A quantitative study on helicity inversion in Majorana neutrino decays at the LHC

We report an analytical and numerical investigation into the impact of helicity inversion in LHC processes that do not conserve lepton number $(L)$. As a case study, we focus on the production and decay of Majorana neutrinos $(N)$ through on- and off-shell $W$ bosons in the Phenomenological Type I Seesaw model. Using the Monte Carlo event generator \texttt{MadGraph5\_aMC@NLO} in conjunction with the \texttt{HeavyN} model libraries, we perform exact matrix element (ME) computations without the narrow width approximation. Despite helicity inversion appearing explicitly in MEs, we report the absence of helicity suppression of $L$-violating collider observables for $1\to4$ and $2\to4$ processes that are dominated by resonant $N$ production. We attribute this incongruity to the different scalings of 4-momenta and squared 4-momenta in MEs and squared MEs, with exact cancelations occurring in the latter when $N$ goes on-shell in the small-width limit. In off-shell regimes, total suppression / enhancement of $L$ violation can emerge. Implications for other neutrino mass models are discussed.