Lepton Polarization in the Decays $B\to X_s{\mu }^{+}{\mu }^{-}$ and $B\to X_s{\tau }^{+}{\tau }^{-}$

Abstract

The effective Hamiltonian for the decay $b\to s{l}^{+}{l}^{-}$ predicts a characteristic polarization for the final state lepton, which can serve as an important test of the underlying theory. The lepton polarization has, in addition to a longitudinal component $P_L$, two orthogonal components $P_T$ and $P_N$, lying in and perpendicular to the decay plane which are proportional to $m_l/m_b$, and therefore significant for the ${\tau }^{+}{\tau }^{-}$ channel. The normal polarization component $P_N$ is a $T$-odd effect connected with the nonhermiticity of the effective Hamiltonian, arising mainly from $c\bar{c}$ intermediate states. We calculate all three polarization components for the decay $B\to X_s{\tau }^{+}{\tau }^{-}$ as a function of the lepton pair mass, and find average values $<P_L>$ = -0.37, $<P_T>$ = -0.63, $<P_N>$ = 0.03. By comparison, the ${\mu }^{-}$ polarization is $<P_L>$ = -0.77, $<P_T>=<P_N>\approx 0$.

Comments: 17 pages, LaTeX, 5 eps figures, uses epsf.sty and cite.sty