Effects of nonstandard neutrino self-interactions and magnetic moment on collective Majorana neutrino oscillations

We derive the effective Hamiltonian describing collective oscillations of Majorana neutrinos with a transition magnetic moment, allowing for the presence of scalar and pseudoscalar nonstandard neutrino self-interactions (NSSIs). Using this Hamiltonian, we analyze new flavor instability channels of collective oscillations in a core-collapse supernova environment that open up in the presence of a small but nonzero neutrino magnetic moment. It turns out that, contrary to certain claims in the literature, within the minimally extended Standard Model (i.e., without NSSIs), no new instabilities arise within the linear order, nor do they produce any observable signatures in the neutrino flavor-energy spectra, at least for magnetic moments up to ${10}^{-15}{\mu }_{\mathrm{B}}$ and quite realistic fields of the order of ${10}^{12}\mathrm{Gauss}$. On the other hand, in the presence of NSSIs, new fast and slow instabilities mixing neutrinos and antineutrinos appear, which show up in the spectra even for tiny magnetic moments of the order of ${10}^{-24}{\mu }_{\mathrm{B}}$, leading to considerable distortions of the spectra and nonstandard spectral splits. We study sensitivity of collective oscillations to these, NSSI-induced instabilities in detail and discuss the observability of the NSSI couplings triggering them.

Figure 1

Growth rates corresponding to a fast unstable mode for a monochromatic neutrino flux, depending on the NSSI coupling $g_{+}$. The plot demonstrates the asymptotic case with both the vacuum oscillation frequency $\omega$ and the matter potentials $V_{e,n}$ neglected.

Figure 2

Instability growth rates for a monochromatic neutrino flux due to the presence of a block-off-diagonal NSSI with parameter $g_{+}$. Inset: instability growth rate as a function of the neutrino number density for a fixed NSSI coupling $g_{+}=0.5$. The background matter density is set to zero in all panels.

Figure 3

Instability growth rates for a monochromatic purely electron neutrino flux due to the presence of a block-off-diagonal NSSI with parameter $g_{+}$. The background matter density is set to zero.

Figure 4

Instability growth rates for a monochromatic neutrino flux due to the presence of a block-off-diagonal NSSI interaction with parameter $g_{+}$. In contrast to Fig. 2, a neutron background is added with Wolfenstein potential $V_n$, while the contribution of background electrons $V_e$ and the vacuum oscillation frequency $\omega$ are neglected.

Figure 5

(a) Comparison of matter (neutron, electron) potentials, the neutrino self-coupling, and the energy scale of vacuum oscillations for a star with luminosity $L={10}^{55}{\sec }^{-1}$. (b) The initial flavor/energy spectra at the neutrino sphere $r=R_{\nu }$ used in the simulations.

Figure 6

The effect of the neutrino magnetic moment on the neutrino spectra without (pseudo)scalar NSSI for $L={10}^{55}{\sec }^{-1}$. The upper and the lower rows correspond to the normal and the inverted hierarchies, respectively. The first column [(a) and (d)] shows the case ${\mu }_{12}=0$, the second [(b) and (e)] the ${\mu }_{12}\ne 0$ case with self-interaction Hamiltonian (69), and the last one [(c) and (f)] also to ${\mu }_{12}\ne 0$, but based on the Hamiltonian (73) from Ref. [6]. Dashed lines sketch the initial spectra at the neutrino sphere [Fig. 5]. In the ${\mu }_{12}=0$ case, the two Hamiltonians produce the same result. Visual identity of [(a) and (c)] and [(b) and (d)] plots, respectively, holds up to at least $|{\mu }_{12}|\sim {10}^{-15}{\mu }_{\mathrm{B}}$.

Figure 7

The effect of the block-off-diagonal NSSI on the neutrino spectra for the neutrino magnetic moment ${\mu }_{12}={10}^{-19}{\mu }_{\mathrm{B}}$ and different NSSI couplings $g_{+}$ and luminosities $L$. The upper and the lower rows correspond to the normal and the inverted hierarchies, respectively. The first [(a) and (d)] and the second [(b) and (e)] columns demonstrate the cases with luminosity $L={10}^{55}{\sec }^{-1}$ and different NSSI couplings; the last column [(c) and (f)] shows the results for $L=3\times {10}^{55}{\sec }^{-1}$. Dashed lines sketch the initial spectra at the neutrino sphere [Fig. 5].

Figure 8

Impact of scalar-pseudoscalar NSSI with $g_{+}=1$ on the neutrino flavor evolution for $L={10}^{55}{\sec }^{-1}$ and a very small magnetic moment ${\mu }_{12}={10}^{-24}{\mu }_{\mathrm{B}}$ for the two mass hierarchies.

Figure 9

Impact of scalar-pseudoscalar NSSI on the neutrino flavor evolution for $L={10}^{55}{\sec }^{-1}$ and ${\mu }_{12}={10}^{-19}{\mu }_{\mathrm{B}}$ for different NSSI couplings and mass hierarchies: (a) evolution of neutrino-to-antineutrino number ratio; (b) evolution of spectral residuals (95).

Figure 10

Sensitivity of collective neutrino oscillations to the NSSI coupling $g_{+}$ in terms of the spectral residual $\mathrm{\Delta }(250\mathrm{km})$, depending on the coupling $g_{+}$ and the luminosity $L$. The magnetic moment is set to ${\mu }_{12}={10}^{-19}{\mu }_{\mathrm{B}}$ and ${10}^{-24}{\mu }_{\mathrm{B}}$ in the two upper and lower panels, respectively.