A study of semi-inclusive charmless $B\to \ddot{I}€X$ decays

Abstract

We study semi-inclusive charmless decays $B\to \ddot{I}€X$ in detail, such as ${\bar{B}}^0\to \ddot{I}{€}^{\pm (0)}X$, $B^0\to \ddot{I}{€}^{\pm (0)}X$, $B^{\pm }\to \ddot{I}{€}^{\pm (0)}X$, where $X$ does not contain a charm (anti)quark. We find that the process ${\bar{B}}^0\to \ddot{I}{€}^{-}X$ ($B^0\to \ddot{I}{€}^{+}X$) can be particularly useful for determination of the CKM matrix element $|V_{ub}|$. We calculate and present the branching ratio (BR) of ${\bar{B}}^0\to \ddot{I}{€}^{-}X$ as a function of $|V_{ub}|$, with an estimate of possible uncertainties. It is expected that the BR is an order of $10^{-4}$. Our estimation indicates that one can phenomenologically determine $|V_{ub}|$ with reasonable accuracy by measuring the BR of ${\bar{B}}^0\to \ddot{I}{€}^{-}X$ ($B^0\to \ddot{I}{€}^{+}X$).

18 pages, 7 figures; Revtex; version accepted for publication in Eur. Phys. J. C