Analytical formulas for elastic neutrino-fermion scattering cross sections

In this paper, analytical formulas for elastic neutrino-fermion scattering cross sections are presented. These are evaluated in the limit where the neutrino mass is neglible compared to the incoming momentum. The fermion mass is taken into account, however, yielding a good approximation to realistic scattering reactions. The intended level of readership is for undergraduates/graduates in the fields of relativistic quantum mechanics and quantum field theory. In addition to a detailed and pedagogical derivation of the analytical expressions, numerical results are also provided for $f=e,n,p$.