One-Loop Single-Real-Emission Contributions to $pp\to H+X$ at Next-to-Next-to-Next-to-Leading Order

Abstract

I compute the contributions of the one-loop single-real-emission amplitudes, $gg\to Hg$, $qg\to Hq$, etc., to inclusive Higgs boson production through next-to-next-to-next-to-leading order (N^3LO) in the strong coupling ${\alpha }_s$. The next-to-leading (NLO) and next-to-next-to-leading order (NNLO) terms are computed in closed form, in terms of $\Gamma$-functions and the hypergeometric functions ${}_2{F}_1$ and ${}_3{F}_2$. I compute the \nnnlo\ terms as Laurent expansions in the dimensional regularization parameter through order $({ϵ}^1)$. To obtain the \nnnlo\ terms, I perform an extended threshold expansion of the phase space integrals and map the resulting coefficients onto a basis of harmonic polylogarithms.

Comments: 32 pages, 4 figures. Complete result available in ancillary file. Minor corrections and references added