Degeneracies in long-baseline neutrino experiments from nonstandard interactions

We study parameter degeneracies that can occur in long-baseline neutrino appearance experiments due to nonstandard interactions (NSI) in neutrino propagation. For a single off-diagonal NSI parameter, and neutrino and antineutrino measurements at a single $L/E$, there exists a continuous four-fold degeneracy (related to the mass hierarchy and ${\theta }_{23}$ octant) that renders the mass hierarchy, octant, and $CP$ phase unknowable. Even with a combination of $\mathrm{NO}\nu \mathrm{A}$ and T2K data, which in principle can resolve the degeneracy, both NSI and the $CP$ phase remain unconstrained because of experimental uncertainties. A wide-band beam experiment like DUNE will resolve this degeneracy if the nonzero off-diagonal NSI parameter is ${\epsilon }_{e\mu }$. If ${\epsilon }_{e\tau }$ is nonzero, or the diagonal NSI parameter ${\epsilon }_{ee}$ is $\mathcal{O}(1)$, a wrong determination of the mass hierarchy and of $CP$ violation can occur at DUNE. The octant degeneracy can be further complicated by ${\epsilon }_{e\tau }$, but is not affected by ${\epsilon }_{ee}$.

Figure 1

Biprobability plots ($P({\overline{\nu }}_{\mu }\to {\overline{\nu }}_e)$ versus $P({\nu }_{\mu }\to {\nu }_e)$) for $L=1300\mathrm{km}$ and $E=3\mathrm{GeV}$. The solid curves show the SM values for fixed mixing angles and varying $\delta$ (one curve for each combination of hierarchy and ${\theta }_{23}$ octant); the dashed (dotted) [dotdashed] curves show the values assuming NSI with ${\epsilon }_{e\mu }=0.05$ (0.10) [0.15], and varying ${\varphi }_{e\mu }$ for the NH and first octant with ${\delta }^{\prime }=0$. The mixing angles and mass-squared differences are set at their best-fit values from Ref. [12].

Figure 2

Values of a single nonzero $\epsilon$ as a function of ${\delta }^{\prime }$ that give $P({\nu }_{\mu }\to {\nu }_e)$ and $P({\overline{\nu }}_{\mu }\to {\overline{\nu }}_e)$ degenerate with the SM with $\delta =0$ and NH, at $\mathrm{NO}\nu \mathrm{A}$ ($L=810\mathrm{km}$, $E=2\mathrm{GeV}$) and T2K ($L=295\mathrm{km}$, $E=0.6\mathrm{GeV}$). The mixing angles and mass-squared differences are the best-fit values in Ref. [12].

Figure 3

$1\sigma$, $2\sigma$ and $3\sigma$ allowed regions for ${\epsilon }_{e\mu }$ and ${\epsilon }_{e\tau }$ (when only one of them is nonzero) from combined $\mathrm{NO}\nu \mathrm{A}$ and T2K data, and from DUNE.

Figure 4

${\nu }_{\mu }\to {\nu }_e$ and ${\overline{\nu }}_{\mu }\to {\overline{\nu }}_e$ oscillation probabilities at DUNE. The mixing angles and mass-squared differences are the best-fit values in Ref. [12].

Figure 5

Same as Fig. 3, except both ${\epsilon }_{e\mu }$ and ${\epsilon }_{e\tau }$ are nonzero.

Figure 6

Same as Fig. 3, except for ${\epsilon }_{ee}$.