Impact of cross-section uncertainties on supernova neutrino spectral parameter fitting in the Deep Underground Neutrino Experiment

A primary goal of the upcoming Deep Underground Neutrino Experiment (DUNE) is to measure the $\mathcal{O}(10)\mathrm{MeV}$ neutrinos produced by a Galactic core-collapse supernova if one should occur during the lifetime of the experiment. The liquid-argon-based detectors planned for DUNE are expected to be uniquely sensitive to the ${\nu }_e$ component of the supernova flux, enabling a wide variety of physics and astrophysics measurements. A key requirement for a correct interpretation of these measurements is a good understanding of the energy-dependent total cross section $\sigma (E_{\nu })$ for charged-current ${\nu }_e$ absorption on argon. In the context of a simulated extraction of supernova ${\nu }_e$ spectral parameters from a toy analysis, we investigate the impact of $\sigma (E_{\nu })$ modeling uncertainties on DUNE’s supernova neutrino physics sensitivity for the first time. We find that the currently large theoretical uncertainties on $\sigma (E_{\nu })$ must be substantially reduced before the ${\nu }_e$ flux parameters can be extracted reliably; in the absence of external constraints, a measurement of the integrated neutrino luminosity with less than 10% bias with DUNE requires $\sigma (E_{\nu })$ to be known to about 5%. The neutrino spectral shape parameters can be known to better than 10% for a 20% uncertainty on the cross-section scale, although they will be sensitive to uncertainties on the shape of $\sigma (E_{\nu })$. A direct measurement of low-energy ${\nu }_e$-argon scattering would be invaluable for improving the theoretical precision to the needed level.

Figure 1

Pinched-thermal neutrino fluences for a supernova at a distance of 10 kpc. Following Ref. [26], the results are time-integrated over the first ten seconds. The initial fluence parameter values for ${\nu }_e$ are $({\alpha }^0,⟨E_{\nu }{⟩}^0,{ϵ}^0)=(2.5,9.5\mathrm{MeV},5\times {10}^{52}\mathrm{ergs})$, for ${\overline{\nu }}_e$ are $({\alpha }^0,⟨E_{\nu }{⟩}^0,{ϵ}^0)=(2.5,12.0\mathrm{MeV},5\times {10}^{52}\mathrm{ergs})$, and for ${\nu }_x$ are $({\alpha }^0,⟨E_{\nu }{⟩}^0,{ϵ}^0)=(2.5,15.6\mathrm{MeV},5\times {10}^{52}\mathrm{ergs})$. Normal mass ordering and Mikheyev-Smirnov-Wolfenstein (MSW) resonances [27, 28] were assumed via Eq. (5).

Figure 2

snowglobes smearing matrix made with marley modeling and 10% Gaussian-smeared reconstructed energy. An energy column contains the reconstructed energy distribution for neutrino-argon events at a given true neutrino energy.

Figure 3

Interacted and observed event rates calculated using snowglobes for ${\nu }_e-{}^{40}\mathrm{Ar}$ interactions in the proposed DUNE far detector. The postsmearing efficiency model imposed a sharp cut at 5 MeV onto the observed rates.

Figure 4

Event rates calculated using snowglobes for a true spectrum with initial fluence parameters $({\alpha }^0,⟨E_{\nu }{⟩}^0,{ϵ}^0)=(2.5,9.5\mathrm{MeV},5\times {10}^{52}\mathrm{ergs})$ and an example grid element with fluence parameters $({\alpha }^0,⟨E_{\nu }{⟩}^0,{ϵ}^0)=(3.8,10.2\mathrm{MeV},5\times {10}^{52}\mathrm{ergs})$ and reduced ${\chi }^2=4.85$ based on Eq. (6). The error bars are statistical.

Figure 5

Sensitivity regions in $(⟨E_{\nu }⟩,ϵ)$ space for three different supernova distances. These regions were generated from the smearing matrix shown in Fig. 2, a cross section model from marley [32], and a step efficiency function with a 5 MeV detection threshold.

Figure 6

Cross-section calculations for the ${\nu }_e-{}^{40}\mathrm{Ar}$ interaction from Refs. [29, 38, 39, 40, 41, 42, 43, 44]. The labels are explained in Table 1. Note the log scale on the $y$-axis.

