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Abstract The rare decay B ¯ $$ \overline{B} $$ → X s γ is an important probe of physics beyond the standard model. The largest uncertainty on the total rate and the CP asymmetry arises from resolved photon contributions. These appear first at order 1/m b and are related to operators other than Q 7γ in the effective weak Hamiltonian. One of the three leading contributions, Q 1 q − Q 7 γ $$ {Q}_1^q-{Q}_{7\gamma } $$ , is described by a non-local function whose moments are related to HQET parameters. We use recent progress in our knowledge of these parameters to reevaluate the resolved photon contribution to B ¯ $$ \overline{B} $$ → X s γ total rate and CP asymmetry.

Abstract Effective field theories such as Heavy Quark Effective Theory (HQET) and Non Relativistic Quantum Chromo-(Electro-) dynamics NRQCD (NRQED) are indispensable tools in controlling the effects of the strong interaction. The increasing experimental precision requires the knowledge of higher dimensional operators. We present a general method that allows for an easy construction of HQET or NRQCD (NRQED) operators that contain two heavy quark or non-relativistic fields and any number of covariant derivatives. As an application of our method, we list these terms in the 1/M 4 NRQCD Lagrangian, where M is the mass of of the spin-half field.