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

Abstract

The moments of the photon spectrum in the inclusive $B\to X_s\,γ$ decay can be calculated to order $α_s$ accuracy at present, without knowing the $α_s$ 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 $α_s$), or equivalently, the matrix elements $\barΛ$ and $λ_1$ of the effective theory.