# Resummation Improved Rapidity Spectrum for Gluon Fusion Higgs Production

## TL;DR

This paper demonstrates that resumming Sudakov logarithms in gluon fusion Higgs production improves the convergence and reduces uncertainties in the rapidity spectrum and total cross section predictions.

## Contribution

It develops a method to incorporate resummed form factors into differential cross section calculations, enhancing perturbative accuracy for Higgs and Drell-Yan processes.

## Key findings

- Reduced perturbative uncertainties at N$^3$LO$+$N$^3$LL$^\prime_\varphi$ for total cross section.
- Improved convergence and smaller uncertainties for the Higgs rapidity spectrum at NNLO$+$NNLL$^\prime_\varphi$.
- Small impact of resummation on bottom quark annihilation Higgs production and Drell-Yan processes.

## Abstract

Gluon-induced processes such as Higgs production typically exhibit large perturbative corrections. These partially arise from large virtual corrections to the gluon form factor, which at timelike momentum transfer contains Sudakov logarithms evaluated at negative arguments $\ln^2(-1) = -\pi^2$. It has been observed that resumming these terms in the timelike form factor leads to a much improved perturbative convergence for the total cross section. We discuss how to consistently incorporate the resummed form factor into the perturbative predictions for generic cross sections differential in the Born kinematics, including in particular the Higgs rapidity spectrum. We verify that this indeed improves the perturbative convergence, leading to smaller and more reliable perturbative uncertainties, and that this is not affected by cancellations between resummed and unresummed contributions. Combining both fixed-order and resummation uncertainties, the perturbative uncertainty for the total cross section at N$^3$LO$+$N$^3$LL$^\prime_\varphi$ is about a factor of two smaller than at N$^3$LO. The perturbative uncertainty of the rapidity spectrum at NNLO$+$NNLL$^\prime_\varphi$ is similarly reduced compared to NNLO. We also study the analogous resummation for quark-induced processes, namely Higgs production through bottom quark annihilation and the Drell-Yan rapidity spectrum. For the former the resummation leads to a small improvement, while for the latter it confirms the already small uncertainties of the fixed-order predictions.