Study of rare top quark decays into a jet plus a charged pseudo-scalar meson

The semi-inclusive decay processes of a top quark into a charged pseudo-scalar meson and a jet are studied within the framework of QCD factorization. The leading power of the decay matrix elements can be factorized into heavy-to-light quark transition current and a hadron matrix element up to next-to-leading order QCD corrections. We calculate one-loop virtual corrections together with real gluon emission corrections at the {\alpha}s order. The numerical results of the branching ratios are presented for the sum of two-body and three-body decays. We also study the energy cut-off dependence of the gluon jet. These processes are hopeful to be detected in the near future experiments, which can serve as probes for new physics.