Figure 7

Cross section calculations for the ${\nu }_e-{}^{40}\mathrm{Ar}$ interaction from Refs. [31, 45]. The labels are explained in Table 1. The $y$-axis range is the same as Fig. 6.

Figure 8

snowglobes event rates for select cross-section calculations from Refs. [31, 41, 43, 44, 45, 46]. The initial fluence parameter values for ${\nu }_e$ are $({\alpha }^0,⟨E_{\nu }{⟩}^0,{ϵ}^0)=(2.5,9.5\mathrm{MeV},5\times {10}^{52}\mathrm{ergs})$, for ${\overline{\nu }}_e$ are $({\alpha }^0,⟨E_{\nu }{⟩}^0,{ϵ}^0)=(2.5,12.0\mathrm{MeV},5\times {10}^{52}\mathrm{ergs})$, and for ${\nu }_x$ are $({\alpha }^0,⟨E_{\nu }{⟩}^0,{ϵ}^0)=(2.5,15.6\mathrm{MeV},5\times {10}^{52}\mathrm{ergs})$. Normal mass ordering and MSW resonance were assumed. Note that “QRPA-C” and “QRPA-S” contain the same type of calculation performed by different groups, with the former by Cheoun et al. [43] and the latter by Samana and dos Santos [44]. More details about the various models are provided in Table 1. The error bars are statistical.

Figure 9

Sensitivity regions (90% C.L.) in $(⟨E_{\nu }⟩,ϵ)$ space generated from the cross-section models in Refs. [31, 44, 45]. Only statistical uncertainties are considered. In each case, the same cross-section model is used both to produce the fake data and to calculate the sensitivity region.

Figure 10

${\nu }_e-{}^{40}\mathrm{Ar}$ cross section versus energy with various scaling factors applied. Reference [31] provided the cross-section model using nuclear matrix element data from Ref. [49].

Figure 11

Sensitivity regions (90% C.L.) for a 10 kpc supernova to study different combinations of assumed and true total cross section normalizations.

Figure 12

2D fractional difference plots to study effects produced by normalization uncertainties on the total cross section.

Figure 13

2D fractional difference plots to study effects produced by different cross section models. Note that “S” stands for the cross section model implemented into snowglobes [29]. Also note that the $ϵ$ color-scale is log to account for the wide range of values. The number scale shows the raw fractional difference values to conform with the $\alpha$ and $⟨E_{\nu }⟩$ plots.

Figure 14

Sensitivity regions (90% C.L.) calculated with different assumed cross-section models for a fake data set generated using the marley b 2009 model. The stars mark the best-fit measurements from the fitting algorithm. The red stars also indicate the true parameter values, i.e., when the assumed cross section model is identical to the true model.

Figure 15

Total cross section predictions for the ${\nu }_e-{}^{40}\mathrm{Ar}$ interaction from the selected subset of models discussed in Sec. 3d. The shaded region represents the adopted uncertainty envelope based on the spread of these models.

Figure 16

snowglobes event rates for the selected cross-section calculations discussed in the text. The error bars are statistical.

Figure 17

Toy total cross-section models for the ${\nu }_e-{}^{40}\mathrm{Ar}$ interaction covering portions of the uncertainty envelope shown in Fig. 15.

Figure 18

2D fractional difference plots to study effects produced by toy models within the cross-section uncertainty envelope discussed in Sec. 3d.

Figure 19

Sensitivity regions (90% C.L.) with different combinations of assumed and true cross-section models. Two of the models are toy models generated from the midpoint (B 2009) and minimum cross-section values from the set of selected models. The stars mark the best-fit values from the fitting algorithm. The black stars also represent the true parameter values.

Figure 20

Cross-section model from Refs. [45, 46] with the interpolation (with a linear spline) and extrapolation (using a quadratic fit) shown. See Table 3 for the quadratic fit parameters for the low-energy fit.

Figure 21

90% C.L. contours for the three parameter spaces with NMO assumptions and the marley b 2009 cross-section model [32]. The contours before interpolation have prominent jagged edges due to a limited number of reference grid points. The edges are most noticeable for the $ϵ$ parameter.