Nonstandard neutrino self-interactions in a supernova and fast flavor conversions

We study the effects of nonstandard self-interactions (NSSI) of neutrinos streaming out of a core-collapse supernova. We show that with NSSI, the standard linear stability analysis gives rise to linearly as well as exponentially growing solutions. For a two-box spectrum, we demonstrate analytically that flavor-preserving NSSI lead to a suppression of bipolar collective oscillations. In the intersecting four-beam model, we show that flavor-violating NSSI can lead to fast oscillations even when the angle between the neutrino and antineutrino beams is obtuse, which is forbidden in the standard model. This leads to the new possibility of fast oscillations in a two-beam system with opposing neutrino-antineutrino fluxes, even in the absence of any spatial inhomogeneities. Finally, we solve the full nonlinear equations of motion in the four-beam model numerically, and explore the interplay of fast and slow flavor conversions in the long-time behavior, in the presence of NSSI.

Figure 1

Top panel: a two-box spectrum [Eq. (19)] with $A=1$ and $B=1.6$. Bottom panel: Plot showing growth rates $\kappa$ in units of $\sqrt{\omega \tilde{\mu }}$ for $u=1/2$. Red (solid) indicates the SM, whereas blue (dashed) represents $g_1=0$, $g_3=0.5$ and black (dotted) shows $g_1=0.5$, $g_3=0$.

Figure 2

Intersecting Four Beam Model.

Figure 3

Dependence of growth rates on $c\equiv \cos \theta$ and the $\nu -\overline{\nu }$ asymmetry $a$, for the left-right symmetry-breaking solution $(Q_{-},{\overline{Q}}_{-})$. Left: $g_1$, $g_3=0$, Center: $g_1=0$, $g_3=0.3$, Right: $g_1=0.3$, $g_3=0$.

Figure 4

Growth rates at $a=0$, as functions of $c\equiv \cos \theta$, for the left-right symmetry-breaking solution $(Q_{-},{\overline{Q}}_{-})$. Top: Only FP-NSSI, Bottom: Only FV-NSSI.

Figure 5

Dependence of growth rates on $c\equiv \cos \theta$ and the $\nu -\overline{\nu }$ asymmetry $a$, for the left-right symmetric solution $(Q_{+},{\overline{Q}}_{+})$, for $g_1=0.1$ and $g_3=0$.

Figure 6

Growth rates in the effective two-beam scenario [the left-right symmetric solution $(Q_{+},{\overline{Q}}_{+})$ with $c=-1$], as functions of neutrino-antineutrino asymmetry $a$.

Figure 7

Onset of fast oscillations from the numerical solution of the fully nonlinear EoM, for $a=0$ and $c=0.5$. The other parameters are chosen to be $\omega /{\mu }_R={10}^{-5}$, and ${\vartheta }_0={10}^{-2}$. The top panel shows quantity $A_{e\mu }={\log }_{10}|S|$ which gives the extent of flavor conversion. The bottom panel shows the ${\nu }_e$ survival probabilities $P_{e\to e}$.

Figure 8

Onset of oscillation in terms of the off-diagonal parameter $|S|$ from the numerical solution of the fully nonlinear EoM for $a=0$. The top panel shows the plot for $c=0.5$ where we expect fast oscillations. The bottom panel shows the case $c=-0.5$, when fast oscillations are absent. The other parameters are chosen to be $\omega /{\mu }_R={10}^{-5}$, and ${\vartheta }_0={10}^{-2}$.

Figure 9

Long-time behavior of collective oscillations in terms of the off-diagonal parameter $|S|$ from the numerical solution of the fully nonlinear EoM for $a=0$ and $c=0.5$. The other parameters are chosen to be $\omega /{\mu }_R={10}^{-4}$, and ${\vartheta }_0={10}^{-2}$. The rapid variations correspond to the fast oscillation frequency while the slowly changing envelope correspond to the slow oscillation frequency. The comparison of two columns indicates the effect of $g_1$ while the comparison of the rows indicates the effects of $g_3$.