Abstract
Precision tests of the Standard Model (SM) require not only accurate experiments, but also precise and reliable theoretical predictions. Triple vector boson production provides a unique opportunity to investigate the quartic gauge couplings and check the validity of the gauge principle in the SM. Since the tree-level predictions alone are inadequate to meet this demand, the next-to-leading order (NLO) calculation becomes compulsory. In this paper, we calculate the NLO QCD + NLO electroweak (EW) corrections to the $W^{\pm}ZZ$ productions with subsequent leptonic decays at the $14~{\rm TeV}$ LHC by adopting an improved narrow width approximation which takes into account the off-shell contributions and spin correlations from the $W^{\pm}$- and $Z$-boson leptonic decays. The NLO QCD+EW corrected integrated cross sections for the $W^{\pm}ZZ$ productions and some kinematic distributions of final products are provided. The results show that both the NLO QCD and NLO EW corrections are significant. In the jet-veto event selection scheme with $p_{T,jet}^{cut} = 50~ {\rm GeV}$, the NLO QCD+EW relative corrections to the integrated cross section are $20.5\%$ and $31.1\%$, while the genuine NLO EW relative corrections are $-5.42\%$ and $-4.58\%$, for the $W^+ZZ$ and $W^-ZZ$ productions, respectively. We also investigate the theoretical dependence of the integrated cross section on the factorization/renormalization scale, and find that the scale uncertainty is underestimated at the LO due to the fact that the strong coupling $\alpha_s$ is not involved in the LO matrix elements.
Highlights
CalculationsWe only take into account the Cabibbo-Kobayashi-Maskawa (CKM) mixing between the first two quark generations since the mixing to the third generation is negligible, i.e., the CKM matrix is 2 ⊕ 1 block-diagonal
Precision tests of the Standard Model (SM) require accurate experiments, and precise and reliable theoretical predictions
We see that the next-to-leading order (NLO) EW correction in the inclusive event selection scheme is positive but very small compared with the corresponding NLO QCD correction in the region of MW +ZZ > 400 GeV
Summary
We only take into account the Cabibbo-Kobayashi-Maskawa (CKM) mixing between the first two quark generations since the mixing to the third generation is negligible, i.e., the CKM matrix is 2 ⊕ 1 block-diagonal. The masses of the first two generations of quarks are set to zero. In this approximation, the CKM matrix factorizes from all the amplitudes, including the tree-level amplitudes for W ZZ, W ZZ + g, W ZZ + γ, W ZZ + q productions and the QCD and EW one-loop amplitudes for W ZZ production. Only one generic amplitude for each category mentioned above has to be evaluated when convoluting the squared matrix elements with the parton distribution functions (PDFs) [18]. We adopt the ’t Hooft-Feynman gauge and the four-flavor scheme in the calculations for the LO and NLO QCD + NLO EW corrections
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