"Signal paramertization for W$\phi$ with ee $\phi$ decay" of "Search for a scalar or pseudoscalar dilepton resonance produced in association with a massive vector boson or top quark-antiquark pair in multilepton events at $\sqrt{s}$ = 13 TeV"

A search for beyond the standard model spin-0 bosons, $\phi$, that decay into pairs of electrons, muons, or tau leptons is presented. The search targets the associated production of such bosons with a $\mathrm{W}$ boson, a $\mathrm{Z}$ boson, or a top quark-antiquark pair, and uses events with three or four charged leptons, including hadronically decaying tau leptons. The proton-proton collision dataset used in the analysis was collected by the CMS experiment at the LHC in 2016-2018 at a center-of-mass energy of $13\,\mathrm{TeV}$, and corresponds to an integrated luminosity of $138\,\mathrm{fb}^{-1}$. The observations are consistent with the expectations from standard model processes. Upper limits at $95\%$ confidence level are placed on the product of the cross sections and branching fractions of such new particles with scalar, pseudoscalar, or Higgs-like couplings, as well as the product of coupling parameters and branching fractions. These are the most restrictive direct limits in these production and decay modes on an extension of the standard model with scalar or pseudoscalar particles. Several model-dependent exclusions are also presented. For a Higgs-like $\phi$ model, limits are set on the mixing angle of the Higgs boson with the $\phi$ boson. For the associated production of a $\phi$ boson with a top quark-antiquark pair, limits are set on the coupling to top quarks. Finally, limits are set for the first time on a fermiophilic dilaton-like model with scalar couplings and an axion-like model with pseudoscalar couplings.