Spin Light of neutrino in polarized matter

The Spin Light of neutrino ($SLν$) is an electromagnetic radiation of the neutrino magnetic moment emitted when neutrino moves in external conditions (fields or matter). The effect can be of significance in the extremely dense matter of compact astrophysical objects such as neutron stars (NS). If detected, this radiation could provide a fair opportunity to study the properties of neutrinos and the medium through which they move, since the properties of the radiation depend on both. Motivated by the possibility of the nuclear matter spin-polarization, in this paper, we study the new properties to $SLν$ obtained under the influence of net matter polarization. We demonstrate that the polarization can enhance or completely suppress the radiation. Also, it introduces a characteristic asymmetry into the total radiation from the compact object, which could be an observable feature dependent on the matter polarization and the magnetic field inside the stellar (if the field is connected to the stellar matter polarization). The research may have implications for the physics of NS and magnetars, bringing us closer to the possibility of studying their internal structure.

💡 Research Summary

The paper investigates how the “spin light of neutrino” (SLν), an electromagnetic radiation emitted by a neutrino possessing a magnetic moment, is modified when the neutrino propagates through matter that is partially spin‑polarized. Starting from the minimally extended Standard Model, the authors recall that a Dirac neutrino acquires a magnetic moment μ≈3×10⁻¹⁹ μB (mν/1 eV), far below current laboratory limits (μ≲10⁻¹² μB) but potentially significant in environments of extreme density and high neutrino energy. They then introduce the effective four‑vector fμ that encodes the coherent forward scattering of neutrinos on background particles. For non‑moving matter the vector reduces to fμ=(−n_n, n_n ζ), where n_n is the neutron number density and ζ (0≤|ζ|≤1) is the average spin polarization of the medium.

Using the modified Dirac equation iγμ∂μ−½γμ(1+γ5)fμ−mΨ=0, the authors derive exact solutions for neutrino wave functions in polarized matter. By constructing a spin integral of motion S that commutes with the Hamiltonian, they obtain two families of energy eigenstates distinguished by the spin quantum number s=±1. In the ultrarelativistic, massless limit the dispersion relations simplify to

E(νL, \barνR)=|p+2 \tilde n ζ|+2 \tilde n, E(νR, \barνL)=p,

with \tilde n=G_F n_n/(2√2). The first branch corresponds to active left‑handed neutrinos (or right‑handed antineutrinos) whose energy is shifted by the matter potential; the second branch describes sterile states that propagate as free particles. The shift depends on the scalar product ζ·p through the angle δ between the neutrino momentum and the polarization direction, effectively replacing \tilde n by \tilde n(1+ζ cosδ). Consequently, when the polarization is aligned with the neutrino motion (ζ·cosδ>0) the effective potential is enhanced up to a factor of two, while anti‑aligned polarization reduces it and can even suppress the radiation completely.

The SLν process is treated as a standard magnetic‑dipole transition with the usual Feynman diagram, but the emitted photon propagates in a dense electron plasma and therefore acquires a plasmon mass mγ≈(2α)½(3√π n_e)^{1/3}≈9 MeV (n_e/10³⁷ cm⁻³)^{1/3}. Energy‑momentum conservation leads to a threshold condition for the initial neutrino momentum:

p_th = mγ² /