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This paper presents a phenomenological study for the differential crosssection of the forward Z boson production in leptonic decay channels as afunction of the angular variable $\phi^{*}_{\eta}$ in proton-proton collisions.The $\phi^{*}_{\eta}$ distribution is predicted for the forward pseudorapidityregion $2.0 < \eta_{l} < 4.5$ of the decay leptons at center-of-mass energies8, 13, and 14 TeV. Accurate prediction of the $\phi^{*}_{\eta}$ distribution isachieved by means of the state-of-the-art calculations including fixed-orderperturbative QCD and large logarithmic corrections. The predicted distributionsare obtained by employing the resummation either at next-to-next-to-leadinglogarithmic (NNLL) or next-to-NNLL (N$^{3}$LL) accuracy which is matched to theperturbative 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 measuredmore precisely than the Z boson transverse momentum though both variables probethe same physics, thereby an accurate description of the $\phi^{*}_{\eta}$variable is required by using theoretical predictions at both NNLO+NNLL andNNLO+N$^{3}$LL accuracies. The matched predictions are compared with theavailable 8 TeV and 13 TeV measurements by the LHCb experiment at the LHC andfound to be in good agreement. The 14 TeV predicted distributions at bothNNLO+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 descriptionof the $\phi^{*}_{\eta}$ distribution throughout its entire phase space region.

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