Measuring the leptonic $CP$ phase in neutrino oscillations with nonunitary mixing

Non-unitary neutrino mixing implies an extra $CP$ violating phase that can fake the leptonic Dirac $CP$ phase ${\delta }_{CP}$ of the simplest three-neutrino mixing benchmark scheme. This would hinder the possibility of probing for $CP$ violation in accelerator-type experiments. We take T2K and T2HK as examples to demonstrate the degeneracy between the “standard” (or “unitary”) and “nonunitary” $CP$ phases. We find, under the assumption of nonunitary mixing, that their $CP$ sensitivities severely deteriorate. Fortunately, the TNT2K proposal of supplementing T2(H)K with a $\mu \mathrm{DAR}$ source for better measurement of ${\delta }_{CP}$ can partially break the $CP$ degeneracy by probing both $\cos {\delta }_{CP}$ and $\sin {\delta }_{CP}$ dependences in the wide spectrum of the $\mu \mathrm{DAR}$ flux. We also show that the further addition of a near detector to the $\mu \mathrm{DAR}$ setup can eliminate the degeneracy completely.

Figure 1

The decomposed $CP$ coefficients for the neutrino oscillation probability $P_{\mu e}$ for T2(H)K.

Figure 2

$R_a$ ratio as given in Eq. (10) for the T2(H)K experimental setup, setting $2|{\alpha }_{21}|/{\alpha }_{22}=5\%$. The solid red line corresponds to $R_2$, while $R_3$ is given by the dashed blue line.

Figure 3

Electron antineutrino appearance probability as a function of $L/E$ for three different assumptions: (i) black solid line: unitary case with ${\delta }_{CP}=0$, (ii) blue dashed line: unitary with ${\delta }_{CP}=3\pi /2$, (iii) red solid line: nonunitary case with ${\delta }_{CP}=0$, $|{\alpha }_{21}|=0.02$ and $\varphi =0.1\pi$.

Figure 4

Left: muon to electron neutrino appearance probability at a baseline of 295 km. Right: the corresponding $CP$ asymmetry between neutrino and antineutrino oscillations. We compare three assumptions: unitary mixing in vacuum (red), unitary mixing in matter (blue) and nonunitary mixing in matter with $|{\alpha }_{21}|=0.02$ and $\varphi =3\pi /2$ (green). In all cases we take ${\delta }_{CP}=3\pi /2$.

Figure 5

The marginalized ${\chi }^2({\delta }_{CP})$ function at T2K and T2HK under the assumptions of unitary mixing (blue) and nonunitary mixing with (red) or without (black) the prior constraint.

Figure 6

Bi-event rate plot for T2K for standard three-neutrino mixing with varying ${\delta }_{CP}$ (black line), and nonunitary mixing with fixed ${\delta }_{CP}$ value and varying $\varphi$ (color lines). Dashed lines correspond to ${\sin }^2{\theta }_a=0.5$ while solid lines correspond to ${\sin }^2{\theta }_a=0.5\pm 0.055$.

Figure 7

The amplitude matrix elements $S_{ij}^{\prime }$ that contribute to the decomposed $CP$ coefficients for the probabilities of antineutrino oscillation at $\mu \mathrm{SK}$ and $\mu \mathrm{HK}$.

Figure 8

The marginalized ${\chi }^2({\delta }_{CP})$ function at TNT2K under the assumptions of unitarity (blue), nonunitary mixing with (red) or without (black) the prior constraint.

Figure 9

Bi-event rate plot for TNT2K for standard three-neutrino mixing with varying ${\delta }_{CP}$ (black line), and nonunitary mixing with fixed ${\delta }_{CP}$ value and varying $\varphi$ (color lines). Dashed lines correspond to ${\sin }^2{\theta }_a=0.5$ while solid lines correspond to ${\sin }^2{\theta }_a=0.5\pm 0.055$.

Figure 10

Event rates (left panel) and the sensitivity on $|{\alpha }_{21}|$ (right panel) at $\mu \text{Near}$ as a function of background rate and detector size. For the sensitivity plot the solid contours are obtained with both 20% uncertainty in the $\mu \mathrm{DAR}$ flux normalization and 50% uncertainty in the background-signal flux ratio. In contrast, the dashed contours are obtained with only 20% uncertainty in the $\mu \mathrm{DAR}$ flux normalization while the background-signal flux ratio is fixed.

Figure 11

The marginalized ${\chi }^2({\delta }_{CP})$ function at $\mathrm{TNT}2\mathrm{K}+\mu \text{Near}$ under the assumptions of unitarity (blue), nonunitary mixing with (black) or without (red) the prior constraint.