Collinear and soft gluon corrections to Higgs production at NNNLO

TL;DR

The paper develops a unified, high-precision framework for Higgs production cross sections by computing complete soft-gluon corrections and leading/subleading collinear corrections up to NNNLO for bbbar -> H and related processes. Using moment-space resummation, it provides explicit SV and C contributions with full color and scale-dependent terms, and demonstrates that soft corrections alone are insufficient without collinear terms at NLO and NNLO. Numerical studies at the Tevatron and LHC show that including collinear logs yields substantial improvements in approximation accuracy and that NNNLO corrections substantially enhance the total cross section, with controlled PDF and scale uncertainties. The work also extends the formalism to gg -> H and Drell-Yan, offering a comprehensive, analytically grounded tool for precision Higgs phenomenology in both SM and MSSM contexts.

Abstract

I present analytical expressions for the collinear and soft gluon corrections to Higgs production via the process b bbar -> H as well as gg -> H through next-to-next-to-next-to-leading order (NNNLO). The soft corrections are complete while the collinear corrections include leading and some subleading logarithms. Numerical results at the Tevatron and the LHC are presented, primarily for b bbar -> H. It is shown that the collinear terms greatly improve the soft and virtual approximation at next-to-leading order (NLO) and next-to-next-to-leading order (NNLO), especially when subleading terms are included. The NNNLO collinear and soft corrections provide significant enhancements to the total cross section. I also provide expressions for the collinear and soft corrections through NNNLO for the related Drell-Yan process.

Figures (6)

• Figure 1: Left: The NLO ratios for $b {\bar{b}} \rightarrow H$ at the Tevatron. Here $\mu=\mu_F=\mu_R=m_H$. Right: The NLO ratios for $gg \rightarrow H$ at the Tevatron.
• Figure 2: Left: The NLO ratios for $b {\bar{b}} \rightarrow H$ at the LHC. Here $\mu=\mu_F=\mu_R=m_H$. Right: The NLO ratios for $gg \rightarrow H$ at the LHC.
• Figure 3: Left: The NNLO ratios for $b {\bar{b}} \rightarrow H$ at the Tevatron. Here $\mu=\mu_F=\mu_R=m_H$. Right: The NNLO ratios for $b {\bar{b}} \rightarrow H$ at the LHC.
• Figure 4: Left: The $K$ factors for $b {\bar{b}} \rightarrow H$ at the Tevatron. Here $\mu=\mu_F=\mu_R=m_H$. Right: The $K$ factors for $b {\bar{b}} \rightarrow H$ at the LHC.
• Figure 5: Left: The cross section for $b {\bar{b}} \rightarrow H$ at the Tevatron with $\mu=\mu_F=\mu_R=m_H$. Right: The cross section for $b {\bar{b}} \rightarrow H$ at the LHC.