The Higgs boson at high $p_T$

TL;DR

This paper develops a near-complete NLO calculation for Higgs plus jet that retains full top-quark mass dependence wherever possible. By decomposing the two-loop virtual amplitude and employing mt^-2/mt^-4 asymptotic expansions only for the finite part, the authors achieve improved convergence and extend reliable top-mass predictions up to about 225–250 GeV, with threshold behavior partially captured. They systematically compare EFT-based rescaling methods and advocate for using mt^2 corrections (NLO*) combined with EFT NNLO results to obtain accurate predictions across a wide kinematic range, providing practical guidance for experimental analyses and implementing the approach in MCFM. The work quantifies the residual mass-related uncertainties and clarifies when full mt-dependent calculations are necessary, especially at high p_T.

Abstract

We present a calculation of $H+j$ at NLO including the effect of a finite top-mass. Where possible we include the complete dependence on $m_t$. This includes the leading order amplitude, the infrared poles of the two-loop amplitude and the real radiation amplitude. The remaining finite piece of the virtual correction is considered in an asymptotic expansion in $m_t$, which is accurate to $m_t^{-4}$. By successively including more $m_t$-exact pieces, the dependence on the asymptotic series diminishes and we find convergent behavior for $p_T^H>m_t$ for the first time. Our results justify rescaling by the $m_t$-exact LO cross section to model top-mass effects in EFT results up to $p_T$ of 250 to 300 GeV. We show that the error made by using the LO rescaling becomes comparable to the NNLO scale uncertainty for such large energies. We implement our results into the Monte Carlo code MCFM.

Figures (10)

• Figure 1: Representative Feynman diagrams for the production of a Higgs boson plus one jet at LO (left) and NLO (center, right). The NLO corrections include two-loop "virtual" topologies (center), and one-loop Higgs plus two parton "real" topologies (right).
• Figure 2: Higgs inclusive $p_T$ spectrum for three different approximations, each taking into account higher orders of an asymptotic expansion in $1/m_t$. The upper panel shows the absolute distribution, while the lower two panels display the ratio to the .9 LO distribution and the .9 NLO$^*$$1/m_t^0$ approximation, respectively.
• Figure 3: Invariant mass spectrum of the Higgs plus hardest jet system at .9 LO. The upper part displays the absolute distribution, while the lower part displays the ratio to the .9 EFT result.
• Figure 4: Invariant mass spectrum of the Higgs plus hardest jet system at .9 NLO. The upper part displays the absolute distribution, while the lower part displays the ratio to the .9 EFT result.
• Figure 5: Ratio of the .9 NLO$^*$ finite virtual piece $\mathcal{F}^\text{in}_{\text{SI}}$ in the asymptotic expansion as in \ref{['eqn:virtmixed']} to the .9 LO rescaled .9 EFT virtual piece $\mathcal{F}^\text{in}\,\text{\scalefont{.9} NLO$^\dagger$}{}$ as in \ref{['eq:nlodag']}.