Computing Massive 1→3 Splitting Kernels for Future Parton Shower Models

Splitting functions are the factorized forms of collinear dynamics in perturbative QCD, used to model complex parton showers. We compute the massive triple-collinear splitting kernels by layering scalar (semi-classical) interaction and fermionic interference terms, and compare to existing results for massive and massless splittings. This decomposition method enables systematic integration of the 1→3 splittings into current Monte-Carlo simulations, extending the precision of parton shower calculations, which are crucial to finding and understanding new physics in collider events.