Exact calculations of vertex $\bar{s}γb$ and $\bar{s} Z b$ in the unitary gauge

Details Exact calculations of vertex $\bar{s}γb$ and $\bar{s} Z b$ in the unitary gauge Exact calculations of vertex $\bar{s}γb$ and $\bar{s} Z b$ in the unitary gauge

2006-12-25

arxiv.org/abs/hep-ph/0612326v1

Commun.Theor.Phys.48:502-508,2007

Physics

High Energy Physics

High Energy Physics - Phenomenology

13 pages, 2 figures, Revtex

Scientific paper

10.1088/0253-6102/48/3/024

In this paper, we present the exact calculations for the vertex $\bar{s}\gamma b$ and $\bar{s} Z b$ in the unitary gauge. We found that (a) the divergent- and $\mu$-dependent terms are left in the effective vertex function $\Gamma^\gamma_\mu(p,k)$ for $b \to s \gamma$ 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 $\bar{s}\gamma b$ and $\bar{s} Z b$ are taken into account simultaneously, and therefore the finite and gauge independent function $Z_0(x_t)=C_0(x_t)+ D_0(x_t)/4$, which governs the semi-leptonic decay $b \to s l^- l^+$, is derived in the unitary gauge.

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