$Zγ$ production at NNLO including anomalous couplings

TL;DR

This work delivers a fully differential NNLO QCD prediction for Zγ production at the LHC, including decays to neutrinos and charged leptons, implemented in MCFM with jettiness slicing. It extends the calculation to include anomalous Zγγ and ZZγ couplings, enabling consistent NNLO constraints on new physics without ad hoc form factors. The authors validate their implementation against existing results, study slicing parameter behavior, and demonstrate modest but important NNLO corrections across 13 TeV phenomenology, including backgrounds to H→Zγ and sensitivity to anomalous couplings. The combination of high numerical precision, robust validation, and public availability makes this a valuable resource for precision electroweak studies and new physics searches at the LHC.

Abstract

In this paper we present a next-to-next-to-leading order (NNLO) QCD calculation of the processes $pp\rightarrow l^+l^-γ$ and $pp\rightarrow ν\barνγ$ that we have implemented in MCFM. Our calculation includes QCD corrections at NNLO both for the Standard Model (SM) and additionally in the presence of $Zγγ$ and $ZZγ$ anomalous couplings. We compare our implementation, obtained using the jettiness slicing approach, with a previous SM calculation and find broad agreement. Focusing on the sensitivity of our results to the slicing parameter, we show that using our setup we are able to compute NNLO cross sections with numerical uncertainties of about $0.1\%$, which is small compared to residual scale uncertainties of a few percent. We study potential improvements using two different jettiness definitions and the inclusion of power corrections. At $\sqrt{s}=13$ TeV we present phenomenological results and consider $Zγ$ as a background to $H\to Zγ$ production. We find that, with typical cuts, the inclusion of NNLO corrections represents a small effect and loosens the extraction of limits on anomalous couplings by about $10\%$.

Figures (14)

• Figure 1: Normalized .9 NLO cross section coefficient for the charged lepton decay channel with standard cuts given in \ref{['tab:cuts-8TeV-Zepem']} and loose cut modifications in \ref{['eq:loosecuts']}. Shown is the dependence on the jettiness slicing cutoff parameter $\tau_\text{cut}$. The results are obtained using the hadronic (.9 MCFM-8.0) jettiness definition with and without power corrections and additionally for the boosted definition. For performance comparison, the cross section is normalized to the cutoff independent Catani-Seymour result.
• Figure 2: Normalized .9 NLO coefficient pseudorapidity distribution for the charged lepton decay channel with standard cuts given in \ref{['tab:cuts-8TeV-Zepem']} and loose cut modifications in \ref{['eq:loosecuts']}. The distributions are obtained with $\tau_\text{cut}=1.6\GeV$ using the boosted and hadronic (.9 MCFM-8.0) jettiness definitions, normalized to the Catani-Seymour obtained result. The numerical uncertainties of the outermost bins are large since the distribution has been generated on the fly for the integrated cross section.
• Figure 3: $\tau_\text{cut}$ dependence of the $Z(\to \nu\bar{\nu})\gamma$.9 NLO cross section coefficient with .9 NLO .9 PDFs and cuts given in \ref{['tab:cuts-8TeV-Znunu']}. The horizontal blue solid and dashed lines represent the C.-S. obtained result of 22.572(3)fb and its numerical uncertainty, respectively. The horizontal red dot-dashed and dotted lines represent the fitted asymptotic value of 22.57(1)fb and its numerical uncertainty, respectively, while the solid black line shows the fitted result.
• Figure 4: $\tau_\text{cut}$ dependence of .9 NNLO cross section coefficient in the neutrino decay channel with given cuts in \ref{['tab:cuts-8TeV-Znunu']} . The horizontal red solid and dashed lines represent the fitted asymptotic value of 8.3±0.1fb and its numerical uncertainty, respectively, while the solid black line shows the fitted result. The blue dot-dashed and dotted lines show the reconstructed .9 NNLO coefficient and its numerical uncertainty, respectively, from the .9 NNLO result given in ref. Grazzini:2015nwa.
• Figure 5: $\tau_\text{cut}$ dependence of the .9 NNLO cross section coefficient in the charged lepton decay channel with cuts given in \ref{['tab:cuts-8TeV-Zepem']}. The horizontal red solid and dashed lines represent the fitted asymptotic value of 22.0±0.2fb and its numerical uncertainty, respectively, while the solid black line shows the fitted result. The blue dot-dashed and dotted lines show the reconstructed .9 NNLO coefficient and its numerical uncertainty, respectively, from the .9 NNLO result given in ref. Grazzini:2015nwa.