Constraining neutrino electromagnetic properties by germanium detectors

The electromagnetic properties of neutrinos, which are either trivial or negligible in the context of the Standard Model, can probe new physics and have significant implications in astrophysics and cosmology. The current best direct limits on the neutrino millicharges and magnetic moments are both derived from data taken with germanium detectors with low thresholds at keV levels. In this paper, we discuss in detail a robust, ab initio method: the multiconfiguration relativistic random-phase approximation, that enables us to reliably understand the germanium detector response at the sub-keV level, where atomic many-body physics matters. By using existing data with sub-keV thresholds, limits on the reactor antineutrino’s millicharge, magnetic moment, and charge radius squared are derived. The projected sensitivities for next-generation experiments are also given and discussed.

Figure 1

Photoabsorption cross sections of Ge. The data are taken from Ref. [39]. The MCRRPA line in panel (a) shows our numerical results; the one in panel (b) is obtained by forcing all shell energies aligned to the experimental edge energies.

Figure 2

Normalized contributions from the series of charge multipole operators $C_J$’s to differential cross sections for (a) weak interaction, (b) magnetic-moment interaction, and (c) millicharge interaction. The incident neutrino has 1 MeV energy and deposits 1 keV energy.

Figure 3

Differential cross sections for germanium ionization by neutrino weak interaction with neutrino incident energies (a) $E_{\nu }=1\mathrm{MeV}$ and (b) $E_{\nu }=10\mathrm{keV}$. (See also Fig. 2 in Ref. [17].)

Figure 4

Differential cross sections for germanium ionization by neutrino magnetic-moment interaction with neutrino incident energies (a) $E_{\nu }=1\mathrm{MeV}$ and (b) $E_{\nu }=10\mathrm{keV}$, in units of ${\mathbb{\kappa }}_{\nu }^{(\text{eff})2}$. (See also Fig. 2 in Ref. [17].)

Figure 5

Differential cross sections for germanium ionization by neutrino millicharge interaction with neutrino incident energies (a) $E_{\nu }=1\mathrm{MeV}$ and (b) $E_{\nu }=10\mathrm{keV}$, in units of ${\mathbb{q}}_{\nu }^2$.

Figure 6

Differential cross sections for germanium ionization by neutrino charge radius interaction with neutrino incident energies (a) $E_{\nu }=1\mathrm{MeV}$ and (b) $E_{\nu }=10\mathrm{keV}$, in units of $2c_V\rho +{\rho }^2$ and $\rho \equiv \frac{\sqrt{2}\pi }{3}\frac{\alpha }{G_F}{⟨{\mathbb{r}}_{\nu }^2⟩}^{(\text{eff})}$.

Figure 7

Expected measurable spectra with Ge on the various neutrino electromagnetic effects from reactor neutrinos (${\overline{\nu }}_e$) at a flux of $10^{13}{\mathrm{cm}}^{-2}{\mathrm{s}}^{-1}$. The spectra from SM weak processes involving the electrons (${\overline{\nu }}_{e}e$) and the nucleus (${\overline{\nu }}_{e}N$) are also included for comparisons.

Figure 8

Differential cross sections of germanium ionization by neutrinos of tritium $\beta$ decay through (a) weak and (b) neutrino magnetic-moment interaction assuming ${\mathbb{\kappa }}_{\nu }^{(\text{eff})}=5\times 10^{-12}{\mu }_{\mathrm{B}}$.