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Two-Loop Master Integrals for Mixed QCD-EW Corrections to $gg \to H$ Through $\mathcal{O}(ε^2)$

Robin Marzucca, Andrew J. McLeod, Christoph Nega

TL;DR

The paper advances analytic control of mixed QCD-EW corrections to Higgs production in gluon fusion by computing all two-loop master integrals relevant when the Higgs couples to the top quark, through $\mathcal{O}(\epsilon^2)$ with full mass dependence. It formulates five integral families, solves their differential equations in a canonical form, and expresses the results as iterated integrals; three families yield multiple polylogarithms, while two elliptic sectors are handled via elliptic-period and one-fold iterated integrals, paving the way for an analytic NNLO treatment. Boundary conditions are fixed using the $s\to0$ limit and the method of regions, with cross-checks against numerical tools confirming the results. The work provides a foundational framework for the complete $gg \to H$ amplitude at $\mathcal{O}(g^3 g_s^2)$, including mass effects from the top quark and electroweak bosons, and offers insights into the interplay between polylogarithmic and elliptic structures in realistic, massive amplitudes.

Abstract

We consider mixed strong-electroweak corrections to Higgs production via gluon fusion, in which the Higgs boson couples to the top quark. Using the method of differential equations, we compute all of the master integrals that contribute to this process at two loops through $\mathcal{O}(ε^2)$ in the dimensional regularization parameter $ε= (d-4)/2$, keeping full analytic dependence on the top quark, Higgs, W, and Z boson masses. We present the results for these master integrals in terms of iterated integrals whose kernels depend on elliptic curves.

Two-Loop Master Integrals for Mixed QCD-EW Corrections to $gg \to H$ Through $\mathcal{O}(ε^2)$

TL;DR

The paper advances analytic control of mixed QCD-EW corrections to Higgs production in gluon fusion by computing all two-loop master integrals relevant when the Higgs couples to the top quark, through with full mass dependence. It formulates five integral families, solves their differential equations in a canonical form, and expresses the results as iterated integrals; three families yield multiple polylogarithms, while two elliptic sectors are handled via elliptic-period and one-fold iterated integrals, paving the way for an analytic NNLO treatment. Boundary conditions are fixed using the limit and the method of regions, with cross-checks against numerical tools confirming the results. The work provides a foundational framework for the complete amplitude at , including mass effects from the top quark and electroweak bosons, and offers insights into the interplay between polylogarithmic and elliptic structures in realistic, massive amplitudes.

Abstract

We consider mixed strong-electroweak corrections to Higgs production via gluon fusion, in which the Higgs boson couples to the top quark. Using the method of differential equations, we compute all of the master integrals that contribute to this process at two loops through in the dimensional regularization parameter , keeping full analytic dependence on the top quark, Higgs, W, and Z boson masses. We present the results for these master integrals in terms of iterated integrals whose kernels depend on elliptic curves.
Paper Structure (15 sections, 31 equations, 1 figure)

This paper contains 15 sections, 31 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Conventions and Definitions
  3. Master Integrals
  4. Families 1 and 4
  5. Family 3
  6. Families 2 and 5
  7. Cross-checks
  8. Analytic Properties
  9. Conclusions
  10. Master Integral Basis
  11. Family 1
  12. Family 2
  13. Family 3
  14. Family 4
  15. Family 5

Figures (1)

  • Figure 1: The five two-loop integral families that appear at $\mathcal{O}(g^3 g_s^2)$ in $gg \to H$, in which the Higgs boson couples to a top quark. The mass $M$ can take the values $m_H$, $m_W$, or $m_Z$. Thin lines represent massless particles, and the dashed line represents the outgoing Higgs boson. Note that families 2 and 5 involve multiple top-level topologies.