Renormalization of the radiative jet function

We show how to compute directly the renormalization/evolution of the radiative jet function that appears in the factorization theorems for B→γa.,"ν and H→γγ through a b-quark loop. We point out that, in order to avoid double counting of soft contributions, one should use in the factorization theorems a subtracted radiative jet function from which soft contributions have been removed. The soft-contribution subtractions are zero-bin subtractions in the terminology of soft-collinear effective theory. We show that they can be factored from the radiative jet function and that the resulting soft-subtraction function gives rise to a nonlocal renormalization of the subtracted radiative jet function. This is a novel instance in which zero-bin subtractions lead to a nonlocality in the renormalization of a subtracted quantity that is not present in the renormalization of the unsubtracted quantity. We demonstrate the use of our formalism by computing the order-αs evolution kernel for the subtracted radiative jet function. Our result is in agreement with the result that had been inferred previously by making use of the factorization theorem for B→γa.,"ν, but that had been ascribed to the unsubtracted radiative jet function.