LHC bounds on Lepton Number Violation mediated by doubly and singly-charged scalars

The only possible doubly-charged scalar decays into two Standard Model particles are into pairs of same-sign charged leptons, H$^{\pm\pm}\rightarrow {l}^\pm {l}^\pm, {l} = e, \mu, \tau$, or gauge bosons, H$^{\pm\pm}\rightarrow W^\pm W^\pm$; being necessary the observation of both to assert the violation of lepton number. However, present ATLAS and CMS limits on doubly-charged scalar production are obtained under specific assumptions on its branching fractions into dileptons only. Although they can be extended to include decays into dibosons and lepton number violating processes. Moreover, the production rates also depend on the type of electroweak multiplet H$^{\pm\pm}$ belongs to. We classify the possible alternatives and provide the Feynman rules and codes for generating the corresponding signals for pair and associated doubly-charged scalar production, including the leading contribution from the $s$-channel exchange of electroweak gauge bosons as well as the vector-boson fusion corrections. Then, using the same analysis criteria as the LHC collaborations we estimate the limits on the H$^{\pm\pm}$ mass as a function of the electroweak multiplet it belongs to, and obtain the bounds on the lepton number violating processes $pp\rightarrow {\rm H}^{\pm\pm}{\rm H}^{\mp\mp} \rightarrow {\ell}^\pm {\ell}^\pm W^\mp W^\mp$ and $pp\rightarrow {\rm H}^{\pm\pm}{\rm H}^{\mp} \rightarrow {\ell}^\pm {\ell}^\pm W^\mp Z$, $\ell = e, \mu$, implied by the ATLAS and CMS doubly-charged scalar searches.