New effect in neutrino spin oscillations in transversal matter currents with nonstandard interactions

Technical Summary: New Effect in Neutrino Spin Oscillations in Transversal Matter Currents with Nonstandard Interactions

Problem Statement
Neutrino flavor oscillations, which imply finite neutrino mass, necessitate an extension of the Standard Model. Beyond flavor transitions, neutrino spin oscillations driven by interactions with a moving external background represent a significant area of study, particularly in astrophysical environments where directed streams of matter are prevalent. While the evolution of the neutrino spin vector in magnetic fields and matter is described by the Bargmann-Michel-Telegdi equation, a specific phenomenon arises when neutrinos propagate through moving matter with a current transverse to their direction of motion. Previous work [1] predicted this effect using a quasiclassical approach, and a consistent quantum description was later provided [3]. However, a systematic study incorporating both standard and nonstandard interactions (NSI) within a quantum treatment, specifically applied to realistic astrophysical scenarios like binary neutron star mergers, remains to be fully explored.

Methodology
The authors employ a consistent quantum-mechanical approach to derive the effective Hamiltonian for neutrino spin evolution. The study considers two-flavor neutrinos ($\nu_e, \nu_\mu$) with two possible helicities propagating in a medium composed of neutrons.

1. Standard Interactions: The evolution equation is constructed using the interaction Lagrangian for standard weak interactions, accounting for the matter potential $f_\mu$ which depends on the neutron number density and the velocity of the matter. The Hamiltonian is decomposed into a term for non-moving matter ($H_0$) and a term accounting for matter motion ($\Delta H_{SM}$).
2. Nonstandard Interactions (NSI): To include NSI, an effective Lagrangian is introduced involving coupling parameters $\epsilon_{\alpha\beta}$. This modifies the evolution equation by adding a term $\Delta H_{NSI}$.
3. Astrophysical Model: The theoretical framework is applied to a model of a binary neutron star merger. Specific parameters are adopted for the medium (transversal velocity $v_\perp = 0.067$, neutron concentration $n = 5 \times 10^{36} \text{ cm}^{-3}$) and neutrinos (energy $p_0 = 10^6 \text{ eV}$, mass squared difference $\Delta m^2_{eff} \approx 10^{-4} \text{ eV}^2$). NSI parameters are set to specific values ($\epsilon_{ee}=0.17, \epsilon_{\mu\mu}=1.5, \epsilon_{e\mu}=0.84$) based on constraints from literature [6].

Key Contributions and Results
The paper derives explicit analytical expressions for the probabilities of neutrino spin and spin-flavor oscillations under the influence of transverse matter currents, both with and without NSI.

• Spin Oscillations ($\nu^L_e \to \nu^R_e$): An exact expression for the probability of spin oscillation in a transverse current is derived (Eq. 10). The probability is shown to be a function of time (or travel distance), dependent on the transverse velocity of the medium and the neutrino Lorentz factor.
• Spin-Flavor Oscillations ($\nu^L_e \to \nu^R_\mu$): The paper provides the full probability for spin-flavor oscillations in arbitrary moving matter, combining the effects of longitudinal and transverse currents (Eq. 11).
• Inclusion of NSI: The authors extend these derivations to include nonstandard interactions. New expressions are obtained for spin oscillation probabilities (Eq. 16) and full spin-flavor probabilities (Eq. 21) in the presence of NSI.
• Numerical Estimations: Using the binary neutron star merger model, numerical values for these probabilities are calculated. The results are presented graphically (Figs. 2–5), comparing oscillation probabilities in standard scenarios versus those with NSI.

Significance and Claims
The paper claims to provide a systematic quantum treatment of neutrino spin and spin-flavor oscillations induced specifically by transverse matter currents. A primary finding is that the amplitudes of neutrino oscillations, when nonstandard interactions are included, are greater than those calculated without NSI. The study offers a detailed theoretical framework and numerical estimations under astrophysical conditions resembling neutron star mergers. By incorporating realistic NSI coupling strengths, the authors provide numerical orders of magnitude that could be relevant for future experimental expectations, thereby refining the understanding of neutrino behavior in extreme, moving matter environments. The work supports the view that directed matter streams in extreme astrophysical objects create suitable conditions for searching for new physics effects beyond the Standard Model.