Study of Kinematic Distributions in W Boson and $D$(*) Meson Production in $pp$ Collisions

The production of a $W$ boson in association with a charm quark is a valuable process to study the relatively unconstrained strange quark parton distribution function of the proton. This work presents an analysis of gluon splitting as an important but not well understood background process to $W+c$ production. The $W$ boson and the $D^+$ meson or $D^*$ meson, collectively referred to as $D^{(*)}$ meson, arising from the hadronization of the charm quark, have opposite-sign charge (OS), while gluon splitting has no preferred charge relation. Therefore, Monte Carlo generated predictions of gluon splitting processes are studied using the ratio of SS (same-sign charge) to the difference between OS and SS distributions. Differential cross sections as a function of the transverse momentum of the $D^{(*)}$ meson, $p_T^{D^{(*)}}$, the absolute pseudorapidity of the $D^{(*)}$ meson, $|\eta(D^{(*)})|$, and the azimuthal angle between the charged lepton and the $D^{(*)}$ meson, $\Delta\phi(\ell, D^{(*)})$, are presented using Monte Carlo generated data. These Monte Carlo samples show that gluon splitting, in comparison to the direct $W+c$ production processes, has dominatly lower $p_T^{D^{(*)}}$, and that the contribution of gluon splitting is enhanced for larger $|\eta(D^{(*)})|$ and smaller $\Delta\phi(\ell, D^{(*)})$. Furthermore, the two generators Sherpa_2.2.11 and MadGraph5_aMCatNLO are compared. It is shown that MadGraph predicts less gluon splitting than Sherpa for low $p_T^{D^{(*)}}$ and high $\Delta\phi(\ell, D^{(*)})$ and also that the two generators make different predictions for gluon splitting in the observable $|\eta(D^{(*)})|$.