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\ensuremath{\rightarrow}${\mathrm{sg}}^{\mathrm{*}}$, ${g}^{\mathrm{*}}$ 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 ${g}^{\mathrm{*}}$\ensuremath{\rightarrow}qq\ifmmode\bar\else\textasciimacron\fi{} and gg splitup. Our findings are as follows: (1) B(b\ensuremath{\rightarrow}${\mathrm{sg}}^{\mathrm{*}}$)\ensuremath{\simeq}1% for three generations; (2) an experimental observation of charmless branching ratio \ensuremath{\ge}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.