In this paper, we present the exact calculations for the vertex ^-sγb and ^sZb in the unitary gauge. We find that （a） the divergent- and μ-dependent terms are left in the effective vertex function Г^γμ（p, k） ...In this paper, we present the exact calculations for the vertex ^-sγb and ^sZb in the unitary gauge. We find that （a） the divergent- and μ-dependent terms are left in the effective vertex function Г^γμ（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 ^sγb and ^sZb are taken into account simultaneously, and therefore the finite and gauge-independent function Zo（xt） = Co（xt） ＋ Do（xt）/4, which governs the semi-leptonic decay b → sl^- l^＋, is derived in the unitary gauge.展开更多
基金The project supported by National Natural Science Foundation of China under Grant No. 10575052 and the Specialized Research Fund for the Doctoral Program of Higher Education （SRFDP） under Grant No. 20050319008
文摘In this paper, we present the exact calculations for the vertex ^-sγb and ^sZb in the unitary gauge. We find that （a） the divergent- and μ-dependent terms are left in the effective vertex function Г^γμ（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 ^sγb and ^sZb are taken into account simultaneously, and therefore the finite and gauge-independent function Zo（xt） = Co（xt） ＋ Do（xt）/4, which governs the semi-leptonic decay b → sl^- l^＋, is derived in the unitary gauge.
