Light quark mediated Higgs boson threshold production in the next-to-leading logarithmic approximation

Building on the recent derivation of a bare factorization theorem for the b-quark induced contribution to the h → γγ decay amplitude based on soft-collinear effective theory, we derive the first renormalized factorization theorem for a process described at subleading power in scale ratios, where λ = mb/Mh « 1 in our case. We prove two refactorization conditions for a matching coefficient and an operator matrix element in the endpoint region, where they exhibit singularities giving rise to divergent convolution integrals. The refactorization conditions ensure that the dependence of the decay amplitude on the rapidity regulator, which regularizes the endpoint singularities, cancels out to all orders of perturbation theory. We establish the renormalized form of the factorization formula, proving that extra contributions arising from the fact that “endpoint regularization” does not commute with renormalization can be absorbed, to all orders, by a redefinition of one of the matching coefficients. We derive the renormalization-group evolution equation satisfied by all quantities in the factorization formula and use them to predict the large logarithms of order $$ {\alpha \alpha}_s^2{L}^k $$ αα s 2 L k in the three-loop decay amplitude, where $$ L=\ln \left(-{M}_h^2/{m}_b^2\right) $$ L = ln − M h 2 / m b 2 and k = 6, 5, 4, 3. We find perfect agreement with existing numerical results for the amplitude and analytical results for the three-loop contributions involving a massless quark loop. On the other hand, we disagree with the results of previous attempts to predict the series of subleading logarithms $$ \sim {\alpha \alpha}_s^n{L}^{2n+1} $$ ∼ αα s n L 2 n + 1 .

Section: Jhep01(2021)077 7 Conclusionsupporting

confidence: 65%

Section: Jhep01(2021)077contrasting

confidence: 56%

See 1 more Smart Citation

Factorization at subleading power and endpoint divergences in h → γγ decay. Part II. Renormalization and scale evolution

Liu

Mecaj

Neubert

et al. 2021

“…Recent interest in this subject has focused on understanding the structure of such logarithmic terms at next-to-leading power (NLP) in λ with the aim of summing them to all orders in α s . This has been accomplished at the leading-logarithmic (LL) order in various contexts, covering final-state event shapes [1,2], threshold resummation in Drell-Yan and Higgs production [3][4][5], and Higgs production or decay through light-quark loops [6][7][8]. A number of methods has been used, but it has become evident that a generalization to the next-to-leadinglogarithmic (NLL) order is not straightforward.…”

Section: Jhep10(2020)196mentioning

confidence: 99%

Large-x resummation of off-diagonal deep-inelastic parton scattering from d-dimensional refactorization

Beneke

Garny

Jaskiewicz

et al. 2020

The off-diagonal parton-scattering channels g + γ* and q + ϕ* in deep-inelastic scattering are power-suppressed near threshold x → 1. We address the next-to-leading power (NLP) resummation of large double logarithms of 1 − x to all orders in the strong coupling, which are present even in the off-diagonal DGLAP splitting kernels. The appearance of divergent convolutions prevents the application of factorization methods known from leading power resummation. Employing d-dimensional consistency relations from requiring 1/ϵ pole cancellations in dimensional regularization between momentum regions, we show that the resummation of the off-diagonal parton-scattering channels at the leading logarithmic order can be bootstrapped from the recently conjectured exponentiation of NLP soft-quark Sudakov logarithms. In particular, we derive a result for the DGLAP kernel in terms of the series of Bernoulli numbers found previously by Vogt directly from algebraic all-order expressions. We identify the off-diagonal DGLAP splitting functions and soft-quark Sudakov logarithms as inherent two-scale quantities in the large-x limit. We use a refactorization of these scales and renormalization group methods inspired by soft-collinear effective theory to derive the conjectured soft-quark Sudakov exponentiation formula.

“…Solutions to this problem at LL accuracy have been found in particular cases by employing consistency relations [13], refactorization conditions [14] and a combination of operator refactorization and consistency relations [15]. At NLL accuracy a solution has been obtained for the h → γγ decay mediated by light-quarks using diagrammatic methods [16] and within the SCET II framework [17,18]. However, a universal solution to these problems is not currently known.…”

Section: Introductionmentioning

confidence: 99%

Next-to-leading power two-loop soft functions for the Drell-Yan process at threshold

Broggio

Jaskiewicz

Vernazza

2021

We calculate the generalized soft functions at $$ \mathcal{O} $$ O ($$ {\alpha}_s^2 $$ α s 2 ) at next-to-leading power accuracy for the Drell-Yan process at threshold. The operator definitions of these objects contain explicit insertions of soft gauge and matter fields, giving rise to a dependence on additional convolution variables with respect to the leading power result. These soft functions constitute the last missing ingredient for the validation of the bare factorization theorem to NNLO accuracy. We carry out the calculations by reducing the soft squared amplitudes into a set of canonical master integrals and we employ the method of differential equations to evaluate them. We retain the exact d-dimensional dependence of the convolution variables at the integration boundaries in order to regulate the fixed-order convolution integrals. After combining the soft functions with the relevant collinear functions, we perform checks of the results at the cross-section level against the literature and expansion-by-regions calculations, at NNLO and partly at N3LO, finding agreement.