Quark mass effects in the soft-collinear effective theory and B̄→Xsγ in the end point region

We consider the effects of a light quark mass in the soft-collinear effective theory (SCET) and we apply them to B̄→Xsγ in the end point 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 B̄→Xsγ. We present strange quark mass corrections to B̄→Xsγ in the end point region as an application. The forward scattering amplitude from the mass corrections is factorized, and it can be expressed as a convolution of the ms2/pX2-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.