CP Violation in the Exclusive Decays B -> pi e^+e^- and B -> rho e^+e^-

Abstract

As a sequel to the calculation of the CP-violating asymmetry in the decay rates of b -> d l^+l^- and \bar{b} -> \bar{d} l^+l^-, we address in this paper the asymmetry in exclusive channels \bar{B} -> pi e^+e^- and \bar{B} -> rho e^+e^-, using form factors from two different models. In the invariant mass region 1GeV < \sqrt{s} < M_{J/psi}, the partial width asymmetry in the channel \bar{B} -> pi is -6% (-2%), and that in the channel \bar{B} -> rho, for one choice of form factors, is -5% (-2%), assuming CKM parameters eta = 0.34, rho = 0.3 (-0.3). We also calculate the forward-backward asymmetry A_{FB} of the e^- in the e^+e^- centre-of-mass system, and find average values <A_{FB}>(\bar{B} -> pi) \equiv 0, <A_{FB}>(\bar{B} -> rho)= -17 %, to be compared with the inclusive result <A_{FB}>(b -> d)= -9%. There is a CP-violating difference between A_{FB} and the corresponding asymmetry in the antiparticle channel \bar{A}_{FB}. Formulae are given that are applicable to any FCNC channel \bar{B} -> P_q (V_q) l^+l^-, q=s, d, with m_l \neq 0, including lepton spin effects. An approximate procedure is used to incorporate the rho, omega, and J/psi resonances.