Measuring $|V_{ub}|$ with B$\to D_s^{+}{X}_u$ transitions

Abstract

We propose the determination of the CKM matrix element $|V_{ub}|$ by the measurement of the spectrum of $B\to D_s^{+}{X}_u$, dominated by the spectator quark model mechanism $\bar{b}\to D_s^{(\ast )+}\bar{u}$. The interest of considering $B\to D_s^{+}{X}_u$ versus the semileptonic decay is that more than 50 % of the spectrum for $B\to D_s^{+}{X}_u$ occurs above the kinematical limit for $B\to D_s^{+}{X}_c$, while most of the spectrum $B\to l\nu X_u$ occurs below the $B\to l\nu X_c$ one. Furthermore, the measure of the hadronic mass $M_X$ is easier in the presence of an identified $D_s$ than when a $\nu$ has been produced. As a consistency check, we point out that the rate $\bar{b}\to D_s^{(\ast )+}\bar{c}$ (including QCD corrections that we present elsewhere) is consistent with the measured $BR(B\to D_s^{\pm }X)$. Although the hadronic complications may be more severe in the mode that we propose than in the semileptonic inclusive decay, the end of the spectrum in $B\to l\nu X_u$ is not well understood on theoretical grounds. We argue that, in our case, the excited $D_s^{\ast \ast }$, decaying into $DK$, do not contribute and, if there is tagging of the $B$ meson, the other mechanisms to produce a $D_s$ of the right sign are presumably small, of $O(10^{-2})$ relative to the spectator amplitude, or can be controlled by kinematical cuts. In the absence of tagging, other hadronic backgrounds deserve careful study. We present a feasability study with the BaBar detector.

Comments: 22 pages, LaTeX