Sensitivity to supernovae average ${\nu }_x$ temperature with neutral current interactions in DUNE

We explore a novel method for measuring the time averaged temperature of the ${\nu }_x$ component in type-II core-collapse supernovae. By measuring neutral current incoherent neutrino-argon interactions in DUNE we can obtain spectral information for the combination of all active neutrino species. Combining this all-neutrino spectral information with detailed charged current measurements of the electron neutrino and electron antineutrino fluxes from DUNE and Hyper-Kamiokande, we can infer the time averaged temperature for the remaining neutrino species in the ${\nu }_x$ component to within a factor 2 for most cases and to 30% for a small range of time averaged ${\nu }_x$ temperatures. Because of the limited energy range of the emitted photons from incoherent neutral current interactions on argon, the ${\nu }_x$ temperature reconstruction demonstrates a degeneracy in the one and two sigma credible regions. Furthermore, while large uncertainties on the neutral current (NC) cross section penalize this measurement, we examined the efficacy of constraining NC cross section uncertainties on improving ${\nu }_x$ measurements. We found that if additional measurements of $\mathrm{B}(\mathrm{M}1\uparrow )$ $1^{+}$ excited state transitions in argon are able to reduce correlated cross section uncertainties from 15% to 7%, the size of the $1\sigma$ allowed regions for $T_{{\nu }_x}$ becomes sample size limited, and approaches the case where there are no uncertainties on the cross section.

Figure 1

$\mathrm{B}(\mathrm{M}1\uparrow )$ neutral current $1^{+}$ transition strengths for ${}^{40}\mathrm{Ar}$. The $\mathrm{B}(\mathrm{M}1\uparrow )$ value for each $1^{+}$ is shown as a function of the transition energy. Fourteen of these $1+$ transitions exist in total.

Figure 2

Supernova neutrino differential fluence for a Fermi-Dirac spectrum. The differential fluence is shown as a function of neutrino energy for each of the three neutrino flux components, assuming a Fermi-Dirac energy distribution, and the baseline supernova scenario described in Sec. 3.

Figure 3

Incoherent NC neutrino-argon cross sections and uncertainties. The NC neutrino-argon cross sections derived in [10] are shown for $\nu$ and $\overline{\nu }$ as a function of incident neutrino energy with bands showing their associated 43% theoretical uncertainties. The solid shading shows $\nu$ cross section uncertainties, and hatched shading shows the same for $\overline{\nu }$.

Figure 4

DUNE FD NC fractional covariance matrix. The uncertainties on the cross section are composed of 15% correlated uncertainties and 40% uncorrelated uncertainties, as described in [10].

Figure 5

DUNE FD NC response matrix. Response matrix for the $\nu$ component of the incoherent NC neutrino interaction in LAr assuming 15% energy resolution for the DUNE FD TPC as described in [12].

Figure 6

DUNE $\mathrm{dE}/\mathrm{dx}$ distribution for electron and photonlike final states. Distribution is normalized to the expected NC and CC event rates for a representative sample where $T_{{\nu }_x}=3.3\mathrm{MeV}$, $T_{\overline{{\nu }_e}}=4.6\mathrm{MeV}$, and $T_{{\nu }_x}=6.4\mathrm{MeV}$.

Figure 7

Expected NC event rate in DUNE FD as a function of ${\nu }_x$ temperature. ${\nu }_e$ and $\overline{{\nu }_e}$ temperatures are fixed to 3.3 and 4.6 MeV, respectively. The black dashed line represents events due to CC interactions in the DUNE FD from the ${\nu }_e$ component of the fluence.

Figure 8

Expected $T_{{\nu }_x}$ credible regions with full cross section uncertainties. The Asimov credible regions for $T_{{\nu }_x}$ are shown as a function of injected $T_{{\nu }_x}$ by the colored regions. Average neutrino temperatures of $T_{{\nu }_e}=3.3\mathrm{MeV}$ and $T_{\overline{{\nu }_e}}=4.6\mathrm{MeV}$ are assumed, along with 40% uncorrelated uncertainties and 15% correlated uncertainties on the NC cross section.

Figure 9

Expected $T_{{\nu }_x}$ credible regions with reduced cross section uncertainties. The Asimov credible regions for $T_{{\nu }_x}$ are shown as a function of injected $T_{{\nu }_x}$ by the colored regions. Average neutrino temperatures of $T_{{\nu }_e}=3.3\mathrm{MeV}$ and $T_{\overline{{\nu }_e}}=4.6\mathrm{MeV}$ are assumed, along with 40% uncorrelated uncertainties and 7% correlated uncertainties on the NC cross section.

Figure 10

Expected $T_{{\nu }_x}$ credible regions with no cross section uncertainties. The Asimov credible regions for $T_{{\nu }_x}$ are shown as a function of injected $T_{{\nu }_x}$ by the colored regions. Average neutrino temperatures of $T_{{\nu }_e}=3.3\mathrm{MeV}$ and $T_{\overline{{\nu }_e}}=4.6\mathrm{MeV}$ are assumed, along no uncertainties on the NC cross section.

Figure 11

Fractional width of the $1\sigma$ credible region. The solid line represents the scenario with 40% uncorrelated uncertainties and 15% correlated uncertainties on the NC cross section. The dashed line represents the scenario with 40% uncorrelated uncertainties and 7% correlated uncertainties on the NC cross section. The dotted line represents the scenario with no uncertainties on the NC cross section.

Figure 12

Expected $T_{{\nu }_x}$ credible regions with a uniform prior from 0.1 to 300 MeV. The Asimov credible regions for $T_{{\nu }_x}$ are shown as a function of injected $T_{{\nu }_x}$ by the colored regions. Average neutrino temperatures of $T_{{\nu }_e}=3.3\mathrm{MeV}$ and $T_{\overline{{\nu }_e}}=4.6\mathrm{MeV}$ are assumed. The credible regions in this figure are computed with a uniform $T_{{\nu }_x}$ prior that extends up 300 MeV; this is in contrast to the credible regions shown in Figs. 8, 9, 10 which limited values of $T_{{\nu }_x}$ to be below 60 MeV.

Figure 13

Fractional width of $1\sigma$ credible regions. The solid lines correspond to the width from the hyperbolic tangent prior, the dotted lines correspond to the width below 60 MeV from the 0.1–300 MeV uniform prior, and the dashed lines correspond to the full width from the from the 0.1–300 MeV uniform prior (which extends up to 35). The three colors correspond to the three cases of cross section uncertainties.