Exact Calculations of Vertex s-bar γb and s-bar Zb in the Unitary Gauge

In this paper, we present the exact calculations for the vertex s-bar γb and s-bar Zb in the unitary gauge. We find that (a) the divergent- and μ-dependent terms are left in the effective vertex function Γγμ(p,k) for b→sγ transition 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-bar γb and s-bar Zb are taken into account simultaneously, and therefore the finite and gauge-independent function Z0(xt) = C0(xt)+D0(xt)/4, which governs the semi-leptonic decay b→sl-l+, is derived in the unitary gauge.