Transverse tau polarization in inclusive $\bar{B}\to \tau \bar{\nu }X$ decays

Abstract

We calculate, in the framework of multi Higgs doublet models, the $CP$ violating transverse tau polarization, $P_{\perp }$, in inclusive semileptonic $B$ meson decays. We find that $P_{\perp }$ diverges at $\mathcal{O}(1/m_b^2)$ of the heavy quark expansion. We discuss the physical reasons for this divergence and show how to regularize it. We find large $1/m_b^2$ corrections that can suppress the $CP$ asymmetry by as much as 30\%. The maximal allowed asymmetry is $a_{CP}\sim 0.34$. We discuss how the allowed range is expected to change in the future.

Comments: 12 pages RevTeX + 1 figure included, WIS-94/39/Sep-PH, CALT-68-1952. (No changes at all; postscript figure submitted separately as requested.)