Elastic neutrino-proton scattering

A general analysis of elastic neutrino- and antineutrino-proton scattering is presented which emphasizes the use of these processes as probes of the space-time structure of the weak neutral current. We begin by exhibiting the most general matrix elements in terms of the scalar (S), pseudoscalar (P), tensor (T), vector (V), and axial-vector (A) form factors. These matrix elements are then used to calculate the differential cross sections dσdt and the proton polarization for incident ν_μ and ν_μ. Based on these results tests are suggested to discriminate between the S,P,T and V,A covariants which respectively flip or preserve the incident neutrino helicity. It is noted that when V, A, and T are all absent from the neutral current, the differential cross sections take the simple form dσ^ν,νdt = tf(t)E_ν^_², where E_ν is the laboratory energy of the incident neutrinos, t is the square of the momentum transfer, and $f(t)$ is a proton form factor. This observation suggests several ways of discriminating between S,P,T and V,A couplings including a comparison of dσ^νdt and dσ^νdt, and an examination of the average momentum transfer $〈t〉$. Since some of these tests are subject to the "confusion theorem" (i.e., the ability of S,P,T to mimic V,A), consideration is given to experiments in which the proton polarization is measured. Although such experiments are difficult to perform, the expected effects are strikingly large, and can lead to an unambiguous disentangling of V,A from S,P,T. A discussion is also given of the ν and ν elastic cross sections which, when compared to experiment, suggest that the neutral current is not predominantly S,P.