Correlations and degeneracies among the NSI parameters with tunable beams at DUNE

The Deep Underground Neutrino Experiment (DUNE) is a leading experiment in neutrino physics which is presently under construction. DUNE aims to measure the yet unknown parameters in the three flavor oscillation scenario which includes discovery of leptonic $CP$ violation, determination of the mass hierarchy and determination of the octant of ${\theta }_{23}$. Additionally, the ancillary goals of DUNE include probing the subdominant effects induced by new physics. A widely studied new physics scenario is that of nonstandard neutrino interactions (NSI) in propagation which impacts the oscillations of neutrinos. We consider some of the essential NSI parameters impacting the oscillation signals at DUNE and explore the space of NSI parameters as well as study their correlations among themselves and with the yet unknown $CP$ violating phase, $\delta$ appearing in the standard paradigm. The experiment utilizes a wide band beam and provides us with a unique opportunity to utilize different beam tunes at DUNE. We demonstrate that combining information from different beam tunes (low energy and medium energy) available at DUNE impacts the ability to probe some of these parameters and leads to altering the allowed regions in two-dimensional space of parameters considered.

Figure 1

The neutrino fluxes (LE and ME) used in the present work. LE beam refers to the standard flux generated by an 80 GeV proton beam as used in [72]. ME beam refers to the flux peaking at a higher energy. See Table 2 for more details.

Figure 2

$P_{\mu e}$ (top row) and $P_{\mu \mu }$ (bottom row) at fixed baseline ($L=1300\mathrm{km}$) and fixed energy values ($E=2.5\mathrm{GeV}$ for $P_{\mu e}$ and $E=5\mathrm{GeV}$ for $P_{\mu \mu }$) plotted as a function of the $CP$ phase, $\delta$. The strength of all NSI terms is taken to be the same ($=0.1$).

Figure 3

Heatmaps corresponding to $|\mathrm{\Delta }{P}_{\mu e}|$ (top row) and $|\mathrm{\Delta }{P}_{\mu \mu }|$ (bottom row) in the two-dimensional plane of individual NSI term (${ϵ}_{\alpha \beta }$) and energy. The NSI phases are set to zero. The dashed white lines indicate the value of energy at 2.5 and 5 GeV.

Figure 4

Heatmaps for $|\mathrm{\Delta }{P}_{\mu e}|$ (top row) and $|\mathrm{\Delta }{P}_{\mu \mu }|$ (bottom row) are shown as the function of a NSI phase ${\phi }_{\alpha \beta }$ (taken one at a time) as the energy is changed, keeping the baseline fixed at 1300 km. The associated NSI amplitudes (${ϵ}_{\alpha \beta }$) were kept fixed at 0.05. The two horizontal dashed white lines correspond to the energies 2.5 and 5 GeVs.

Figure 5

Heatmaps for $|\mathrm{\Delta }{P}_{\mu e}|$ are shown for a fixed baseline of 1300 km in the parameter space of $\delta -{ϵ}_{\alpha \beta }$ for two fixed energies: 2.5 GeV (top row) and 5 GeV (bottom). A single NSI parameter was considered at a time and the associated NSI phases were taken to be zero. The dashed horizontal white line corresponds to the best-fit value of the Dirac $CP$ phase $\delta$ ($\approx -0.68\pi$) taken from Table 1.

Figure 6

Similar to Fig. 5 but for the ${\nu }_{\mu }\to {\nu }_{\mu }$ channel.

Figure 7

Heatmaps for $|\mathrm{\Delta }{P}_{\mu e}|$ are shown for a fixed baseline of 1300 km in the parameter space of $\delta -{\phi }_{\alpha \beta }$ for two values of energies, 2.5 GeV (top row) and 5 GeV (bottom row). Note that $|{ϵ}_{\alpha \beta }|$ was fixed to 0.05. The dashed horizontal white line corresponds to the best-fit value of the Dirac $CP$ phase $\delta$ ($\approx -0.68\pi$) taken from Table 1.

Figure 8

Similar to Fig. 7 but for the ${\nu }_{\mu }\to {\nu }_{\mu }$ channel.

Figure 9

A comparison of the sensitivity of DUNE to probe the NSI parameters at 99% confidence level when a standard low energy (LE) beam tune is used (cyan region) and when a combination of low and medium energy ($\mathrm{LE}+\text{ME}$) beam tune is used (black hatched region), keeping the total run-time the same (3.5 years of $\nu +3.5\mathrm{years}$ of $\overline{\nu }$ run) for both scenarios. In the latter case, the total run-time is distributed between the LE beam (2 years of $\nu +2\mathrm{years}$ of $\overline{\nu }$) and the medium energy beam (1.5 years of $\nu +1.5\mathrm{years}$ of $\overline{\nu }$). The panels with a light yellow (white) background indicate significant improvement (no improvement) by using $\mathrm{LE}+\mathrm{ME}$ beam over using LE only. The numbers in the light yellow shaded panels correspond to the area lying outside the contour for the two cases (cyan for LE and black for $\mathrm{LE}+\mathrm{ME}$) expressed as a percentage of the total parameter space plotted. These numbers quantify the improvement over the LE only option when the ME beam tune is used in conjunction with the LE beam tune in these panels.

Figure 10

The terms (denoted by green, blue and cyan curves) in the right-hand side (rhs) of Eq. (a1) (first column), (a2) (second column) and (a3) (third column) are plotted as functions of $\delta$ for two fixed energies 2.5 GeV (top row) and 5 GeV (bottom row). The overall $\mathrm{\Delta }{P}_{\mu e}$ is represented by the red curve and the small red circles denote where it becomes zero.

Figure 11

$D_1^{e\mu }$ and $D_1^{e\tau }$ are plotted as functions of energy (left panel). ${\gamma }_1^{e\mu }$ and ${\gamma }_1^{e\tau }$ are plotted as functions of energy in the right panel. The standard oscillation parameters are at their b.f. value (Table 1).

Figure 12

The terms (denoted by green, blue and cyan curves) in the rhs of Eq. (b1) (first column), (b2) (second column) and (b3) (third column) are plotted as functions of $\delta$ for two fixed energies 2.5 GeV (top row) and 5 GeV (bottom row). The overall $\mathrm{\Delta }{P}_{\mu \mu }$ (sum of the three terms) is represented by the red curve and the small red circles denote where it becomes zero.

Figure 13

SI-NSI difference at the level of event rates for ${\nu }_{\mu }\to {\nu }_e$ channel (top row) and ${\nu }_{\mu }\to {\nu }_{\mu }$ channel (bottom row) and for different NSI parameters. The LE flux has been used.