Next to Soft Threshold Resummation for $VH$ Production

TL;DR

This work addresses precision predictions for Higgs–vector boson associated production ($VH$, with $V=Z,W$) at the LHC by incorporating threshold effects through soft-virtual (SV) and next-to-soft virtual (NSV) resummation to $\overline{\rm NNLL}$ accuracy and matching to NNLO fixed order. The authors formulate the cross section in Mellin space, separating SV and NSV contributions in the diagonal $q\bar{q}$ initial-state channel, and employ a minimal-prescription matching to fixed order using process-specific $C_0$ coefficients. Numerically, using MSHT20 NNLO PDFs and a $G_{\mu}$-scheme EW setup, they predict the invariant-mass distribution and total cross sections for $ZH$, $W^+H$, and $W^-H$ at $\sqrt{S}=13.6$ TeV, with SV providing $\sim$0.37–0.40\% enhancements to NNLO and NSV contributing an additional $\sim$0.53–0.61\%, yielding total NSV corrections around $0.89$–$1.02\%$. The NSV effects are modest but non-negligible, and while they can slightly raise scale uncertainties in some regions due to neglected channels, the $q\bar{q}$-initiated sector shows reduced $\mu_R$-uncertainties at high $Q$, and PDFs contribute up to ~5\% uncertainty at high invariant masses. Overall, the results refine Higgs precision predictions and bolster the reliability of coupling determinations and new-physics probes in VH production across current and future collider energies.

Abstract

We study the threshold effects for the associated production of a Higgs boson with a massive vector boson $(V=Z,W)$ in the $q\bar{q} \rightarrow V^\star \rightarrow VH$ process at the LHC. By leveraging the universality of threshold logarithms and employing soft-virtual (SV) and next-to-soft virtual (NSV) resummation techniques, we compute threshold corrections to next-to-next-to-leading logarithmic accuracy. After matching the resummed predictions to the Next-to-Next-to-Leading order (NNLO) fixed order results, we present the invariant mass distribution to NNLO$+\overline{\text{NNLL}}$ accuracy in QCD for the current LHC energies and the total production cross sections. The $VH$ production channel is crucial for studying the couplings of the Higgs boson to the vector bosons $(W,Z)$ and understanding the mechanism of electroweak symmetry breaking. Precision measurements of this process help test the validity of the standard model (SM) and can reveal potential deviations indicating new physics.

Figures (8)

• Figure 1: The invariant mass distribution with K-factor FO (left), SV (middle) and NSV (right) are shown for the $q\bar{q} \to ZH$ process at $13.6$ TeV LHC.
• Figure 2: The invariant mass distribution with K-factor FO (left), SV (middle) and NSV (right) are shown for the $q\bar{q}^{\prime} \to W^+H$ process at $13.6$ TeV LHC.
• Figure 3: The invariant mass distribution with K-factor FO (left), SV (middle) and NSV (right) are shown for the $q\bar{q}^{\prime} \to W^-H$ process at $13.6$ TeV LHC.
• Figure 4: The 7-point scale uncertainty $ZH$ (left), $W^+H$ (middle) and $W^-H$ (right) are shown at $13.6$ TeV LHC.
• Figure 5: The $\mu_R$ scale uncertainty $ZH$ (left), $W^+H$ (middle) and $W^-H$ (right) are shown at $13.6$ TeV LHC.