Large-Width New Physics at Colliders: A Gauge-Invariant Resummation Approach

Broad resonances challenge the standard Monte-Carlo treatment of unstable particles, which introduces a Breit-Wigner width into leading-order matrix elements and can generate unphysical gauge artifacts. We develop a gauge-consistent framework that combines a Dyson-resummed propagator with Slavnov-Taylor-identity-implied resummed vertices, enabling a consistent implementation in MadGraph5. In the Type-I seesaw model, heavy Majorana neutrinos naturally satisfy $\Gamma \sim m$, leading to strong departures from the Breit-Wigner lineshape, distorted angular correlations, and significant modifications to both $s$- and $t$-channel dynamics. Comparing with the normal and complex-mass schemes, we find that standard treatments can substantially misestimate cross sections and kinematic distributions in the large-width regime. Our results show that existing collider limits on heavy neutrinos-and, more generally, on any broad resonance-should be revisited within a fully resummed framework, opening new opportunities for both experimental searches and theoretical model building.