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

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.Comment: 29 pages, uses epsfig.sty, 12 postscript figures include

RI'/SMOM scheme amplitudes for quark currents at two loops

We determine the two loop corrections to the Green's function of a quark current inserted in a quark 2-point function at the symmetric subtraction point. The amplitudes for the scalar, vector and tensor currents are presented in both the MSbar and RI'/SMOM renormalization schemes. The RI'/SMOM scheme two loop renormalization for the scalar and tensor cases agree with previous work. The vector current renormalization requires special treatment as it must be consistent with the Slavnov-Taylor identity which we demonstrate. We also discuss the possibility of an alternative definition of the RI'/SMOM scheme in the case of the tensor current.Comment: 36 latex pages, 1 figure, 21 tables, anc directory contains txt file with data in table

Euclidean Configuration Space Renormalization, Residues and Dilation Anomaly1

Configuration (x-)space renormalization of euclidean Feynman amplitudes in a massless quantum field theory is reduced to the study of local extensions of associate homogeneous distributions. Primitively divergent graphs are renormalized, in particular, by subtracting the residue of an analytically regularized expression. Examples are given of computing residues that involve zeta values. The renormalized Green functions are again associate homogeneous distributions of the same degree that transform under indecomposable representations of the dilation group

Calculations of the modal photon densities and gain in a K/Cl resonantly photopumped X-ray laser

UD integrals published by N. Usyukina and A. Davydychev in 1992-1993 are integrals corresponding to ladder-type Feynman diagrams. The results are UD functions $\Phi^{(L)},$ where $L$ is the number of loops. They play an important role in N=4 supersymmetic Yang-Mills theory. The integrals were defined and calculated in the momentum space. In this paper the position space representation of UD functions is investigated. We show that Fourier transforms of UD functions are UD functions of space-time intervals but this correspondence is indirect. For example, the Fourier transform of the second UD integral is the second UD integral

Analytic integration of real-virtual counterterms in NNLO jet cross sections II

We present analytic expressions of all integrals required to complete the explicit evaluation of the real-virtual integrated counterterms needed to define a recently proposed subtraction scheme for jet cross sections at next-to-next-to-leading order in QCD. We use the Mellin-Barnes representation of these integrals in $4-2\epsilon$ dimensions to obtain the coefficients of their Laurent expansions around $\epsilon=0$. These coefficients are given by linear combinations of multidimensional Mellin-Barnes integrals. We compute the coefficients of such expansions in $\epsilon$ both numerically and analytically by complex integration over the Mellin-Barnes contours.Comment: 27 pages, 6 figure