We review the theory and phenomenology of neutrino electromagnetic interactions, which give us powerful tools to probe the physics beyond the Standard Model. After a derivation of the general structure of the electromagnetic interactions of Dirac and Majorana neutrinos in the one-photon approximation, we discuss the effects of neutrino electromagnetic interactions in terrestrial experiments and in astrophysical environments. We present the experimental bounds on neutrino electromagnetic properties and we confront them with the predictions of theories beyond the Standard Model.

The main goal of the paper is to give a short review on neutrino electromagnetic properties. In the introductory part of the paper a summary on what we really know about neutrinos is given: we discuss the basics of neutrino mass and mixing as well as the phenomenology of neutrino oscillations. This is important for the following discussion on neutrino electromagnetic properties that starts with a derivation of the neutrino electromagnetic vertex function in the most general form, that follows from the requirement of Lorentz invariance, for both the Dirac and Majorana cases. Then, the problem of the neutrino form factors definition and calculation within gauge models is considered. In particular, we discuss the neutrino electric charge form factor and charge radius, dipole magnetic and electric and anapole form factors. Available experimental constraints on neutrino electromagnetic properties are also discussed, and the recently obtained experimental limits on neutrino magnetic moments are reviewed. The most important neutrino electromagnetic processes involving a direct neutrino coupling with photons (such as neutrino radiative decay, neutrino Cherenkov radiation, spin light of neutrino and plasmon decay into neutrino-antineutrino pair in media) and neutrino resonant spin-flavor precession in a magnetic field are discussed at the end of the paper.

In this review 1 we discuss the main theoretical aspects and experimental effects of neutrino electromagnetic properties. We start with a general description of the electromagnetic form factors of Dirac and Majorana neutrinos. Then, we discuss the theory and phenomenology of the magnetic and electric dipole moments, summarizing the experimental results and the theoretical predictions. We discuss also the phenomenology of a neutrino charge radius and radiative decay. Finally, we describe the theory of neutrino spin and spin-flavor precession in a transverse magnetic field and we summarize its phenomenological applications.

On the basis of the exact solutions of the modified Dirac equation for a massive neutrino moving in matter we develop the quantum theory of the spin light of neutrino (SLν). The expression for the emitted photon energy is derived as a function of the density of matter for different matter compositions. The dependence of the photon energy on the helicities of the initial and final neutrino states is shown explicitly.The rate and radiation power of the SLν in matter are obtained with the emitted photon linear and circular polarizations being accounted for. The developed quantum approach to the SLν in matter (which is similar to the Furry representation of electrodynamics) can be used in the studies of other processes with neutrinos in the presence of matter.

The derivation of the quasiclassical Lorentz invariant neutrino spin evolution equation taking into account general types of neutrino non-derivative interactions with external fields is presented. We discuss the constraints on the characteristics of matter and neutrino under which this quasiclassical approach is valid. The application of the obtained equation for the case of the Standard Model neutrino interactions with moving and polarized background matter is considered.It is commonly believed that neutrino physics provides strong evidence for physics beyond the Standard Model. In different extensions of the Standard Model new types of interactions are predicted for massive neutrinos. The problem of neutrino propagation in matter in the case of a general set of interactions with the background fermions has attracted considerable attention (see, for example [1,2]). Recently, we have developed the Lorentz invariant formalism for description of neutrino spin-flavor and flavor oscillations with the Standard Model vector and axial-vector interactions in moving matter under the influence of an arbitrary electromagnetic fields [3,4,5]. In particular, we have derived, within general assumption like Lorentz invariance and linearity over neutrino spin vector S µ and also over such characteristics of matter like fermions currents and polarizations, the evolution equation for the neutrino spin. We have used this evolution equation for description of neutrino oscillations in electromagnetic fields accounting for neutrino vector and axial-vector interactions with background fermions that corresponds to the case of the Standard Model weak interactions. Note that quasiclassical approach to the problem of neutrino spin relaxation in stochastic electromagnetic fields was used in ref. [6]. However, the problem of the neutrino spin evolution equation accounting also for more general new types of neutrino interactions is still remained open.We discuss below neutrino spin evolution in background matter in the case of a new physics model that admits a general set of new neutrino interac-1

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A new type of electromagnetic radiation by a neutrino with non-zero magnetic (and/or electric) moment moving in background matter and electromagnetic field is considered. This radiation originates from the quantum spin flip transitions and we have named it as "spin light of neutrino"($SL\nu$). The neutrino initially unpolarized beam (equal mixture of $\nu_{L}$ and $\nu_{R}$) can be converted to the totally polarized beam composed of only $\nu_{R}$ by the neutrino spin light in matter and electromagnetic fields. The quasi-classical theory of this radiation is developed on the basis of the generalized Bargmann-Michel-Telegdi equation. The considered radiation is important for environments with high effective densities, $n$, because the total radiation power is proportional to $n^{4}$. The spin light of neutrino, in contrast to the Cherenkov or transition radiation of neutrino in matter, does not vanish in the case of the refractive index of matter is equal to unit. The specific features of this new radiation are: (i) the total power of the radiation is proportional to $\gamma ^{4}$, and (ii) the radiation is beamed within a small angle $\delta \theta \sim \gamma^{-1}$, where $\gamma$ is the neutrino Lorentz factor. Applications of this new type of neutrino radiation to astrophysics, in particular to gamma-ray bursts, and the early universe should be important.Comment: accepted for publication in Phys.Lett.

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