Single pion resonant production in BSM scenarios: cross sections and amplitudes

TL;DR

This paper develops a theoretical framework for single pion resonant production via inelastic dark fermion-nucleon interactions, extending existing models to include various mediators and providing tools for dark sector research.

Contribution

It extends the Rein-Sehgal approach to include dark sector mediators and computes transition amplitudes using a relativistic quark model, offering new methods for dark matter interaction analysis.

Findings

Derived differential cross sections for dark fermion-nucleon scattering.

Extended the model to include vector, axial, scalar, and pseudoscalar mediators.

Provided a comprehensive framework for interpreting experimental dark matter data.

Abstract

We present a comprehensive theoretical framework describing single pion resonant production through inelastic dark fermion-nucleon interactions mediated by resonances in the GeV-scale regime. Building upon the Rein-Sehgal approach, we derive differential cross sections for processes in which an incoming dark fermion scatters off a nucleon, exciting a resonance that subsequently decays into a nucleon and a pion. Our formulation accommodates various mediator types-namely, dark photons with vector and axial couplings, as well as scalar and pseudoscalar mediators-thereby extending the conventional approach that Rein, Sehgal and Berger performed for neutrino interactions. Transition amplitudes for the nucleon-to-resonance conversion are computed using the relativistic harmonic-oscillator quark model from Feynman, Kislinger and Ravndal, while a Breit-Wigner prescription is employed to incorporate finite resonance widths. This framework offers a robust tool for interpreting experimental data in dark sector and matter searches and represents a contribution to elucidate the role of resonances in GeV-scale phenomenology.