Octant of ${\theta }_{23}$ in Danger with a Light Sterile Neutrino

Present global fits of world neutrino data hint towards nonmaximal ${\theta }_{23}$ with two nearly degenerate solutions, one in the lower octant (${\theta }_{23}<\pi /4$), and the other in the higher octant (${\theta }_{23}>\pi /4$). This octant ambiguity of ${\theta }_{23}$ is one of the fundamental issues in the neutrino sector, and its resolution is a crucial goal of next-generation long-baseline (LBL) experiments. In this Letter, we address, for the first time, the impact of a light eV-scale sterile neutrino towards such a measurement, taking the Deep Underground Neutrino Experiment as a case study. In the so-called $3+1$ scheme involving three active and one sterile neutrinos, the ${\nu }_{\mu }\to {\nu }_e$ transition probability probed in the LBL experiments acquires a new interference term via active-sterile oscillations. We find that this interference term can mimic a swap of the ${\theta }_{23}$ octant, even if one uses the information from both neutrino and antineutrino channels. As a consequence, the sensitivity to the octant of ${\theta }_{23}$ can be completely lost, and this may have serious implications for our understanding of neutrinos from both the experimental and theoretical perspectives.

Figure 1

Bievent plot corresponding to the DUNE setup. The ellipses represent the three-flavor case, while the colored blobs correspond to the $3+1$ scheme (see the legend). We take ${\sin }^2{\theta }_{23}=0.42$ (0.58) as the benchmark value for the LO (HO). In the three-flavor ellipses, the running parameter is ${\delta }_{13}$, varying in the range $[-\pi ,\pi ]$. In the four-flavor blobs there are two running parameters, ${\delta }_{13}$ and ${\delta }_{14}$, both varying in their allowed ranges $[-\pi ,\pi ]$. In the $3+1$ case, we have assumed that ${\theta }_{34}=0°$.

Figure 2

Discovery potential for excluding the wrong octant as a function of true ${\delta }_{13}$ assuming LO-NH (left panel) and HO-NH (right panel) as the true choices. We take ${\sin }^2{\theta }_{23}=0.42$ (0.58) as the benchmark value for the LO (HO). In each panel, we present the results for the three-flavor case (the black line), and for the $3+1$ scheme considering four different values of true ${\delta }_{14}$ (the colored lines). In the $3\nu$ case, we marginalize away (${\theta }_{23}$, ${\delta }_{13}$) (test). In the $3+1$ scheme, we fix ${\theta }_{14}={\theta }_{24}=9°$ and ${\theta }_{34}=0$ and marginalize over (${\theta }_{23}$, ${\delta }_{13}$, ${\delta }_{14}$) (test).

Figure 3

Discovery potential for excluding the wrong octant in the (${\sin }^2{\theta }_{23}$, ${\delta }_{13}$) (true) plane, assuming NH as the true choice. The left (right) panel corresponds to the $3\nu$ ($3+1$) case. In the three-flavor case, we marginalize away (${\theta }_{23}$, ${\delta }_{13}$) (test). In the $3+1$ case, in addition, we marginalize over ${\delta }_{14}$ (true) and ${\delta }_{14}$ (test), fixing ${\theta }_{14}={\theta }_{24}=9°$ and ${\theta }_{34}=0$. The solid blue, dashed magenta, and dotted black curves correspond, respectively, to the $2\sigma$, $3\sigma$, and $4\sigma$ confidence levels (1 d.o.f.).