Nonstandard neutrino interactions in supernovae

Nonstandard interactions (NSI) of neutrinos with matter can significantly alter neutrino flavor evolution in supernovae with the potential to impact explosion dynamics, nucleosynthesis, and the neutrinos signal. In this paper, we explore, both numerically and analytically, the landscape of neutrino flavor transformation effects in supernovae due to NSI and find a new, heretofore unseen transformation processes can occur. These new transformations can take place with NSI strengths well below current experimental limits. Within a broad swath of NSI parameter space, we observe symmetric and standard matter-neutrino resonances for supernovae neutrinos, a transformation effect previously only seen in compact object merger scenarios; in another region of the parameter space we find the NSI can induce neutrino collective effects in scenarios where none would appear with only the standard case of neutrino oscillation physics; and in a third region the NSI can lead to the disappearance of the high density Mikheyev-Smirnov-Wolfenstein resonance. Using a variety of analytical tools, we are able to describe quantitatively the numerical results allowing us to partition the NSI parameter according to the transformation processes observed. Our results indicate nonstandard interactions of supernova neutrinos provide a sensitive probe of beyond the Standard Model physics complementary to present and future terrestrial experiments.

Figure 1

Normal hierarchy survival probabilities, $P_{ee}=P({\nu }_e\to {\nu }_e)$, ${\overline{P}}_{ee}=P({\overline{\nu }}_e\to {\overline{\nu }}_e)$, for electron neutrinos (blue) and antineutrinos (red). The top figure shows the results of our calculations in the absence of any NSI. The middle figure includes NSI terms with the parameters set to $\delta {\epsilon }^n=-0.84$ and ${\epsilon }_0=0.00025$, and one observes an I resonance at $r\sim 40\mathrm{km}$ and a bipolar/nutation oscillations beginning at $r\sim 150\mathrm{km}$. Finally, in the bottom figure, we increase ${\epsilon }_0$ to 0.001 and observe that the I resonance is now followed by a new type of transition which we shall show is a standard MNR.

Figure 2

The nonzero diagonal element of the total matter potential $V_M=V_{\mathrm{MSW}}+V_{\mathrm{NSI}}$ as a function of $r$ for eight different values of $\delta {\epsilon }^n$ and the $V_{\nu }$ scaling parameter, ${\mu }_{\nu }$. The shaded red region is set by the requirement that the I resonance occurs entirely outside the neutrinosphere.

Figure 3

Outline of the parameter space considered in this paper. The magenta region represents areas where we expect to see NSI effects due to the I resonance. The white region represents areas where our model is not applicable. The blue region contains uncertain NSI effects where the neutrinosphere and I resonance overlap. The dashed purple line shows the location where the solution for the I resonance becomes nonphysical, i.e. $r_I\le 0$. The six dots in the red region represent the six test cases shown in Figs. 5, 6, 7, 8, 9, and 10 from left to right.

Figure 4

Survival probabilities of electron neutrinos (blue) and antineutrinos (red) for the normal (top) and inverted (bottom) hierarchies in the absence of NSI. The vertical shaded band indicates the region where linear stability analysis predicts a bipolar/nutation transformation should occur due to neutrino-neutrino interaction. The position of the H resonance for neutrinos in the normal hierarchy and for antineutrinos in the inverted hierarchy is shown as a vertical dash-dotted line at $r_H\approx 1200\mathrm{km}$.

Figure 5

The same as in Fig. 4 but with NSI parameters set to $\delta {\epsilon }^n=-0.6556$ and ${\epsilon }_0=0.0007$, corresponding to point A in Fig. 3. Again, the shaded band indicates where linear stability analysis predicts a bipolar/nutation transformation should occur due to neutrino-neutrino interaction. The vertical gray dot-dashed line at $r\approx 20\mathrm{km}$ is the predicted location of the I resonance according to Eq. (27), and the vertical dot-dashed line at $r\approx 1000\mathrm{km}$ is the H resonance for neutrinos or antineutrinos.

Figure 6

The same as in Fig. 5 but with NSI parameters set to $\delta {\epsilon }^n=-0.7516$ and ${\epsilon }_0=0.002$ corresponding to point B in Fig. 3. The vertical gray dot-dashed line at $r\approx 30\mathrm{km}$ is the predicted location of the I resonance according to Eq. (27), and the vertical dot-dashed line at $r\approx 1000\mathrm{km}$ is the H resonance for neutrinos or antineutrinos. At this combination of NSI parameters, a MNR occurs starting at $r\sim 40\mathrm{km}$, and the analytical prediction for the evolution of the transition probabilities using Eq. (37) is shown as the black and green dashed lines for electron neutrinos and antineutrinos respectively.

