Electromagnetic neutrino properties: present status and future prospects

Abstract

There is no doubt [1-3] that neutrino electromagnetic properties open a window to new physics. The most general form [1] of a neutrino electromagnetic vertex function $\Lambda_{\mu}^{ij}(q) = \left( \gamma_{\mu} - q_{\mu} {q}/q^{2} \right) \left[ f_{Q}^{ij}(q^{2}) + f_{A}^{ij}(q^{2}) q^{2} \gamma_{5} \right] \nonumber - i \sigma_{\mu\nu} q^{\nu} \left[ f_{M}^{ij}(q^{2}) + i f_{E}^{ij}(q^{2}) \gamma_{5} \right]$ , where $\Lambda_{\mu}(q)$ and form factors $f_{Q,A,M,E}(q^2)$ are $3\times 3$ matrices in the space of massive neutrinos, in the case of coupling with a real photon ($q^2=0$) provides four sets of neutrino electromagnetic characteristics: 1) the dipole magnetic moments $\mu_{ij}=f_{M}^{ij}(0)$, 2) the dipole electric moments $\epsilon_{ij}=f_{E}^{ij}(0)$, 3) the millicharges $q_{ij}=f_{Q}^{ij}(0)$ and 4) the anapole moments $a_{ij}=f_{A}^{ij}(0)$. So far, there are no indications in favour of nonzero electromagnetic properties of neutrinos from either data from laboratory experiments with neutrino fluxes from ground-based sources or from astrophysics observations. However, the study of the electromagnetic properties of neutrinos attracts considerable attention. The most well understood and studied are the dipole magnetic and electric moments. In a minimal extension of the Standard Model the diagonal magnetic moment of a Dirac neutrino is given [4] by $\mu^{D}_{ii} = \frac{3e G_F m_{i}}{8\sqrt {2} \pi ^2}\approx 3.2\times 10^{-19} \Big(\frac{m_i}{1 \mathrm{eV} }\Big) \mu_{B}$ ($\mu_B$ is the Bohr magneton). Majorana neutrinos can have only transition (off-diagonal) magnetic moments $\mu^{M}_{i\neq j}$. The most stringent constraints on the effective neutrino magnetic moment are obtained with the reactor antineutrinos: $\mu_{\nu} < 2.9 \times 10^{-11} \mu_{B}$ (GEMMA Collaboration [5]), and solar neutrinos: ${\mu}_{\nu_e}\leq 2.8 \times 10^{-11} \mu _B$ (Borexino Collaboration [6]). An astrophysical bound (for both Dirac and Majorana neutrinos) is provided [7-9] by observations of the properties of globular cluster stars: $\Big( \sum _{i,j}\left| \mu_{ij}\right| ^2\Big) ^{1/2}\leq (2.2{-}2.6) \times 10^{-12} \mu _B$. A general and termed model-independent upper bound on the Dirac neutrino magnetic moment, that can be generated by an effective theory beyond a minimal extension of the Standard Model, has been derived in [10]: $\mu_{\nu}\leq 10^{-14}\mu_B$. The corresponding limit for transition moments of Majorana neutrinos is much weaker [11]. In the theoretical framework with $CP$ violation a neutrino can have nonzero electric moments $\epsilon_{ij}$. In the laboratory neutrino scattering experiments for searching $\mu_{\nu}$ (for instance, in the GEMMA experiment) the electric moment $\epsilon_{ij}$ contributions interfere with those due to $\mu_{ij}$. Thus, these kind of experiments also provide constraints on $\epsilon_{ij}$. The astrophysical bounds on $\mu_{ij}$ are also applicable for constraining $\epsilon_{ij}$ (see [7-9] and [12]). In what follows below we give a fast flash on less know neutrino electromagnetic characteristics, namely on the neutrino millicharge, charge radius and anapole moment and give some comments on the future prospects of neutrino electromagnetic properties.