Some surprises in the neutrino cross sections associated with neutrino spin

It is generally assumed that neutrino masses can be neglected to a high degree of approximation in cross section calculations. This assumption seems very reasonable since the neutrino masses are extremely small and the neutrinos are ultrarelativistic fermions at the energy scales of current experiments. Consequently, in cross section calculations in the Quantum Field Theory, the Standard Model neutrinos are frequently assumed to be described by 100% negative helicity states. This assumption is true in a sense that in the Standard Model processes the positive helicity states can be safely neglected for ultrarelativistic neutrinos. On the other hand, the assumption tacitly assert that the neutrino fields are completely longitudinally polarized, i.e., the contribution to the cross section coming from transverse polarization can be neglected. We show that this tacit assertion is not correct. Although the Standard Model cross section for a neutrino with positive helicity goes to zero as m-> 0, the cross section for a neutrino with transverse polarization remains finite in that limit. Thus the contribution coming from transverse polarization cannot be neglected even in the ultrarelativistic/zero-mass limit. We examine the consequences of this fact and deduce that it has some unexpected results in the neutrino cross sections.