Magnetic moments of active and sterile neutrinos

Since most of the neutrino parameters are well measured, we illustrate precisely the prediction of the Standard Model, minimally extended to allow massive neutrinos, for the electron neutrino magnetic moment. We elaborate on the effects of light sterile neutrinos on the effective electron neutrino magnetic moment measured at the reactors. We explicitly show that the kinematical effects of the neutrino masses are negligible even for light sterile neutrinos.

Figure 1

The fractional ratio of Eq. (2.2) as a function of the neutrino mass. The solid line is for the case $m_j=0$; i.e., the $x$ axis of the plot is $m_i$. The dotted line is when $m_i=m_j=\text{variable}$ of the $x$ axis. The dashed line is for the case $m_i=0$; i.e., the variable in the $x$ axis is $m_j$. The electron recoil energy is taken to be GEMMA’s threshold energy of 2.8 keV.

Figure 2

Log-log plot of the weak and electromagnetic components of the differential cross section for neutrino-electron scattering averaged over the antineutrino spectrum of fissioning ${}^{235}\mathrm{U}$. The inset plot is the weak correction on the linear scale both with (dashed line) and without (solid line) radiative corrections [21].

Figure 3

Standard Model prediction for the magnetic moment of a Dirac neutrino as a function of the lowest neutrino mass, measured in a reactor experiment. NH and IH denote normal and inverted mass hierarchies, respectively. The neutrino mass differences and mixing angles are taken from the compilation of the Particle Data Group [24]. The error bands represent the experimental errors in the mass splittings and the mixing angles.

Figure 4

Standard Model prediction for the magnetic moment of a Dirac neutrino as a function of the sum of neutrino masses, measured in a reactor experiment. NH and IH denote normal and inverted mass hierarchies, respectively. The vertical lines denote the range $0.32\le \sum _i{m}_i\le 0.98\mathrm{eV}$ from the analysis of the most recent Planck data [26].

Figure 5

Standard Model prediction for the magnetic moment of a Majorana neutrino measured in a reactor experiment. NH and IH denote normal and inverted mass hierarchies, respectively. The error bands represent the experimental errors in the mass splittings and the mixing angles as well as the range of the Majorana phases ${\alpha }_1$ and ${\alpha }_2$ (see the Appendix) while keeping $\delta =0$.

Figure 6

Same as Fig. 4 but for a Majorana neutrino. NH and IH denote normal and inverted mass hierarchies, respectively.

Figure 7

The contribution of the phases with arguments $(E_4-E_i)L\sim (\delta m_{4i}^{2}L)/2E$ to the count rate as a function of the distance from the point of neutrino production $L$. The dashed (black) line is for $\delta m_{4i}^2=1{\mathrm{eV}}^2$, the solid (red) line is for $\delta m_{4i}^2=1.78{\mathrm{eV}}^2$, and the dotted (blue) line is for $\delta m_{4i}^2=3{\mathrm{eV}}^2$. The electron kinetic energy is taken to be $T_e=2.8\mathrm{keV}$ (GEMMA’s threshold).

Figure 8

The allowed regions of the sterile neutrino contribution ${\mu }_{i4}^2$ vs the combination $\sum _{i,j=1}^3{\mu }_{ij}^2$ coming from the active flavors only in the case that neutrinos are Majorana. The GEMMA and the low-mass red giant (LMRG) limits are shown. The black band is the Standard Model prediction for the active flavor masses between ${10}^{-4}$ and 1 eV.