Resummation Effects in Vector-Boson and Higgs Associated Production

TL;DR

The paper addresses the challenge of predicting VH (V=W,Z) production at hadron colliders in the presence of large logarithms that arise near partonic threshold and at low transverse momentum. It combines fixed-order QCD calculations up to NNLO with separate soft-gluon resummations for threshold and $p_T$—logarithms, using $b$-space resummation and SCET-inspired threshold factorization, with careful matching to fixed-order results. The main findings show that NNLL/NNNNL threshold resummation barely shifts the total cross section from the NNLO result, and the NNNLL result closely tracks NNLO, indicating excellent perturbative convergence; the $p_T$ resummation yields reliable low-$p_T$ predictions and clarifies the impact of jet vetoes. These results enhance the precision of VH rate predictions and can be extended to other electroweak color-singlet productions, aiding Higgs coupling studies and searches at the LHC.

Abstract

Fixed-order QCD radiative corrections to the vector-boson and Higgs associated production channels, pp -> VH (V=W, Z), at hadron colliders are well understood. We combine higher order perturbative QCD calculations with soft-gluon resummation of both threshold logarithms and logarithms which are important at low transverse momentum of the VH pair. We study the effects of both types of logarithms on the scale dependence of the total cross section and on various kinematic distributions. The next-to-next-to-next-to-leading logarithmic (NNNLL) resummed total cross sections at the LHC are almost identical to the fixed-order perturbative next-to-next-to-leading order (NNLO) rates, indicating the excellent convergence of the perturbative QCD series. Resummation of the VH transverse momentum (p_T) spectrum provides reliable results for small values of p_T and suggests that implementing a jet-veto will significantly decrease the cross sections.

Figures (7)

• Figure 1: The (a) soft scale, (b) hard scale, and (c) factorization scale dependence of the threshold resummed cross section for $pp\rightarrow ZH$ at NLL between the dotted lines dotted, NNLL between the dashed lines, and NNNLL between the solid lines normalized to the LO result (the $K$-factor is defined in Eqs. (\ref{['eq:K']}) and (\ref{['eq:Kthresh']})). The invariant mass $M_{ZH}$ is fixed at $1$ TeV.
• Figure 2: Scale dependence of the fixed order (dashed) and threshold resummed matched (solid) cross sections for (a,b) $ZH$ and (c,d) $WH$ production at (a,c)$\sqrt{s}= 8$ TeV and (b,d) $\sqrt{s}=14$ TeV. The NNLO and NNNLL-NNLO matched $ZH$ results include the contribution from the $gg$ initial state.
• Figure 3: Transverse-momentum distributions for (a,c) $ZH$, and (b,d) $WH$ production at the LHC. In (a) and (b), the matched distribution is shown with a solid line, the resummed distribution with a dot-dash line, the fixed-order expansion of the resummed distribution with a dashed line and the fixed-order perturbative distribution with a dotted line at $\sqrt{s}=14$ TeV. In (c) and (d), the normalized matched transverse-momentum distributions are shown for both $\sqrt{s}=8$ TeV (dashed) and $\sqrt{s}=14$ TeV (solid) LHC.
• Figure 4: Integrated matched transverse-momentum distributions normalized to the total cross section for both (a) $ZH$ and (b) $WH$ production. Results for $\sqrt{s}=8$ TeV and $\sqrt{s}=14$ TeV are shown with dashed and solid lines, respectively.
• Figure 5: $K$-factor distributions at $\sqrt{s}=14$ TeV for (a) $ZH$ and (b) $WH$ production. The NNLL-NLO matched result is shown with solid lines, the NNLL threshold resummed result with dot-dashed lines, the leading threshold singularity of the NLO fixed-order result with dotted lines, and the NLO fixed-order result with dashed lines.