Figure 7

The same as in Fig. 6 but with NSI parameters set to $\delta {\epsilon }^n=-0.9436$ and ${\epsilon }_0=0.0045$, corresponding to point C in Fig. 3. Here, we see the effects of the increasing width of the I resonance causing an overlap with the standard MNR and a change in the behavior during the resonance.

Figure 8

The same as in Fig. 6 but with NSI parameters set to $\delta {\epsilon }^n=-1.2124$ and ${\epsilon }_0=0.008$, corresponding to point D in Fig. 3. The vertical dot-dashed line at $r\approx 100\mathrm{km}=10^7\mathrm{cm}$ is the I resonance, and the vertical dot-dashed line at $r\approx 900\mathrm{km}$ is the H resonance. Here, we see the I resonance followed by a nutation/bipolar transition. In this case, the width of the I resonance has completely covered the MNR, suppressing it and preventing the system from stabilizing against the nutation region at $r\sim 150\mathrm{km}$.

Figure 9

The same as in Fig. 6 but with NSI parameters set to $\delta {\epsilon }^n=-1.4428$ and ${\epsilon }_0=0.00275$, corresponding to point E in Fig. 3. Here, the resonance prediction lines show how tightly packed the various resonances have become, causing a mixture of different behaviors the form of which changes with slight modifications to either $\delta {\epsilon }^n$ or ${\epsilon }_0$ in the yellow region.

Figure 10

The same as in Fig. 6 but with NSI parameters set to $\delta {\epsilon }^n=-1.6156$ and ${\epsilon }_0=0.0005$, corresponding to point F in Fig. 3. In this case, there is no longer an I resonance or H resonance for the neutrinos in the normal hierarchy (nor or antineutrinos in the inverted hierarchy). Only the I resonance for the (anti)neutrinos in the normal (inverted) hierarchy remains along with the bipolar/nutation transition in the inverted hierarchy.

Figure 11

The partition of the parameter space in the normal (right) and inverted (left) hierarchies. The different colored regions represent different behavior of the numerical solutions. The light blue region is the same as that shown in Fig. 3 and is the region where the I resonance overlaps with the surface of the neutrinosphere. The yellow region shows where significant overlap between multiple resonances causes chaotic collective behavior. The soft blue region in the right panel shows where the I and H resonances disappear for neutrinos. The dark blue region in the left panel shows where the region where the I and H resonances disappear from antineutrinos after undergoing a bipolar transition. Green represents no collective oscillations between the I resonance and the H resonance. Purple represents results where we observed a bipolar/nutation transition. The red regions are where MNR behavior is observed. The six black points represent the locations in parameter space of the example cases also seen in Fig. 3, the survival probability plots of which are shown in Figs. 5, 6, 7, 8, 9, and 10.

Figure 12

The location of the I resonance, $r_I$ (solid black line), its width $r_I\pm {\sigma }_I$ for two different values of ${\epsilon }_0$ (green dashed line and blue dot-dashed line), and the starting location (solid red line) and ending location (dot-dashed red line) of the MNR as a function of the NSI parameter $-\delta {\epsilon }^n$.

Figure 13

Similar to Fig. 11 but with a further division of the MNR (red) region from Fig. 11 into two regions. The red region now shows the parameter space where we observed the normal, complete, MNR as seen in Fig. 6 and the orange region where the I resonance and MNR interfere with each other, as seen in Fig. 7. The two lines roughly predict the boundary between the full MNR and partial MNR (dot-dashed blue) and where the solution transitions from MNR back to bipolar transitions (solid blue). The green dot-dashed line represents the point at which the predicted location of the I resonance lies within the instability region predicted by the stability matrix in Eq. (38). The black dot-dashed line is the value of $\delta {\epsilon }^n$ where the diagonal component of the matter potential no longer crosses the positive vacuum scale causing the I resonance and H resonance to disappear from the neutrinos; however, the antineutrinos still undergo an I resonance. The other colors are the same as in Fig. 11: the light blue region is where the I resonance overlaps with the surface of the neutrinosphere, yellow is chaotic collective effects, soft blue is the absence of I and H resonances in normal hierarchy neutrinos, darker blue is the onset of the bipolar transition followed by an I resonance with no H resonance, green represents no collective oscillations between the I resonance and the H resonance, and purple represents results where we observed a bipolar/nutation transition.