Fermion-fermion scattering in a Rarita-Schwinger model with Yukawa-like interaction

In this work, we investigate the scattering of spin-$3\mathrm{/}2$ fermionic particles mediated by a Yukawa-like coupling in the context of the massive Rarita-Schwinger model. The interaction is introduced by replacing $m\to m_{\psi }+g\phi$ in the free spin-$3\mathrm{/}2$ Lagrangian. The analysis is performed at both zero and finite temperatures. In the latter case, thermal effects are incorporated using the Thermofield Dynamics (TFD) formalism. In both regimes, we obtain the differential and total cross sections and examine their behavior in the short-range ($m_{\phi }\mathrm{\ne }0$) and long-range ($m_{\phi }=0$) limits, in order to analyze the influence of zero- and finite-temperature effects.