Exact quark-mass dependence of the Higgs-gluon form factor at three loops in QCD

148

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.

Section: Higher-order Logarithmic Contributions To the Decay Amplitudesupporting

confidence: 54%

Section: Introductioncontrasting

confidence: 47%

“…The authors of [15] have confirmed to us in a private communication that this is indeed the correct expression for the coefficient of the subleading logarithmic contribution.…”

Section: Higher-order Logarithmic Contributions To the Decay Amplitudementioning

confidence: 58%

Section: Higher-order Logarithmic Contributions To the Decay Amplitudementioning

confidence: 75%

Section: Higher-order Logarithmic Contributions To the Decay Amplitudementioning

confidence: 99%

See 3 more Smart Citations

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

Liu

Neubert

2020

148

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

Liu

Mecaj

Neubert

et al. 2021

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 .

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

Anastasiou

Penin

2021