Higgs boson pair production: top quark mass effects at NLO and NNLO

TL;DR

This study extends Higgs-boson pair production calculations in gluon fusion beyond the infinite-top-mass (EFT) limit by performing a large-$M_t$ expansion and constructing a soft-virtual approximation up to NNLO. It compares two LO-factorization approaches, finding differential factorization w.r.t. the Higgs-pair invariant mass to be more stable, and computes finite-$M_t$ corrections up to 1/$M_t^4$ at NNLO through two independent methods (amplitude-based and optical theorem). The results show finite-top-mass effects shift the cross section by about 10% at NLO and about 5% at NNLO, quantifying the reliability of the EFT and providing benchmarks for future exact calculations. Overall, the SV-based NNLO predictions with mass corrections offer robust, practical estimates for Higgs self-coupling studies at the LHC, with controlled uncertainties.

Abstract

We compute next-to-next-to-leading order QCD corrections to the gluon-induced production cross section of Higgs boson pairs in the large top quark mass limit using the soft-virtual approximation. In the limit of infinitely-heavy top quark we confirm the results in the literature. We add two more expansion terms in the inverse top quark mass to the $M_t\to\infty$ result. Since the $1/M_t$ expansion converges poorly, we try to improve on it by factorizing the exact leading order cross section. We discuss two ways of doing that and conclude that the finite top quark mass effects shift the cross section at most by about 10\% at next-to-leading order and by about 5\% at next-to-next-to-leading order.

Figures (14)

• Figure 1: Partonic cross section as a function the center-of-mass energy including various orders in the inverse top quark mass. The dotted and dashed curves show the breakup of the complete result (solid lines) into soft-virtual and hard contribution.
• Figure 2: Partonic cross section as a function the center-of-mass energy including various orders in the inverse top quark mass. The dashed and solid curves correspond to the factorization for the total and differential cross section, respectively. The colour coding is taken over from Fig. \ref{['fig::sig_part']}.
• Figure 3: Partonic NLO $K$ factor for the factorization performed at the level of the total (dashed) and differential (solid) cross section.
• Figure 4: NLO hadronic cross section and $K$ factor as a function of $\sqrt{s_{\rm cut}}$.
• Figure 5: Splitting of partonic cross section (solid lines) into real (uppser dashed lines) and virtual (lower dotted lines) contributions (see text for details).