Moments of the photon spectrum in the inclusive $B\to X_s\gamma$ decay

Abstract

The moments of the photon spectrum in the inclusive $B\to X_s\,\gamma$ decay can be calculated to order $\alpha_s$ accuracy at present, without knowing the $\alpha_s$ corrections to the effective Hamiltonian. We discuss the standard model predictions, and how the moments of the photon spectrum are related to certain matrix elements of the heavy quark effective theory. The sensitivity of these moments to new physics is small, and they provide a model-independent determination of the $b$ quark pole mass (at order $\alpha_s$), or equivalently, the matrix elements $\bar\Lambda$ and $\lambda_1$ of the effective theory.