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.

本文介绍了轻子衰变通道中正向 Z 玻色子产生的微分截面的现象学研究，该截面是质子 - 质子碰撞中角变量\(\phi ^{*}_{\eta }\)的函数。的\（\披^ {*} _ {\ ETA} \）分布被预测用于正向赝区域\（2.0 <\ ETA _ {\文本{1}} <4.5 \）的衰减轻子在中心的- 8、13 和 14 TeV 的质量能量。\(\phi ^{*}_{\eta }\) 的准确预测分布是通过最先进的计算实现的，包括固定阶微扰 QCD 和大对数校正。预测分布是通过采用与微扰 QCD 匹配的next-to-next-to-leading 对数 (NNLL) 或 next-to-NNLL (N \(^{3}\) LL) 精度求和来获得的以紧邻前导顺序 (NNLO) 精度计算，即分别为 NNLO+NNLL 和 NNLO+N \(^{3}\) LL。Z 玻色子\(\phi ^{*}_{\eta }\)变量在实验上更可取，因为它比 Z 玻色子横向动量更精确地测量，尽管这两个变量探测相同的物理；因此，对\(\phi ^{*}_{\eta }\)变量需要使用 NNLO+NNLL 和 NNLO+N \(^{3}\) LL 精度的理论预测。通过 LHC 的 LHCb 实验，将匹配的预测与可用的 8-TeV 和 13-TeV 测量值进行比较，发现非常一致。还报告了 NNLO+NNLL 和 NNLO+N \(^{3}\) LL的 14-TeV 预测分布。在所有预测结果中，NNLO+N \(^{3}\) LL 为整个相空间中\(\phi ^{*}_{\eta }\)分布的可靠描述提供了更高的准确性地区。