The $q_T$ spectrum for Higgs production via heavy quark annihilation at N$^3$LL$'$+aN$^3$LO

TL;DR

This paper provides the most precise theoretical predictions for the Higgs boson transverse momentum spectrum produced via heavy quark annihilation, using advanced resummation and matching techniques up to N$^3$LL$'$+aN$^3$LO, with special treatment for bottom-quark initiated processes.

Contribution

It introduces a novel matching method combining resummed and fixed-order calculations at three-loop accuracy for heavy quark initiated Higgs production, including a detailed uncertainty analysis.

Findings

Most accurate predictions for small $q_T$ Higgs spectrum to date.

Effective treatment of bottom-quark initiated processes with large nonsingular corrections.

Potential to improve Higgs Yukawa coupling measurements.

Abstract

We study the transverse momentum ($q_T$) spectrum of the Higgs boson produced via the annihilation of heavy quarks ($s,c,b$) in proton-proton collisions. Using soft-collinear effective theory (SCET) and working in the five-flavour scheme, we provide predictions at three-loop order in resummed perturbation theory (N$^3$LL$'$). We match the resummed calculation to full fixed-order results at next-to-next-to-leading order (NNLO), and introduce a decorrelation method to enable a consistent matching to an approximate N$^3$LO (aN$^3$LO) result. Since the $b$-quark initiated process exhibits large nonsingular corrections, it requires special care in the matching procedure and estimation of associated theoretical uncertainties, which we discuss in detail. Our results constitute the most accurate predictions to date for these processes in the small $q_T$ region and could be used to improve the determination of Higgs Yukawa couplings from the shape of the measured Higgs $q_T$ spectrum.