Rare top quark decay t --> u_1 \bar{u}_2 u_2 in the standard model

Abstract

The one-loop induced top quark decay $t\to u_1{\bar{u}}_2{u}_2$ ($u_i=u,c$) is calculated in the context of the standard model. The dominant contribution to this top quark decay arises from the Feynman diagrams induced by the off-shell $t{u}_1{g}^{\ast }$ vertex, whereas the box diagrams are negligibly small. In contrast with the on-shell $t{u}_{1}g$ vertex, which only gives rise to a pure dipolar effect, the off-shell $t{u}_1{g}^{\ast }$ coupling also involves a monopolar term, which gives a larger contribution than the dipolar one. It is found that the branching ratio for the three-body decay $t\to u_1{\bar{u}}_2{u}_2$ is about of the same order of magnitude of the two-body decay $t\to u_{1}g$, the latter being slightly larger, which stems from the fact that the three-body decay is dominated by a monopolar term.

Comments: 8 pages, 3 figures, branching ratio is evaluated using the running quark masses at the top quark mass scale, results and conclusion changes slightly, new results agree with those presented in hep-ph/0601151, missing references are added