Measurements of the production of W$^{ pm}$ and Z$^0$ bosons in pp collisions at $ sqrt{s} = 13$ TeV

Measurements of the production of the W$^{\pm}$ and Z$^0$ bosons at midrapidity in pp collisions at $\sqrt{s} = 13$ TeV with ALICE at the Large Hadron Collider (LHC) are presented. The W$^{\pm}$ and Z$^0$ bosons are detected via their (di)electronic decay channels, with the electron reconstruction performed in the midrapidity region ($|y|< 0.6$). The $p_{\rm T}$-integrated and $p_{\rm T}$-differential production cross sections of electrons from W$^{\pm}$ decays in the interval $30 < p_{\rm T} < 60$ GeV/$c$, as well as the $p_{\rm T}$-integrated production cross section of Z$^0$ bosons, are measured. The results are described by perturbative QCD calculations using different sets of parton distribution functions. The production of W$^{\pm}$ bosons and azimuthally correlated associated hadrons is also measured as a function of the charged-particle multiplicity for the first time at the LHC. The former increases approximately linearly with the charged-particle multiplicity, while for the latter, there are hints of a faster-than-linear increase. These observations are compared with theoretical calculations.