This paper presents the impact of lepton transverse momentum $p^{ l}_{ T}$ threshold on the $W$ boson charge asymmetry predictions in perturbative QCD for the inclusive $W^{ \pm}+X \rightarrow l^{ \pm} \nu +X$ production in proton-proton ($pp$) collisions. The predictions are obtained with various low-$p^{ l}_{ T}$ thresholds $p^{ l}_{ T} >$ 20, 25, 30, and 40 GeV in a fiducial region encompassing both central and forward detector acceptances in terms of the lepton pseudorapidty 0 $\leq \eta_{ l} \leq$ 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 $p^{ l}_{ T}$ 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 $p^{ W}_{ T}$ ($A_{ p^{ W}_{ T}}$). The NNLO predictions for the $A_{ \eta_{ l}}$, $A_{ y_{ W}}$, and $A_{ p^{ W}_{ T}}$ distributions are assessed to be in close correlation with the $p^{ l}_{ T}$ value. The $A_{ \eta_{ l}}$ and $A_{ y_{ W}}$ distributions are particularly shown to be more correlated at a higher $p^{ l}_{ T}$ threshold. The $A_{ p^{ W}_{ T}}$ 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 $p^{ l}_{ T}$ 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 $10^{ -4} < x < 1$.
Categories: hep-ph