Quark mass effects in the soft-collinear effective theory and B -> X_s + photon in the endpoint region

Abstract

We consider the effects of a light quark mass in the soft-collinear effective theory (SCET) and we apply them to B -> X_s gamma in the endpoint region. We find that the reparameterization invariance can be extended by including the collinear quark mass in the SCET Lagrangian. This symmetry constrains the theory with the quark mass terms, and we present explicit results at one loop. It also relates the Wilson coefficients of some mass operators to those of the leading operators, which are useful in organizing the subleading effects due to the quark mass in B -> X_s gamma. We present strange quark mass corrections to B -> X_s gamma in the endpoint region as an application. The forward scattering amplitude from the mass corrections is factorized, and it can be expressed as a convolution of the m_s^2/p_X^2-suppressed jet function and the leading-order shape function of the B meson. This contribution should be added to the existing subleading contributions from the B meson shape functions to obtain complete subleading corrections.