Neutrino flavor oscillations in stochastic gravitational waves

We study neutrino flavor oscillations in a plane gravitational wave (GW) with circular polarization. For this purpose, we use the solution of the Hamilton-Jacobi equation to get the contribution of GW to the effective Hamiltonian for the neutrino mass eigenstates. Then, considering stochastic GWs, we derive the equation for the density matrix for flavor neutrinos and analytically solve it in the two flavors approximation. The equation for the density matrix for the three neutrino flavors is also derived and solved numerically. In both cases of two and three neutrino flavors, we predict the ratios of fluxes of different flavors at a detector for cosmic neutrinos with relatively low energies owing to the interaction with such a GW background. The obtained results are compared with the recent observation of the flavor content of the astrophysical neutrino fluxes.

Figure 1

The numerical solution of Eqs. (3.8) and (3.9), rewritten in the two flavors approximation, for ${\nu }_e\leftrightarrow {\nu }_{\mu }$ oscillations in stochastic GWs. The propagation distance $L=1\mathrm{Gpc}$, $\mathrm{\Delta }{m}_{21}^2=\mathrm{\Delta }{m}_{\odot }^2=7.39\times {10}^{-5}{\mathrm{eV}}^2$, ${\theta }_{12}={\theta }_{\odot }=0.59$, and $E=0.5\mathrm{MeV}$. (a) The fluxes of electron neutrinos $F_e=⟨{\rho }_{11}⟩$ (red line) and muon neutrinos $F_{\mu }=⟨{\rho }_{22}⟩$ (blue line) versus the dimensionless time $t^{\prime }=t/L$. (b) The ratio of fluxes $F_e/F_{\mu }$ as a function of $t^{\prime }$.

Figure 2

The numerical solution of Eqs. (3.8) and (3.9) for three flavor neutrinos oscillations in stochastic GWs. The flux of electron neutrinos $F_e=⟨{\rho }_{11}⟩$ versus the dimensionless time $t^{\prime }$ is shown by the red line, the flux of muon neutrinos $F_{\mu }=⟨{\rho }_{22}⟩$ is represented by the blue line, and the flux of tau neutrinos $F_{\tau }=⟨{\rho }_{33}⟩$ is depicted by the green line. The neutrino energy $E=0.5\mathrm{MeV}$ and the propagation distance $L=1\mathrm{Gpc}$. (a) Normal ordering with $\mathrm{\Delta }{m}_{21}^2=7.39\times {10}^{-5}{\mathrm{eV}}^2$, $\mathrm{\Delta }{m}_{31}^2=2.53\times {10}^{-3}{\mathrm{eV}}^2$, ${\theta }_{12}=0.59$, ${\theta }_{23}=0.87$, ${\theta }_{13}=0.15$, and ${\delta }_{\mathrm{CP}}=4.83$. (b) Inverted ordering with $\mathrm{\Delta }{m}_{21}^2=7.39\times {10}^{-5}{\mathrm{eV}}^2$, $\mathrm{\Delta }{m}_{31}^2=-2.51\times {10}^{-3}{\mathrm{eV}}^2$, ${\theta }_{12}=0.59$, ${\theta }_{23}=0.87$, ${\theta }_{13}=0.15$, and ${\delta }_{\mathrm{CP}}=4.87$.