Threshold Resummation of Drell-Yan type colorless processes at LHC

TL;DR

This paper enhances the precision of theoretical predictions for Drell-Yan and Higgs production at the LHC by applying third-order threshold resummation techniques, significantly reducing scale uncertainties.

Contribution

It introduces a method to incorporate N$^3$LL threshold logarithms with N$^3$LO results for improved accuracy in LHC process predictions.

Findings

Scale uncertainties reduced from 0.4% to less than 0.1% at high invariant mass.

Achieved higher-order resummation up to N$^3$LL matched with N$^3$LO calculations.

Provided numerical results for invariant mass distributions and total cross sections.

Abstract

We look at the threshold effects in neutral and charged Drell-Yan production, Higgs boson production with a massive vector boson, and Higgs production in bottom quark annihilation at the Large Hadron Collider (LHC), up to the third order in QCD. Using third-order soft-virtual (SV) results and the universal properties of threshold logarithms, we find the process-dependent coefficients and improve the accuracy by including large threshold logarithms up to next-to-next-to-next-to-leading logarithmic (N$^3$LL) order and matched with the latest N$^3$LO results. We also show numerical results for the invariant mass distributions and total production cross sections for these processes. Our findings show that the theoretical scale uncertainties, which are about $0.4\%$ at N$^3$LO in fixed-order calculations, decrease to less than $0.1\%$ at N$^3$LO+N$^3$LL after SV threshold resummation in the high invariant mass region.