Reducing theoretical uncertainties for exclusive Higgs plus one-jet production at the LHC

TL;DR

This work advances precision predictions for exclusive Higgs production in association with one jet by performing a full one-loop soft function calculation to achieve NLL' resummation accuracy and matching to NLO. The approach systematically factorizes the cross section into hard, soft, beam, and jet sectors within SCET, enabling controlled resummation of jet-veto logarithms in the Higgs+one-jet channel. Numerical studies for LHC-like cuts show that the RG-improved NLL'+NLO predictions drastically reduce theoretical uncertainties compared to fixed-order results, with significant impact on Higgs analyses relying on exclusive jet bins. The results support incorporating resummed predictions into experimental analyses and point to further refinements in low-p_T^J regimes and non-global effects.

Abstract

We resum a class of large Sudakov logarithms affecting Higgs boson production in the exclusive one-jet bin at the LHC. We extend previous results by calculating the full one-loop soft function for this process, which extends the accuracy of the resummation to include the leading three logarithmic corrections at each order in the QCD coupling constant. We match this result to the next-to-leading order cross section and present a detailed numerical study assuming realistic LHC cuts. Careful attention is paid to the matching procedure, and to the theoretical uncertainties induced by residual scale variation. We find that the matched NLL'+ NLO cross section has significantly smaller uncertainties than the fixed-order result, and can be used to alleviate the theoretical errors hindering current Higgs analyses at the LHC.

Figures (5)

• Figure 1: Shown are the fractional differences $(\sigma_{\rm NLO}-\sigma^{\rm exp}_{{\rm NLL}'})/\sigma_{\rm NLO}$ for $R = 0.4$ (solid blue), $0.1$(dashed orange) and $0.06$ (dotted red), respectively. The colored bands represent the estimated numerical uncertainties. The differences between the expanded $\text{NLL}^{\prime}$ and the fixed-order NLO calculations are small compared with the total cross section.
• Figure 2: $\Delta\sigma/\Delta p_T^J$ is the bin-integrated cross section for Higgs plus one jet as a function of $p_T^J$ divided by the bin width. We assume $p_T^{veto} = 30\,{\rm GeV}$. If we define the lower boundary of the $p_T^J \sim {\cal O}(m_H)$ region by $p_T^J=m_H/2$, we can estimate the contribution from $p_T^J \sim {\cal O}(m_H)$ to be around $30\%$.
• Figure 3: Shown is the interpolation between the resummed result and the fixed-order one proposed in Eq. (\ref{['inter']}). The blue solid and dotted lines are for $\kappa = 0.04$ and the red dashed and dot-dashed lines are for $\kappa = 0.2$. When $p_T^J$ is less than $p_{\rm off}$, all the scales merge to $\mu$ and the cross section takes its NLO value. We have demonstrated this behavior for the hard and soft scales in the plot.
• Figure 4: Presented here are the ${\rm NLO}$ v.s. ${\rm NLL}'+{\rm NLO}$ integrated cross sections with $p_T^J > 120\,{\rm GeV}$. The blue solid line is for the RG-improved cross section and the yellow dashed line is the NLO prediction . The narrow blue band is obtained using Eq. (\ref{['UNLL']}) for the uncertainty after resummation, while the wide yellow band comes from using Eq. (\ref{['UNLO']}) for the fixed-order uncertainty.
• Figure 5: Shown are the ${\rm NLL}^{\prime}+ {\rm NLO}$ (blue band) and NLO (yellow band) cross sections for fixed $p_T^{veto} = 30\,{\rm GeV}$ as a function of the lower cut on $p_T^J$.