NLO QCD Corrections to Higgs Pair Production including Dimension-6 Operators

TL;DR

This work computes NLO QCD corrections to Higgs pair production via gluon fusion within an effective field theory framework that includes dimension-6 operators, implemented in the large top-mass limit. It employs an effective Lagrangian with modified Higgs-top and Higgs-gluon interactions, introducing new vertices and a two-Higgs-two-top coupling, and derives the LO and NLO cross sections with the corresponding form factors and correction coefficient C. The numerical analysis shows that, while the K-factor receives only modest shifts (a few percent) from the new operators, the total cross section can exhibit more noticeable changes within experimentally allowed parameter ranges, and at high collider energy the corrections exhibit sizable but controlled variations. The results underscore the necessity of including NLO QCD effects when predicting Higgs pair production in EFT scenarios for reliable interpretation of experimental constraints on dimension-6 operators.

Abstract

New Physics that becomes relevant at some high scale $Λ$ beyond the experimental reach, can be described in the effective theory approach by adding higher-dimensional operators to the Standard Model (SM) Lagrangian. In Higgs pair production through gluon fusion, which gives access to the trilinear Higgs self-coupling, this leads not only to modifications of the SM couplings but also induces novel couplings not present in the SM. For a proper prediction of the cross section, higher order QCD corrections that are important for this process, have to be taken into account. The various higher-dimensional contributions are affected differently by the QCD corrections. In this paper, we provide the next-to-leading order (NLO) QCD corrections to Higgs pair production including dimension-6 operators in the limit of large top quark masses. Depending on the dimension-6 coefficients entering the Lagrangian, the new operators affect the relative NLO QCD corrections by several per cent, while modifying the cross section by up to an order of magnitude.

Figures (6)

• Figure 1: Feynman rules for the effective two-gluon couplings to one and two Higgs bosons in the heavy quark limit, including NLO QCD corrections. The incoming four-momenta of the gluons are denoted by $k_1$ and $k_2$.
• Figure 2: Generic diagrams contributing to Higgs pair production in gluon fusion at LO.
• Figure 3: Sample effective diagrams contributing to the virtual (upper) and the real (lower) corrections to gluon fusion into Higgs pairs.
• Figure 4: $K$-factors of the QCD-corrected gluon fusion cross section $\sigma (pp \to hh +X)$ at the LHC with c.m. energy $\sqrt{s}=14$ TeV. The dashed lines show the individual contributions of the four terms of the QCD corrections given in Eq. (\ref{['eq:nlosigma']}), i.e.$K_i=\Delta \sigma_i/\sigma_{\text{LO}}$ ($i=\text{virt},gg, gq, q\bar{q}$). We have set the SM values $c_3=c_t=1$, $c_{tt}=0$ and varied $c_g$ with $c_{gg}=0$ (upper), respectively, varied $c_{gg}$ with $c_g=0$ (lower).
• Figure 5: Same as Fig. \ref{['fig:kfactorcgandcgg']}, but now we have set the SM values $c_3=c_t=1$, $c_g=c_{gg}=0$ and varied $c_{tt}$.