Accurate prediction of the $$\phi ^{*}_{\eta }$$ distribution for the forward Z boson production in pp collisions through NNLO+N$$^{3}$$LL

Abstract

This paper presents a phenomenological study for the differential cross section of the forward Z boson production in leptonic decay channels as a function of the angular variable \(\phi ^{*}_{\eta }\) in proton–proton collisions. The \(\phi ^{*}_{\eta }\) distribution is predicted for the forward pseudorapidity region \(2.0< \eta _{\text {l}} < 4.5\) of the decay leptons at center-of-mass energies of 8, 13, and 14 TeV. Accurate prediction of the \(\phi ^{*}_{\eta }\) distribution is achieved by means of state-of-the-art calculations including fixed-order perturbative QCD and large logarithmic corrections. The predicted distributions are obtained by employing the resummation either at next-to-next-to-leading logarithmic (NNLL) or next-to-NNLL (N\(^{3}\)LL) accuracy which is matched to the perturbative QCD calculation at next-to-next-to-leading order (NNLO) accuracy, that is at NNLO+NNLL and NNLO+N\(^{3}\)LL, respectively. The Z boson \(\phi ^{*}_{\eta }\) variable is experimentally preferable as it has been measured more precisely than the Z boson transverse momentum, though both variables probe the same physics; therefore, an accurate description of the \(\phi ^{*}_{\eta }\) variable is required using theoretical predictions at both NNLO+NNLL and NNLO+N\(^{3}\)LL accuracies. The matched predictions are compared with the available 8-TeV and 13-TeV measurements by the LHCb experiment at the LHC and found to be in good agreement. The 14-TeV predicted distributions at both NNLO+NNLL and NNLO+N\(^{3}\)LL are also reported. In all the predicted results, the NNLO+N\(^{3}\)LL provides more improved accuracy for the reliable description of the \(\phi ^{*}_{\eta }\) distribution throughout its entire phase space region.