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

Some surprises in the neutrino cross sections associated with neutrino spin