Virtual $O(\a_s)$ corrections to the inclusive decay $b\to s\gamma$

Abstract

We present in detail the calculation of the $O(\a_s)$ virtual corrections to the matrix element for $b \to s \g$. Besides the one-loop virtual corrections of the electromagnetic and color dipole operators $O_7$ and $O_8$, we include the important two-loop contribution of the four-Fermi operator $O_2$. By applying the Mellin-Barnes representation to certain internal propagators, the result of the two-loop diagrams is obtained analytically as an expansion in $m_c/m_b$. These results are then combined with existing $O(\a_s)$ Bremsstrahlung corrections in order to obtain the inclusive rate for $B \to X_s \g$. The new contributions drastically reduce the large renormalization scale dependence of the leading logarithmic result. Thus a very precise Standard Model prediction for this inclusive process will become possible once also the corrections to the Wilson coefficients are available.

29 pages, uses epsfig.sty, 12 postscript figures included

References in corpus (1)

• Bremsstrahlung corrections to the decay $b\to s\gamma$

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