[Paper Review] Next-to-Leading Order Corrections to Higgs Boson Pair Production in Gluon Fusion

Matthias Kerner|arXiv (Cornell University)|Aug 12, 2016

Particle physics theoretical and experimental studies30 references3 citations

TL;DR

This paper presents a next-to-leading order (NLO) QCD calculation of Higgs boson pair production in gluon fusion with full top-quark mass dependence, using numerical two-loop integrations via SecDec. The results show a 14% reduction in the total cross section compared to the heavy-top limit approximation, with significant deviations—up to 30%—at high invariant masses, highlighting the necessity of including top-quark mass effects for accurate LHC predictions.

ABSTRACT

We present a calculation of the next-to-leading order QCD corrections to the production of Higgs boson pairs in gluon fusion keeping the full dependence on the mass of the top quark. The virtual corrections, involving two-loop integrals with up to four mass scales, have been calculated numerically and we present an efficient algorithm to obtain accurate results of the virtual amplitude using numerical integrations. Taking the top quark mass into account we obtain significant differences compared to results obtained in the heavy top limit.

Motivation & Objective

• To compute next-to-leading order QCD corrections to Higgs boson pair production in gluon fusion with full top-quark mass dependence.
• To address the limitations of the heavy-top approximation, which underperforms in phase space regions where the top quark mass is not the dominant energy scale.
• To develop and validate a numerical framework for evaluating two-loop amplitudes with multiple mass scales.
• To provide a benchmark for future automated tools in multi-loop amplitude calculations.

Proposed method

• The virtual amplitude is computed numerically using an interface to the SecDec program, enabling integration of two-loop integrals with up to four mass scales.
• Feynman diagrams are generated via Qgraf, projected onto form factors using Form, and reduced to master integrals using Reduze, with mass scales fixed at mt = 173 GeV and mh = 125 GeV during reduction.
• Non-planar tensor integrals are rewritten in terms of scalar products to enable numerical evaluation, resulting in 327 total integrals including crossing variants.
• A quasi-Monte Carlo integration algorithm with dynamic sampling point adjustment is used to compute the virtual amplitude with high precision.
• The calculation is validated against a second implementation and compared to HEFT and 1/m_t^2 expansion results.
• Scale uncertainties are estimated by varying μR and μF by a factor of two around μ = mhh/2.

Experimental results

Research questions

• RQ1 How do full top-quark mass effects modify the NLO cross section for Higgs boson pair production in gluon fusion compared to the heavy-top approximation?
• RQ2 To what extent does the Born-improved Higgs Effective Field Theory (HEFT) fail in describing the differential distributions at high invariant masses or transverse momenta?
• RQ3 Can numerical two-loop integration techniques accurately capture the virtual amplitude when analytical solutions are unavailable?
• RQ4 How do the NLO corrections vary across different phase space regions, particularly near the top-quark threshold?
• RQ5 What is the quantitative impact of top-quark mass effects on the total cross section and K-factors in the differential distributions?

Key findings

• The total NLO cross section is 32.90+14%−13% fb, a 14% reduction compared to the HEFT approximation of 38.32 fb.
• At high invariant masses (mhh > 400 GeV), the top-quark mass effects reduce the cross section by 20–30% compared to the HEFT result.
• The K-factor (NLO/LO) decreases significantly at high mhh, while the HEFT approximation shows an increasing K-factor, indicating a breakdown of the approximation in this region.
• The NLO result shows a nearly constant K-factor in the transverse momentum distribution, in contrast to the HEFT approximation, which overestimates corrections at high pT,h.
• The 1/m_t^2 expansion converges to the full amplitude only below the top-threshold (mhh < 2mt), but fails to describe the amplitude accurately at higher invariant masses.
• The virtual amplitude computed numerically agrees well with the 1/m_t^2 expansion at low mhh but diverges at high mhh, confirming the importance of full top-quark mass dependence.