On the vanishing of evanescent operators

Subleading-power corrections to the radiative leptonic B → γℓν decay in QCD

“…We further turn to determine the IR subtraction term Z (1) Ei (i = 1, 2) originated from the renormalization mixing of the evanescenet operators O E, µ into the physical SCET operators O 1, µ and O 2, µ . As discussed in [21][22][23], the renormalization constants Z (1) Ei (i = 1, 2) will be determined by implementing the prescription that the IR finite matrix element of the evanescent operator O E, µ vanishes, when applying dimensional regularization only to the UV divergences and regularizing the IR singularities with any other scheme different from the dimensions of spacetime. In accordance with (3.30) this amounts to…”

Heavy pair production currents with general quantum numbers in dimensionally regularized nonrelativistic QCD

“…(31,32,33) where the proper contraction of spinor indices is in analogy to Eqs. (30,34). Note that the correlator of two spin triplet currents with the same J but different L vanishes, as the spinorbit potential commutes with the squared angular momentum operator L 2 .…”

“…Thus to achieve that spin-dependent potentials do not contribute for physical predictions involving spin singlet currents, in general additional finite renormalizations are required in analogy to Ref. [34], unless a scheme for potentials or currents is chosen such that they vanish automatically. However, even if such a scheme is adopted, matrix elements, matching conditions and anomalous dimensions can depend on the spin-dependent potentials at nontrivial subleading order 4 .…”

“…In Ref. [34] it was shown that a renormalization scheme can be adopted such that a mixing of evanescent operators into physical ones does not arise. Moreover it is also known [35,36] that modifications of the evanescent operator basis (e.g.…”

“…For explicit computations a specific choice of basis has to be made, which is associated to a specific choice of a renormalization scheme. A very similar problem has been treated systematically already some time ago in the framework of relativistic QCD and the effective weak Hamiltonian [34,35,36], and much of the statements that apply for the relativistic case can be directly transferred to the nonrelativistic theory. However, due to the nonrelativistic power counting some even more specific statements, can be made.…”