mode (Br ~ 40%) : –In 20 fb –1, B A B A R has ~900 signal events in each of B  D ( * )   +, with ~180 background (didn’t try too hard to reduce the background) m(a 0 + ) > m(  + ) by ~200 MeV  (a 0 + ) ~ 1/3 – 2/3 of  (  + ), Assume harder cuts (down to 700 B  D ( * )   + events), likelihood analysis –Assume B  D ( * )  a 0 + 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)

21. Ambiguities in sin(   ) S’ exchange =     S’ sign =     S  =      

22. Conclusions 600 fb  1 at an e + e  Y(4S) machine is likely to yield   ~ 5  10% from B  DK  sin(2  +  ~ 0.05 from B  D ( * )   + /  + /a 1 + (corresponding to  2  +   ~3 o ). NOTE: This is without the proposed sensitivity enhancements Machine-independent statements for these values of    &  2  +   –Large   : S exchange & S’ exchange in principle resolved, but significantly limit sensitivity S  significantly limits sensitivity –Small   : Better sensitivity since ambiguities are far from  true : S exchange allows  S  allows  Ambiguities allow  &  –In any case, S sign allows  true , S’ sign allows  true , limiting sensitivity –Don’t forget accidental ambiguities –Possible theory advances  Unless theory dictates  & can be trusted

23. …Conclusions With 6 ab  1 at an e + e  Y(4S) machine:   ~ 1.5  3 o from B  DK  2  +  ~ 1 o from B  D ( * )   + /  + /a 1 + (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