Precision Predictions at N$^3$LO for the Higgs Boson Rapidity Distribution at the LHC

TL;DR

This work delivers a precise, differential prediction for the Higgs boson rapidity distribution in gluon fusion at $N^3$LO in QCD by exploiting a systematic threshold expansion within a heavy-top EFT. The authors analytically determine the partonic coefficient functions $η_{ij}(x_1,x_2)$ through $N^3$LO and match to the inclusive cross section to ensure consistency of the rapidity-integrated rate. They demonstrate a mild $N^3$LO correction and a substantial reduction in perturbative scale uncertainty across the full rapidity range, with an approximately flat $N^3$LO/NNLO ratio, highlighting the strong stabilization of differential Higgs phenomenology. This milestone solidifies the theoretical precision needed for LHC Higgs studies and provides a framework for fully differential predictions in Higgs production.

Abstract

We present precise predictions for the Higgs boson rapidity distribution at the LHC in the gluon fusion production mode. Our approach relies on the fully analytic computation of six terms in a systematic expansion of the partonic differential cross section around the production threshold of the Higgs boson at next-to-next-to-next-to leading order (N$^3$LO) in QCD perturbation theory. We observe a mild correction compared to the previous perturbative order and a significant reduction of the dependence of the cross section on the perturbative scale throughout the entire rapidity range.

Figures (2)

• Figure 1:
• Figure 2: The Higgs boson rapidity distribution at different orders in perturbation theory. The lower panel shows the N$^3$LO and NNLO predictions normalised to the N$^3$LO prediction for $\mu=m_h/2$.