QCD Corrections to b→sγγb\to s\gamma\gamma and Exclusive Bs→γγB_s\to \gamma\gamma Decay

The short distance QCD corrections to $b\to s\gamma \gamma$ are calculated in the leading logarithmic approximation. The equivalence of operator basis reduction for S-matrix elements by using the equations of motion or by proving a low energy theorem is discussed. We apply the above results to the exclusive $B_s\to \gamma\gamma$ decay. The branching ratio of this decay is found to be $5\times 10^{-7}$ in the Standard Model. We also found that QCD corrections modify considerably the ratio between CP-even and CP-odd two-photon amplitudes.Comment: revtex, 15 pages, 2 figures; revised version with corrections from electroweak penguin discussed, the conclusion remains unchange

Electron-hole symmetry and solutions of Richardson pairing model

Richardson approach provides an exact solution of the pairing Hamiltonian. This Hamiltonian is characterized by the electron-hole pairing symmetry, which is however hidden in Richardson equations. By analyzing this symmetry and using an additional conjecture, fulfilled in solvable limits, we suggest a simple expression of the ground state energy for an equally-spaced energy-level model, which is applicable along the whole crossover from the superconducting state to the pairing fluctuation regime. Solving Richardson equations numerically, we demonstrate a good accuracy of our expression.Comment: 9 pages, 1 figure; accepted for publication in Eur. Phys. J.