Effective theory description of weak annihilation effects in B X u l n

1. J.J. Sanz-Cillero IPN-Orsay Effective theory description of weak annihilation effects in BXu l n BEACH 06 Lancaster, July 2nd-8th 2006 ( In collaboration with G. Paz; PRELIMINAR) Special thanks to M. Neubert Dominant decay • Operator Product Expansion: W l • B2u=B1u=1, B2d,s=B1d,s=0, in the factorization limit • Expected 10% deviations • Dependence on light quark in Bq n Bq N3LO in 1/mb Xu Weak Annihilation (WA) WA amplitude • Low EH effect [Bigi & Uraltse’94] • N3LO in 1/mb : O(1/mb3) suppression • NLO in 1/NC • Related to production of chiral singlets • Difference between B+ - B0 rates W l • Constant N3LO Weak-Annihilation effect: n Bu+ Xu [ Voloshin’01 ] I=Y=0 (chiral singlet) HMcPT in BP l n Chiral limit + Large NC limit mP=0 Isolation of WA effects + Removal of BXC l n background: Hadronic energy cut-off EXu<Lcut<MD • Large NC + HM •  Amplitudes given by the tree-level exchange of the B* 1 1 1/2 + 1/6 + 1/3 1 h0 h8 p+ K+ p0 • CORRECTIONS: • Couplings • Masses “Mild” corrections, under control Bd0 Bs0 Bu+ mp2 = B0 (mu+md) mh02 Quark masses 1/NCcontributions to the h0 mass Kinematical enhancement (mP/Lcut)2 1 (chiral limit) COMBINATION OF EXPANSIONS with • 1/NC large NC • (mP/Lc)2 cPT expansion in mu,d,s • QCD/MB 1/mb expansion • cut/MB 1/mb expansion + cut-off • (mP/Lcut)2 cut-off (kinematical) • Dominance of one particle production: • BP l n (P=p,K,h8,h0) • (dominant up to EXu ~ 1 GeV) • BV l n (V=r,K*,w,f) • (relevant beyond EXu ~ 1 GeV) • Suppression of two-particle production: • Bppln suppressed with respect to Bp l n with …and also available the leptonic energy spectrum with the cut EXu<Lcut Under control In addition, it is noticed the importance of … SU(3)-breaking effects at NC∞ WA effects at mq0 • Difference between Bd0-Bs0: • Difference between B0-B+ (WA) • 1/MB3 suppression (fB2~ 1/MB) • (mK2–mp2) suppression • 1/MB3 suppression (fB2~ 1/MB) • 1/NC suppression EH=1.25 GeV EH=1.25 GeV for EH<1.25 GeV PRELIMINAR PRELIMINAR • The analysis in terms of the leptonic energy spectrumis also available Conclusions • OUT-LOOK: • Contribution from B->V l nu (accuracy) • Study of double-pole expressions (removal of the residual log(e) dependence) • Importance in D decays • EFT explanation of WA effects from OPE • Revisited estimate of WA • Importance of SU(3) breaking effects (similar to WA) • Need of higher precision on fB and g