Testing neutrino magnetic moment in ionization of atoms by neutrino impact

Abstract

The atomic ionization processes induced by scattering of neutrinos play key roles in the experimental searches for a neutrino magnetic moment. Current experiments with reactor (anti)neutrinos employ germanium detectors having energy threshold comparable to typical binding energies of atomic electrons, which fact must be taken into account in the interpretation of the data. Our theoretical analysis shows that the so-called stepping approximation to the neutrino-impact ionization is well applicable for the lowest bound Coulomb states, and it becomes exact in the semiclassical limit. Numerical evidence is presented using the Thomas-Fermi model for the germanium atom.The neutrino magnetic moments (NMM) expected in the Standard Model are very small and proportional to the neutrino masses [1]: µ ν ≈ 3 × 10 −19 µ B (m ν /1 eV) with µ B = e/2m being the electron Bohr magneton, and m is the electron mass. Thus any larger value of µ ν can arise only from physics beyond the Standard Model (a recent review of this subject can be found in Ref.[2]). Current direct experimental searches [3,4,5] for a magnetic moment of the electron (anti)neutrinos from reactors have lowered the upper limit on µ ν down to µ ν < 3.2 × 10 −11 µ B [5]. These ultra low background experiments use germanium crystal detectors exposed to the neutrino flux from a reactor and search for scattering events by measuring the energy T deposited by the neutrino scattering in the detector. The sensitivity of such a search to NMM crucially depends on lowering the threshold for the energy transfer T , due to the enhancement of the magnetic scattering relative to the standard electroweak one at low T . Namely, the differential cross section dσ/dT is given by the incoherent sum of the magnetic and the standard cross section, and for the scattering on free electrons the NMM contribution is given by the formula [6,7] dσ (µ) dT = 4παµwhere E ν is the energy of the incident neutrino, and displays a 1/T enhancement at low energy transfer. The 1)

Electromagnetic Properties of Neutrinos

“…It was proposed in [49] that electron binding in atoms (the "atomic ionization" effect in neutrino interactions on Ge target) can significantly increase the electromagnetic contribution to the differential cross section with respect to the free electron approximation. However, detailed considerations of the atomic ionization effect in (anti)neutrino atomic electron scattering experiments presented in [50][51][52][53][54][55] show that the effect is by far too small to have measurable consequences even in the case of the low energy threshold of 2.8 keV reached in the GEMMA experiment [56].…”

Theory of Neutrino-Atom Collisions: The History, Present Status, and BSM Physics

“…4.1 to the onset of the K shell step, i.e. just above 10.9 keV, the difference from the shown in the plot step function would be practically invisible in the scale of Figure 5: The atomic factor f for germanium in the stepping approximation with the actual energies of the orbitals (solid line) and its interpolation in the Thomas-Fermi model (dashed) [49].…”

Electromagnetic interactions of neutrinos in processes of low-energy elastic neutrino-electron scattering

“…This approximation is supposed to be generally applicable if the energy-transfer value T is much larger than the electron binding energy in the detector (for the analysis and discussion of the effects beyond the free-electron approximation see, for instance, Refs. [8][9][10][11][12] and references therein). In the scattering experiments the observables are the kinetic energy T e of the recoil electron and/or its solid angle Ω e .…”