Impact of lepton $p_T$ threshold on the charge asymmetry predictions for the inclusive $W$ boson production in $pp$ collisions at 13 TeV

Abstract

This paper presents the impact of lepton transverse momentum $p_T^l$ threshold on the $W$ boson charge asymmetry predictions in perturbative QCD for the inclusive $W^{\pm }+X\to l^{\pm }\nu +X$ production in proton-proton ($pp$) collisions. The predictions are obtained with various low-$p_T^l$ thresholds $p_T^l>$ 20, 25, 30, and 40 GeV in a fiducial region encompassing both central and forward detector acceptances in terms of the lepton pseudorapidty 0 $\le {\eta }_l\le$ 4.5. The predicted distributions for the lepton charge asymmetry, which is defined by means of the ${\eta }_l$ ($A_{{\eta }_l}$), at next-to-next-to-leading order (NNLO) accuracy are compared with the CMS and LHCb data at 8 TeV center-of-mass collision energy. The 8 TeV predictions are observed to reproduce the data fairly well within the quoted uncertainties. The 13 TeV predictions by using various $p_T^l$ thresholds are reported for the $A_{{\eta }_l}$ and also the charge asymmetries that are defined in terms of the differential cross sections in bins of the $W$ boson rapidity $y_W$ ($A_{y_W}$) and transverse momentum $p_T^W$ ($A_{p_T^W}$). The NNLO predictions for the $A_{{\eta }_l}$, $A_{y_W}$, and $A_{p_T^W}$ distributions are assessed to be in close correlation with the $p_T^l$ value. The $A_{{\eta }_l}$ and $A_{y_W}$ distributions are particularly shown to be more correlated at a higher $p_T^l$ threshold. The $A_{p_T^W}$ distributions are also reported from the merged predictions with improved accuracy by the inclusion of next-to-next-to-next-to-leading logarithm (N${}^3$LL) corrections, i.e., at NNLO+N${}^3$LL. The predicted distributions from various $p_T^l$ thresholds represent also a finer probe to provide more constraints on the ratio of $u$ and $d$ quark distribution functions in the parton momentum fraction range $10^{-4}<x<1$.

11 pages, 7 figures

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