$W^\pm Z$ production at the LHC: fiducial cross sections and distributions in NNLO QCD

TL;DR

The paper tackles the need for precise W^Z predictions by delivering the first fully differential NNLO QCD calculation that includes leptonic decays with off-shell effects, spin correlations, and interference, in SF and DF channels. The calculation employs the MATRIX framework with q_T-subtraction, integrating OpenLoops for amplitudes and Collier for tensor integrals, and uses a complex-mass scheme to handle resonances.Phenomenological results show NNLO corrections of about 10% over NLO for fiducial cross sections, with significantly reduced scale uncertainties, and improved agreement with ATLAS data at 8/13 TeV, while CMS 13 TeV fiducial results show a notable but explicable tension due to cut definitions and dataset size.The work provides high-precision differential predictions for W^Z that are crucial for EW precision tests and for modeling SM backgrounds in new-physics searches, and it sets the stage for public availability of the Matrix implementation.

Abstract

We report on the first fully differential calculation for $W^\pm Z$ production in hadron collisions up to next-to-next-to-leading order (NNLO) in QCD perturbation theory. Leptonic decays of the $W$ and $Z$ bosons are consistently taken into account, i.e. we include all resonant and non-resonant diagrams that contribute to the process $pp\to \ell^{'\pm} ν_{\ell^{'}} \ell^+\ell^-+X$ both in the same-flavour ($\ell'=\ell$) and the different-flavour ($\ell'\neq \ell$) channel. Fiducial cross sections and distributions are presented in the presence of standard selection cuts applied in the experimental $W^\pm Z$ analyses by ATLAS and CMS at centre-of-mass energies of 8 and 13\,TeV. As previously shown for the inclusive cross section, NNLO corrections increase the NLO result by about $10\%$, thereby leading to an improved agreement with experimental data. The importance of NNLO accurate predictions is also shown in the case of new-physics scenarios, where, especially in high-$p_T$ categories, their impact can reach ${\cal O}(20\%)$. The availability of differential NNLO predictions will play a crucial role in the rich physics programme that is based on precision studies of $W^\pm Z$ signatures at the LHC.

Figures (18)

• Figure 1: Sample of Born diagrams contributing to $W^+Z$ production both in the different-flavour channel ($\ell\neq \ell^\prime$) and in the same-flavour channel ($\ell=\ell^\prime$). The analogous diagrams for $W^-Z$ production are achieved by charge conjugation.
• Figure 2: Dependence of the $pp\rightarrow\ell'^\pm{\nu}_{\ell^\prime} \ell^-\ell^++X$ cross sections on the $q_T$-subtraction cut, $r_{\mathrm{cut}}{}$, for both NLO (left plots) and NNLO (right plots) results in the ATLAS signal region at 13 TeV (upper plots) and in the CMS signal region at 8 TeV cuts (lower plots). NLO results are normalized to the $r_{\mathrm{cut}}$-independent NLO cross section computed with Catani--Seymour subtraction, and the NNLO results are normalized to their values at $r_{\mathrm{cut}}\rightarrow0$, with a conservative extrapolation error indicated by the blue bands.
• Figure 3: Distribution in the transverse momentum of the reconstructed (a) $Z$ and (b) $W$ bosons at LO (black, dotted), NLO (red, dashed) and NNLO (blue, solid) compared to the corresponding ATLAS data at 8 TeV (green points with error bars). The lower panel shows the ratio over the NLO prediction.
• Figure 4: Same as Figure \ref{['fig:pTZW']}, but for (a) the transverse mass of the $WZ$ system as defined in Eq. (\ref{['eq:mTWZ']}) and (b) the missing transverse energy.
• Figure 5: Same as Figure \ref{['fig:pTmissmTWZ']} (b), but separated by (a) $W^-Z$ and (b) $W^+Z$ production.