Two loop correction to interference in $gg \to ZZ$

TL;DR

The paper addresses the interference between Higgs-mediated and continuum $gg\to ZZ$ production, computing two-loop (NLO) corrections and including heavy-quark mass effects via a large-mass expansion. It combines expansion-by-regions, rescaling, conformal mapping, and Padé approximants to extend the validity of the massive-quark contributions and validates these approaches against known exact results. The authors provide comprehensive virtual corrections for massive quark loops, separate non-anomalous and anomalous diagrams, and include real-emission contributions, delivering predictions for LHC phenomenology. Their results show negative interference that remains significant in the high-$M_{ZZ}$ region, with $K$-factors around 2, and they offer robust off-shell predictions to help bound the Higgs width. This work furnishes practical, theoretically controlled inputs for off-shell Higgs analyses and width extractions at the LHC.

Abstract

We present results for the production of a pair of on-shell Z bosons via gluon fusion. This process occurs both through the production and decay of the Higgs boson, and through continuum production where the Z boson couples to a loop of massless quarks or to a massive quark. We calculate the interference of the two processes and its contribution to the cross section up to and including order O(alpha_s^3). The two-loop contributions to the amplitude are all known analytically, except for the continuum production through loops of top quarks of mass m. The latter contribution is important for the invariant mass of the two Z bosons, (as measured by the mass of their leptonic decay products, m_4l), in a regime where m_4l > 2m because of the contributions of longitudinal bosons. We examine all the contributions to the virtual amplitude involving top quarks, as expansions about the heavy top quark limit. Comparison with the analytic results, where known, allows us to assess the validity of the heavy quark expansion, and it extensions. We give results for the NLO corrections to this interference, including both real and virtual radiation.

Figures (16)

• Figure 1: Representative diagrams for the $ZZ$ production. In the following we will suppress the $Z$-decays to leptons.
• Figure 2: Representative diagrams for the LO+NLO virtual $gg\to H\to ZZ$ amplitude.
• Figure 3: Left panel: Leading-order $gg\to H\to ZZ$ cross section. 1.) LME up to $1/m^{20}$ (orange). 2.) Exact result (black), LME with conformal mapping (blue) and Padé approximants$[4/4],[4/5],[5/4],[5/5]$ (yellow, purple, green, brown) agree perfectly. Right panel: Virtual NLO corrections to $gg\to H\to ZZ$ cross section. See text for details. Color code as in left panel. The bottom plots show the relative deviations with respect to the exact (N)LO results. The vertical dashed line denotes the top quark pair-production threshold.
• Figure 4: Virtual NLO corrections to $gg\to H\to ZZ$ cross section with rescaling from Eq. \ref{['eq:LME_rescaled']}. See text for details. 1.) Exact NLO result (black). 2.) Varying orders of rescaled LMEs are indicated by shaded grey area. Its envelope is given by $\sigma_{\text{imp},1}^\text{NLO}$ (orange) and $\sigma_{\text{imp},10}^\text{NLO}$ (blue). The bottom plot shows the relative deviations with respect to the exact NLO results. The vertical dashed line denotes the top quark pair-production threshold.
• Figure 5: Representative diagrams for the LO and virtual NLO $gg\to ZZ$ amplitude.