Branching-ratio and CP violation in semi-inclusive flavor-changing top decays

Abstract

Semi-inclusive top decays, t \to q_i \v, are examined in the framework of the standard model, with $q_i=u\mathrm{or}c$, \v : vector meson formed by $q_j{\text{qb}}_j$ ($q_j=d,s,b$). By using a simple model of hadronization, that is $0\text{l}|{\text{qb}}_j{\gamma }^{\mu }{q}_j\mathring{|}\check{=}\text{mv}\text{fv}{\text{evj}}^{\mu }$, the total branching ratio is expected to be $\text{br}(\text{tivj})<(\text{l}|{\text{vij}}^{\ast }\text{vtj}\mathring{|}/\text{l}|\text{vtb}\mathring{|}{)}^2\times O({10}^{-3})$ depends on the size of the coupling constant $\text{fv}$. On the other hand, the CP asymmetry should be induced only by the long-distance effects of intermediate state $q_k{\text{qb}}_k$ ($q_k=d,s,b$) that subsequent scatters into the vector meson. The analytical results including the continuum contributions are given with keeping all masses. However, it yields the CP asymmetry to be small, i.e. $\text{acp}(\text{tivj})<\text{im}[({\text{vij}}^{\ast }\text{vtj}{)}^{\ast }({\text{vik}}^{\ast }\text{vtk})]/\text{l}|{\text{vij}}^{\ast }\text{vtj}{\mathring{|}}^2\times O({10}^{-2})$ for an identified $q_k{\text{qb}}_k$ intermediate state, and suppressed more again by a factor of $\sim ({m_b}^2-{m_s}^2)/{\text{mv}}^2$ for summing up all of them. Particularly, $\text{acp}(t\to u{\rm Y})\simeq \pm 1$, induced by the intermediate state $d\bar{d}$ or $s\bar{s}$.

Comments: 6 pages, LaTeX, no figure, revised version for publication