Higgs-differential cross section at NNLO in dimensional regularisation

TL;DR

The paper develops a Higgs-differential framework to compute differential cross sections for Higgs production in gluon fusion at NNLO, differential in Higgs momentum and inclusive in associated radiation, while preserving the full $\epsilon$ dependence.It leverages reverse unitarity to map phase-space integrals to loop integrals and uses IBP to reduce to a small set of master integrals, which are computed analytically via differential equations and direct integration, expressed with hypergeometric functions expandable in $\epsilon$.The authors provide analytic NNLO partonic coefficient functions $\eta^{(k)}_{ij}(z,x,\lambda)$ including higher-order $\epsilon$ terms, enabling construction of $N^3LO$ counterterms, and implement these results in a numerical code to generate Higgs observables such as the diphoton final state.Numerical results for inclusive Higgs distributions and Higgs decays to $\gamma\gamma$ are validated against existing codes (HNNLO, MCFM) and demonstrate the framework’s applicability to realistic LHC analyses and potential extension to higher orders and other colourless final states.

Abstract

We present an analytic computation of the Higgs production cross section in the gluon fusion channel, which is differential in the components of the Higgs momentum and inclusive in the associated partonic radiation through NNLO in perturbative QCD. Our computation includes the necessary higher order terms in the dimensional regulator beyond the finite part that are required for renormalisation and collinear factorisation at N$^3$LO. We outline in detail the computational methods which we employ. We present numerical predictions for realistic final state observables, specifically distributions for the decay products of the Higgs boson in the $γγ$ decay channel.

Figures (4)

• Figure 1: Double-real master integrals
• Figure 2: Rapidity and $p_T$ distributions for the inclusive production of a Higgs boson via gluon fusion for different orders in perturbative QCD through NNLO. The bands represent the variation of the cross section under changes of the unphysical scale $\mu$ w.r.t. the central value (thick lines) by a factor of two.
• Figure 3: The Higgs boson rapidity for different orders in perturbative QCD through NNLO in the fiducial volume for the diphoton decay. The bands represent the variation of the cross section under changes of the unphysical scale $\mu$ w.r.t. the central value (thick lines) by a factor of two.
• Figure 4: Differential distributions for the decay products of the Higgs boson for different orders in perturbative QCD through NNLO in the fiducial volume for the diphoton decay. The bands represent the variation of the cross section under changes of the unphysical scale $\mu$ w.r.t. the central value (thick lines) by a factor of two.