NLO Corrections to Light-Quark Mixed QCD-EW Contributions to Higgs Production

TL;DR

The paper computes the exact NLO QCD corrections to the light-quark part of the mixed QCD-EW contributions to Higgs production in gluon fusion at the LHC, retaining full electroweak boson mass dependence. It uses a dynamic generalised power-series solution of differential equations for master integrals to obtain the two-loop real-emission amplitudes and performs phase-space integration with local IR subtraction via two independent schemes, validated against each other. The study finds that the gluon-induced light-quark contribution at NLO is σ^{(α_s^2α^2+α_s^3α^2)}_{gg→H+X} ≈ 1.467 pb with sizable scale uncertainties, and reports a best estimate for the EW-origin Higgs cross section of around 2.11–2.19 pb depending on scale choices, indicating modest violations of the EW-QCD factorisation. The results are cross-validated against HEFT limits, show a flat Higgs rapidity differential K-factor, and provide a public MadGraph plugin to facilitate future inclusion of these exact-mass EW effects in phenomenological predictions, thereby reducing a prior ~1% theory uncertainty on the EW gluon-induced contribution.

Abstract

We present for the first time the exact NLO QCD corrections to the light-quark part of the mixed QCD-EW contributions to Higgs production via gluon fusion at LHC13, with exact EW-boson mass dependence. The relevant two-loop real-emission matrix element is computed using a dynamic one-dimensional series expansion strategy whose stability and speed allows for a numerical phase-space integration using local IR subtraction counterterms. For $μ_R=μ_F=M_H$, we find: \begin{equation}σ^{(α_s^2α^2+α_s^3α^2)}_{g g\rightarrow H+X} = 1.467(2)^{\;+18.7\%}_{\;-14.6\%}\;(μ_R\;\text{var.})\;\pm 2\%\;(\text{PDF}) \ \textrm{pb},\end{equation} which we use to provide the best result including an estimate of suppressed contributions: \begin{equation}σ^{(\text{EW},\textrm{best})}_{p p\rightarrow H+X} = 2.11 \pm 0.28 \ (\textrm{theory}) \ \mathrm{pb}.\end{equation}

Figures (4)

• Figure 1: Numerical stability of the 2-loop real-emission matrix element, locally subtracted with our modified implementation of CoLoRFuL, compared to their HEFT tree-level counterpart when approaching the soft and collinear limits. The approach parameter $\lambda$ is defined so that the scaling of the real-emission matrix when approaching the IR limit is $\lambda^{-1}$. The weighted integrand shown includes the Jacobian of the parameterisation so that it must scale like $\lambda^{\alpha}$ with $\alpha>\frac{1}{2}$ in order to be integrable.
• Figure 2: Differential prediction for the $\mathcal{O}(\alpha_s^3\alpha^2)$ correction to the Higgs rapidity distribution.
• Figure 3: Differential prediction for the $\mathcal{O}(\alpha_s^3\alpha^2)$ EW contribution to the Higgs transverse momentum distribution, compared to its LO HEFT counterpart.
• Figure 4: Plot of the quantity $\frac{\left( \mathcal{M}_{gg\rightarrow Hg}^{(\alpha_s^3\alpha^2)}/\mathcal{M}_{gg\rightarrow Hg}^{(\alpha_s^3\alpha)}-R^{\text{NLO}}\right)}{R^{\text{NLO}}}$ with ${R^{\text{NLO}}=\sigma^{(\alpha_s^3\alpha^2)}_{g g\rightarrow H+X}/\sigma^{(\textrm{HEFT},\alpha_s^3\alpha)}_{g g\rightarrow H+X}}$ in terms of the rescaled kinematic invariants $z=M_H^2/s$ and $l=t/(M_H^2-s)$, for a sample of $\sim 150$K phase-space points. The lines of constant deviation span the range $[-0.75,0.15]$ in increments of $0.05$.