Factorization at subleading power and endpoint-divergent convolutions in h → γγ decay

Abstract

It is by now well known that, at subleading power in scale ratios, factorization theorems for high-energy cross sections and decay amplitudes contain endpoint-divergent convolution integrals. The presence of endpoint divergences hints at a violation of simple scale separation. At the technical level, they indicate an unexpected failure of dimensional regularization and the MS subtraction scheme. In this paper we start a detailed discussion of factorization at subleading power within the framework of soft-collinear effective theory. As a concrete example, we factorize the decay amplitude for the radiative Higgs-boson decay h → γγ mediated by a b-quark loop, for which endpoint-divergent convolution integrals require both dimensional and rapidity regulators. We derive a factorization theorem for the decay amplitude in terms of bare Wilson coefficients and operator matrix elements. We show that endpoint divergences caused by rapidity divergences cancel to all orders of perturbation theory, while endpoint divergences that are regularized dimensionally can be removed by rearranging the terms in the factorization theorem. We use our result to resum the leading double-logarithmic corrections of order α n s ln 2n+2 (−M 2 h /m 2 b ) to the decay amplitude to all orders of perturbation theory.

Higgs decay to fermion pairs at NLO in SMEFT

“…Since C HG itself gets NNLO corrections of order α 2 s ln 4 (m 2 c /m 2 H ), which are substantial, it is clear that more reliable predictions for h → cc would involve a resummation of the logarithmic terms. While techniques for such a resummation exist for the virtual h → AA amplitudes (where A = γ, g) [62][63][64][65][66], it is not clear how to translate them to the inclusive h → ff decay rate, which receives double-logarithmic corrections from both real and virtual contributions.…”

Two-loop radiative jet function for exclusive B-meson and Higgs decays

“…The results presented in this paper will play an important role in the renormalization of the factorization theorem for the light-quark induced h → γγ decay amplitude derived in [20]. Using the evolution equations of the radiative jet function derived here and of a hard function well known in SCET, we will be able to derive the two-loop evolution equation satisfied by the soft-quark soft function [63], another central object in the theory of factorization beyond the leading power.…”

“…In this process the soft spectator quark of the B meson couples to a collinear photon and an off-shell collinear quark, which then connects to the weak-interaction vertex, where it annihilates the b-quark and turns into a virtual W − boson. Interestingly, the same radiative jet function has recently been encountered in a completely different context: in the theoretical description of the contribution to the radiative Higgs-boson decay h → γγ that is induced by light b-quark loops [20,21]. (This is not the dominant contribution to the decay amplitude, but it is a particularly interesting one with regard to its factorization properties.…”

“…We have derived the two-loop result (4.7) for J(p 2 ) in a second, totally independent way by performing a two-loop calculation of the hard matching coefficients H 2 (z) and H 3 in the factorization formula for the h → γγ decay amplitude derived in [20]. Further details about this rather difficult calculation will be presented elsewhere.…”

“…Following our recent work [20], we define the radiative jet function J(p 2 ) in terms of the matrix element…”