The Soft-Virtual Higgs Cross-section at N3LO and the Convergence of the Threshold Expansion

TL;DR

The paper addresses the precision of Higgs boson production cross-sections at hadron colliders, focusing on the reliability of the soft-virtual approximation and the threshold expansion for gluon-fusion in perturbative QCD up to N3LO. It analyzes the convergence properties of the threshold expansion by introducing a $g(z)$ function to probe truncation effects and by comparing to known NNLO results, highlighting the sensitivity to sub-leading terms. The study finds that, while the threshold expansion can converge at lower orders, truncation uncertainties at NLO and NNLO are substantial and N3LO SV exhibits large ambiguity across $g(z)$ choices, suggesting that several sub-leading terms are required for stable predictions and that full N3LO calculations are highly desirable. The results underscore the importance of improved theoretical control for precise Higgs cross-sections at the LHC and for discriminating potential deviations from the Standard Model.

Abstract

We discuss the validity of the soft-virtual approximation and the threshold expansion for the Higgs boson production cross-section at hadron colliders in perturbative QCD up to next-to- next-to-next-to-leading order (N3LO).

Figures (3)

• Figure 1: Threshold approximation for the Higgs boson cross-section at 13 TeV at the LHC
• Figure 2: Percent difference of the threshold expansion to the full Higgs boson cross-section at NLO and NNLO at 13 TeV at the LHC evaluated at $\mu=\frac{m_H}{2}$ as a function of the order where the series is truncated. Different lines correspond to different choices for the function g(z).
• Figure 3: The gluon-fusion cross-section at 13 TeV at the LHC as a function of $\mu=\mu_R=\mu_F$ up to LO (black), NLO (red), NNLO (green) and soft-virtual N${}^3$LO (blue). The N${}^3$LO SV approximation is modified with different functions g(z).