On the two-loop virtual QCD corrections to Higgs boson pair production in the Standard Model

TL;DR

The paper addresses the challenge of predicting Higgs boson pair production via gluon fusion at NLO by computing the virtual two-loop QCD corrections in the SM. It delivers exact results for the reducible double-triangle contributions and uses a heavy-top-mass expansion up to ${\cal O}(1/m_t^8)$ for the irreducible two-loop diagrams, yielding analytic spin-0 and spin-2 form factors. Finite-$m_t$ effects are quantified and found to reduce the hadronic cross section by up to about 10%, with the double-triangle part contributing notably at the partonic level but little to the hadronic rate. These results provide improved NLO predictions and practical inputs for Monte Carlo codes, while highlighting the need to include real corrections and high-energy contributions for a full two-loop calculation.

Abstract

We compute the next-to-leading order virtual QCD corrections to Higgs pair production via gluon fusion. We present analytic results for the two-loop contributions to the spin-0 and spin-2 form factors in the amplitude. The reducible contributions, given by the double-triangle diagrams, are evaluated exactly while the two-loop irreducible diagrams are evaluated by an asymptotic expansion in heavy top quark mass up to and including terms of $\mathcal{O}(1/m_t^8)$. Assuming that the finite top-quark mass effects are of similar size in the entire range of partonic energies we estimate that mass effects can reduce the hadronic cross section by at most $10\%$.

Figures (5)

• Figure 1: Generic Feynman diagrams for box and triangle topologies for Higgs pair production.
• Figure 2: Sample of Feynman diagrams for the virtual two-loop corrections to Higgs pair production via gluon fusion.
• Figure 3: a) LET result for $F_1^{1\ell}$ normalized to the real part of the exact $F_1^{1\ell}$ form factor. b) The sum of first five terms of the large top-mass expansion of $F_1^{1\ell}$ (eqs. \ref{['F1tria']} and \ref{['F1box']}) normalized to the real part of exact $F_1^{1\ell}$ form factor.
• Figure 4: Leading order partonic cross section as a function of the partonic center-of-mass energy. The solid line corresponds to the exact result, the dashed ones to the results obtained using different terms in the large top-mass expansion.
• Figure 5: Double-triangle contribution to the partonic cross section as a function of the partonic center-of-mass energy. The solid line represents the exact result using eqs. \ref{['eq:doubletri1']} and \ref{['eq:doubletri2']} while the dashed one the result obtained in the LET approximation using eq. \ref{['eq:doubletriLET']}.