We offer to your attention a study “On scattering of massive neutral lepton on nucleus” published in the Physics of Elementary Particles and Atomic Nuclei journal. The author is Vadim Bednyakov (DLNP JINR). A theoretical approach to the description of the relativistic scattering of a massive (neutral) lepton on a nucleus, in which the latter retains its integrity, is presented in this paper.

The measured cross section of such a process includes an elastic (or coherent) contribution when the nucleus remains in its original quantum state and an inelastic (incoherent) contribution when the nucleus goes into another (excited) quantum state. Transition from the elastic scattering regime to the inelastic scattering regime is regulated automatically by the dependence of the nucleon-nucleus form factors on the momentum transferred to the nucleus. At small momentum transfers, elastic scattering dominates, with an increase in the transferred momentum, the proportion of inelastic scattering increases, which, in turn, becomes dominant at sufficiently large transferred momenta. The interaction of a point lepton with structureless nucleons of the target nucleus is considered as fundamental. This interaction is parameterized in a rather general form with four effective coupling constants, reflecting the (axial) vector nature of the weak interaction.

The scattering of massive (anti)neutrinos interacting with nucleons through the V ∓ A currents of the Standard Model is considered in detail. Due to the nonzero mass of the (anti)neutrino, an additional possibility arises for elastic and inelastic scattering of (anti)neutrinos on nuclei, due to the possibility of changing the helicity of these (anti)neutrinos. For example, despite the smallness of the mass of neutrinos at (kinetic) energies of (anti)neutrinos much lower than the mass of neutrinos (for example, relic ones), the cross section of their interaction with the nucleus turns out to be many times stronger, at least due to the “nucleus coherence effect”.

The obtained expressions for the cross sections are applicable in all cases of precision data analysis involving neutrinos and antineutrinos, especially when nonzero neutrino masses must be taken into account. These expressions could also be used in the analysis results of experiments on direct detection of neutral massive weakly interacting relativistic dark matter particles since, unlike the generally accepted case, both elastic and inelastic interactions of the particles with the target are simultaneously taken into account. In this case, the presence of an “inelastic signal” with its characteristic signature may be the only one registered evidence of the act of interaction of a particle of dark matter with the nucleus.

The study has been carried out at the Dzhelepov Laboratory of Nuclear Problems JINR.

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