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On the light quark mass effects in Higgs boson production in gluon fusion

Kirill Melnikov, Alexander Penin

TL;DR

The paper addresses light-quark mass effects in Higgs production via gluon fusion with a jet, focusing on abelian double-logarithmic corrections that enhance mb-suppressed amplitudes. It computes the one- and two-loop DL contributions to the gg→Hg helicity amplitudes, then resums these abelian DL corrections to all orders using Sudakov-like exponentiation, and assesses their impact on the Higgs p_T distribution. Numerically, the one-loop DL reduces the cross section by about 16% while the two-loop piece adds ~1.5%, with the p_T-dependent part being unusually small due to cancellations; these results suggest non-abelian corrections could be more sizeable and warrant further study. Overall, the work provides a calculational framework for including light-quark DL effects and highlights the need to address non-abelian contributions for high-precision predictions.

Abstract

Production of Higgs bosons at the LHC is affected by the contribution of light quarks, that mediate the gg \to Hg transition. Although their impact is suppressed by small Yukawa couplings, it is enhanced by large logarithms of the ratio of the Higgs boson mass or its transverse momentum to light quark masses. We study the origin of this enhancement, focusing on the abelian corrections to gg \to Hg amplitudes of the form (C_F alphas L^{2})^n, where $L \in { ln(s/mb^2), ln(p_\perp^2/mb^2) }. We show how these non-Sudakov double logarithmic terms can be resummed to all orders in the strong coupling constant. Interestingly, we find that the transverse momentum dependence of these corrections is very weak due to a peculiar cancellation between different logarithmic terms. Although the abelian part of QCD corrections is not expected to be dominant, it can be used to estimate missing higher-order corrections to light quark contributions to Higgs boson production at the LHC.

On the light quark mass effects in Higgs boson production in gluon fusion

TL;DR

The paper addresses light-quark mass effects in Higgs production via gluon fusion with a jet, focusing on abelian double-logarithmic corrections that enhance mb-suppressed amplitudes. It computes the one- and two-loop DL contributions to the gg→Hg helicity amplitudes, then resums these abelian DL corrections to all orders using Sudakov-like exponentiation, and assesses their impact on the Higgs p_T distribution. Numerically, the one-loop DL reduces the cross section by about 16% while the two-loop piece adds ~1.5%, with the p_T-dependent part being unusually small due to cancellations; these results suggest non-abelian corrections could be more sizeable and warrant further study. Overall, the work provides a calculational framework for including light-quark DL effects and highlights the need to address non-abelian contributions for high-precision predictions.

Abstract

Production of Higgs bosons at the LHC is affected by the contribution of light quarks, that mediate the gg \to Hg transition. Although their impact is suppressed by small Yukawa couplings, it is enhanced by large logarithms of the ratio of the Higgs boson mass or its transverse momentum to light quark masses. We study the origin of this enhancement, focusing on the abelian corrections to gg \to Hg amplitudes of the form (C_F alphas L^{2})^n, where $L \in { ln(s/mb^2), ln(p_\perp^2/mb^2) }. We show how these non-Sudakov double logarithmic terms can be resummed to all orders in the strong coupling constant. Interestingly, we find that the transverse momentum dependence of these corrections is very weak due to a peculiar cancellation between different logarithmic terms. Although the abelian part of QCD corrections is not expected to be dominant, it can be used to estimate missing higher-order corrections to light quark contributions to Higgs boson production at the LHC.

Paper Structure

This paper contains 8 sections, 52 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Setup and notations
  3. One-loop helicity amplitudes in the double logarithmic approximation
  4. Two-loop helicity amplitudes in the double logarithmic approximation
  5. Resummation of the abelian double logarithmic contributions
  6. Double logarithmic corrections to the differential cross section
  7. Conclusion
  8. Polarization vectors

Figures (2)

  • Figure 1: One-loop diagrams representing the leading order bottom quark contribution to $gg \to Hg$ process. Symmetric diagrams corresponding to the opposite direction of the quark flow and to the soft emissions off the opposite gluon/quark line are not shown.
  • Figure 2: Two-loop diagrams contributing to the abelian double logarithmic corrections. Diagrams that differ by the direction of the fermion flow are not shown.