Charmless decays of bottom mesons and a fourth generation

Abstract

B decays to charmless inclusive final states are discussed. The generic process is the loop-induced b→${\mathrm{sg}}^{\mathrm{*}}$, $g^{\mathrm{*}}$ being an on-shell or off-shell gluon. We include the cases when the gluon momentum is lightlike, timelike, and spacelike. The timelike case includes $g^{\mathrm{*}}$→qq¯ and gg splitup. Our findings are as follows: (1) B(b→${\mathrm{sg}}^{\mathrm{*}}$)≃1% for three generations; (2) an experimental observation of charmless branching ratio ≥5% would (conservatively) imply the possibility of a fourth generation; and (3) charmless branching ratio >20% would be difficult to accomodate in the standard model even with four families.