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Virtual corrections to gg -> H to two loops in the heavy top limit

Robert V. Harlander

TL;DR

This paper computes the gauge-invariant NNLO virtual corrections to Higgs production via gluon fusion in the heavy-top limit by employing an effective Higgs–gluon interaction and the Baikov–Smirnov method to map two-loop vertex diagrams onto massless three-loop two-point functions. The calculation uses the MSbar-renormalized five-flavor theory and provides explicit expressions for the NNLO virtual contribution, including the pole structure and finite parts, validated by cross-checks with known form factors and gauge invariance checks. A key diagnostic is the time-like versus space-like form-factor ratio, which is computed to O(alpha_s^2) and yields a numerically significant but perturbatively tractable correction, supporting the potential convergence of the series. Together with the planned inclusion of real-emission contributions and PDF convolution, this work advances toward a complete NNLO prediction for gg -> H and reduced theoretical uncertainties for Higgs phenomenology at hadron colliders.

Abstract

The virtual corrections to the production cross section of a Standard Model Higgs boson are computed up to order α_s^4. Using an effective Lagrangian for the limit M_t -> \infty, we evaluate the relevant massless two-loop vertex diagrams by mapping them onto three-loop two-point functions, following a method recently introduced by Baikov and Smirnov. As a result, we find a gauge-invariant contribution to the total Higgs production cross section at NNLO.

Virtual corrections to gg -> H to two loops in the heavy top limit

TL;DR

This paper computes the gauge-invariant NNLO virtual corrections to Higgs production via gluon fusion in the heavy-top limit by employing an effective Higgs–gluon interaction and the Baikov–Smirnov method to map two-loop vertex diagrams onto massless three-loop two-point functions. The calculation uses the MSbar-renormalized five-flavor theory and provides explicit expressions for the NNLO virtual contribution, including the pole structure and finite parts, validated by cross-checks with known form factors and gauge invariance checks. A key diagnostic is the time-like versus space-like form-factor ratio, which is computed to O(alpha_s^2) and yields a numerically significant but perturbatively tractable correction, supporting the potential convergence of the series. Together with the planned inclusion of real-emission contributions and PDF convolution, this work advances toward a complete NNLO prediction for gg -> H and reduced theoretical uncertainties for Higgs phenomenology at hadron colliders.

Abstract

The virtual corrections to the production cross section of a Standard Model Higgs boson are computed up to order α_s^4. Using an effective Lagrangian for the limit M_t -> \infty, we evaluate the relevant massless two-loop vertex diagrams by mapping them onto three-loop two-point functions, following a method recently introduced by Baikov and Smirnov. As a result, we find a gauge-invariant contribution to the total Higgs production cross section at NNLO.

Paper Structure

This paper contains 6 sections, 19 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Effective Lagrangian
  3. Calculation of the two-loop diagrams
  4. Results
  5. Ratio of time-like to space-like form factor
  6. Conclusions and Outlook

Figures (2)

  • Figure 1: Leading order diagram to the process $gg\to H$: (a) in the full and (b) in the effective theory. The "$\otimes$" denotes the effective vertex of Eq. (\ref{['eq::leff']}).
  • Figure 2: Sample two-loop diagrams contributing to $gg\to H$ at NNLO. The right vertex stands for the effective coupling of the Higgs particle to gluons. The bubble in diagram (e) represents any quark except for the top quark.