Charmless Semileptonic Baryonic $B_{u,d,s}$ Decays

Abstract

We study $\bar B_q\to {{\rm\bf B}\bar{\rm\bf B}}' l \bar\nu$ and $\bar B_q\to {{\rm\bf B}\bar{\rm\bf B}}' \nu \bar\nu$ decays with all low lying octet and decuplet baryons using a topological amplitude approach. In tree induced $\bar B_q\to {{\rm\bf B}\bar{\rm\bf B}}' l \bar\nu$ decay modes, we need 2 tree and 1 annihilation amplitudes in octet-anti-octet decay modes, 1 tree amplitude in octet-anti-decuplet decay modes, 1 tree amplitude in decuplet-anti-octet decay modes and 1 tree and 1 annihilation amplitudes in decuplet-anti-decuplet decay modes. In loop induced $\bar B_q\to {{\rm\bf B}\bar{\rm\bf B}}' \nu \bar\nu$ decay modes, similar numbers of penguin-box and penguin-box-annihilation amplitudes are needed. Relations on these semileptonic baryonic $B_q$ decay amplitudes are found. Furthermore, the ratios of loop topological amplitudes and tree topological amplitudes are fixed by known CKM factors and loop functions. The observed $B^-\to p\bar p \mu^-\bar\nu$ differential rate exhibits threshold enhancement, which is expected to hold in all other semileptonic baryonic modes. The threshold enhancement squeezes the phase space and leads to very large SU(3) breaking effects in the decay rates. They are estimated using the measured $B^-\to p\bar p \mu^-\bar\nu$ differential rate and model calculations. Modes with relatively unsuppressed rates and good detectability are identified. These modes can be searched experimentally in near future and the rate estimations can be improved when more modes are discovered. Ratios of rates of some loop induced $\bar B_q\to {{\rm\bf B}\bar{\rm\bf B}}' \nu \bar\nu$ decays and tree induced $\bar B_q\to {{\rm\bf B}\bar{\rm\bf B}}' l \bar\nu$ decays are predicted and can be checked experimentally. They can be tests of the SM. Some implications on $\bar B_{q}\to {{\rm\bf B}\bar{\rm\bf B}}' l^+ l^-$ decays are also given.