Exact Calculations Of Vertex (?)γb And (?)Zb In The Unitary Gauge

The inclusive rare radiative decays of b quark, b→sV (with V =γ, Z) followed by the decays V→qq|-, l⁺l^-, are induced by the flavor changing neutral current (FCNC) and play an important role in testing the standard model (SM) and searching for the signal or evidence of the new physics beyond the SM.Because of its great importance, these rare decays have been studied extensively during the past three decades. An exact calculation of the d|-sg vertex was made in the unitary gauge by Chia et al., where the Ward-Takahashi identity was used to renormalize the vertex. For the quark-photon vertex d|-sγin the unitary gauge, it was also firstly calculated by Chia et al., but the results given there were not correct.In our paper, we present the exact calculations for the vertex s|-γb and s|-Zb in the unitary gauge. We found that (a) the divergent- andμ-dependent terms are left in the effective vertex functionΓ_μ^γ(p, k) for b→sγtransition even after we sum up the contributions from four related Feynman diagrams; (b) for an on-shell photon, such terms do not contribute et al; (c) for off-shell photon, these terms will be canceled when the contributions from both vertex s|-γb and s|-Zb are taken into account simultaneously, and therefore the finite and gauge independent function Z₀(x_t) = C₀(x_t) + D₀(x_t)/4:, which governs the semi-leptonic decay b→sl^-l⁺, is derived in the unitary gauge.This paper is organized as follows. In Chapter II, the standard model is reviewed and Feynman rules for our calculations are presented. In Chapter III, IV and V, we give our calculations in detail. In the last chapter, a short summary of this paper is given.