Probing $CPT$ breaking induced by quantum decoherence at DUNE

We show that the decoherence phenomena applied to the neutrino system could lead to an observable breaking of the fundamental $CPT$ symmetry. We require specific textures of nondiagonal decoherence matrices, with nonzero ${\delta }_{CP}$, for making such observations. Using the information from the $CPT$ conjugate channels ${\nu }_{\mu }\to {\nu }_{\mu }$ and ${\overline{\nu }}_{\mu }\to {\overline{\nu }}_{\mu }$ and their corresponding backgrounds, we have estimated the sensitivity of the DUNE experiment for testing $CPT$ under the previous conditions. Four scenarios for energy-dependent decoherence parameters, ${\mathrm{\Gamma }}_{E_{\nu }}=\mathrm{\Gamma }\times (E_{\nu }/\mathrm{GeV}{)}^n$, $n=-1$, 0, 1, and 2, are taken into account, and for most of them, DUNE is able to achieve a $5\sigma$ discovery potential, having $\mathrm{\Gamma }$ in $\mathcal{O}({10}^{-23}\mathrm{GeV})$ for ${\delta }_{CP}=3\pi /2$. Meanwhile, for ${\delta }_{CP}=\pi /2$, we reach $3\sigma$ for $\mathrm{\Gamma }$ in $\mathcal{O}({10}^{-24}\mathrm{GeV})$.

Figure 1

$\mathrm{\Delta }{P}_{\cancel{CPT}}$ vs $E_{\nu }$, evaluated for $\mathrm{\Gamma }={10}^{-23}\mathrm{GeV}$ and ${\delta }_{CP}=3\pi /2$. (a) Group 1 with ${\beta }_{28}$, ${\beta }_{53}$, ${\beta }_{73}=\mathrm{\Gamma }/\sqrt{3}$, ${\beta }_{58}$, ${\beta }_{78}=\mathrm{\Gamma }/\sqrt{7}$, ${\beta }_{12}$, ${\beta }_{23}$, ${\beta }_{45}$, ${\beta }_{67}=\mathrm{\Gamma }/3$. (b) Group 2 with all $\beta$’s equal to $\mathrm{\Gamma }/\sqrt{3}$. The remaining parameters are given in Table 3.

Figure 2

Isocontour curves of $\mathrm{\Delta }{P}_{\cancel{CPT}}$ at the plane $\mathrm{\Gamma }$ vs ${\delta }_{CP}$ evaluated for ${\beta }_{28}=\mathrm{\Gamma }/\sqrt{3}$ and ${\beta }_{56}=\mathrm{\Gamma }/\sqrt{3}$ and for a fixed $E_{\nu }=2.4\mathrm{GeV}$. The two plots at the top correspond to the vacuum oscillation case, while the two plots at the bottom correspond to the matter oscillation case.

Figure 3

$\mathrm{\Delta }{P}_{\cancel{CPT}}$ vs $\mathrm{\Gamma }$, evaluated for different energy dependences $n=-1$, 0, 1, 2; $E_{\nu }=2.4\mathrm{GeV}$; ${\delta }_{CP}=3\pi /2$; and fixing ${\beta }_{28}=\mathrm{\Gamma }/\sqrt{3}$. We have (a) the vacuum oscillation case, and (b) the matter oscillation case. In both plots we use the same scale.

Figure 4

Here we display $\mathcal{R}$ vs $\mathrm{\Gamma }$ for the four energy dependences $n=-1$, 0, 1, and 2, showing the signal (blue) and background (red). We consider ${\delta }_{CP}=3\pi /2$.

Figure 5

Here we have two plots: ${\theta }_{23}$ vs ${\theta }_{12}$ and ${\theta }_{23}$ vs ${\theta }_{13}$, varying the mixing angles within the $3\sigma$ range, showing the percentual variation of $\mathcal{R}$ with respect to the value obtained for the best-fit oscillation parameters given in Table 3. The mixing angle that does not appear in the corresponding plot is fixed at its best-fit value. In all the plots, we fix $\mathrm{\Gamma }={10}^{-23}\mathrm{GeV}$ and ${\delta }_{CP}=3\pi /2$.

Figure 6

We analyze the confidence levels for the maximum values for $\mathcal{R}$. For ${\delta }_{\mathrm{CP}}\sim \pi /2$ we have $2.9\sigma$, $3.4\sigma$, $4.7\sigma$, and $5.5\sigma$ of confidence for $n=-1$, 0, 1, and 2, respectively. On the other hand, for ${\delta }_{\mathrm{CP}}\sim 3\pi /2$ we have $10.3\sigma$, $9.8\sigma$, $9.6\sigma$, and $9.7\sigma$ of confidence for $n=-1$, 0, 1 and 2, respectively.

Figure 7

The black horizontal dashed line is the expected value in the SO. The blue dashed line corresponds to the case of a DDM. Meanwhile, the solid black line corresponds to the case of a NDM, with both cases evaluated at ${\delta }_{CP}=3\pi /2$. The red fringes (small, medium, and large) represent the statistical error for $1\sigma$, $3\sigma$, and $5\sigma$ (respectively). The $\beta$’s used correspond to the ones given in Sec. 2b5. The intersection between the black horizontal dashed line and the vertical one marks the $5\sigma$ significance of the NDM case relative to the SO case.

Figure 8

Similar to Fig. 7, but for ${\delta }_{CP}=\pi /2$. Here, the intersection between the black horizontal dashed line and the vertical one marks the $3\sigma$ significance of the NDM case relative to the SO case.