Small-$x$ phenomenology at the LHC and beyond: HELL 3.0 and the case of the Higgs cross section

TL;DR

This paper develops a theoretical framework and implements small-$x$ resummation in the HELL 3.0 code to improve predictions of Higgs production cross sections at the LHC and FCC, highlighting significant effects on precision calculations.

Contribution

It introduces a new resummation machinery for collider observables and applies it to Higgs production, demonstrating its impact on cross section predictions at high energies.

Findings

Small-$x$ resummation increases Higgs cross section predictions by up to 10% at FCC.

Resummation effects are smaller but still relevant at LHC energies (+1%).

Implementation in HELL 3.0 enables more accurate collider phenomenology.

Abstract

Small-$x$ resummation has been proven recently to be a crucial ingredient for describing small-$x$ HERA data, and the inclusion of small-$x$ resummation in parton distribution function (PDF) determination has a sizeable effect on the PDFs even at the electroweak scale. In this work we explore the implications of small-$x$ resummation at the Large Hadron Collider (LHC) and at a Future Circular Collider (FCC). We construct the theoretical machinery for resumming physical inclusive observables at hadron colliders, and describe its implementation in the public code HELL 3.0. We focus on Higgs production in gluon fusion as a prototypical example, both because it is sensitive to small-$x$ gluons and because of its importance for the LHC physics programme. We find that adding small-$x$ resummation to the N$^3$LO Higgs production cross section can lead to an increase of up to 10% at FCC, while the effect is smaller (+1%) at LHC but still important to achieve a high level of precision.