Quantum dissipation and $CP$ violation in MINOS

We use the open quantum systems framework to analyze the MINOS data and perform this analysis considering two different dissipative models. In the first model, the dissipative parameter describes the decoherence effect and in the second, the dissipative parameter describes other dissipative effects including decoherence. With the second model it is possible to study $CP$ violation since we consider Majorana neutrinos. The analysis from the muon neutrino and antineutrino beam assigns different values to all the parameters of the models, but is consistent between them. Assuming that neutrinos are equivalent to antineutrinos, the global analysis presents a nonvanishing Majorana $CP$ phase depending on the energetic parametrization of the dissipative parameter.

Figure 1

The graphics were made using the oscillation parameter values obtained with the equivalence condition between ${\nu }_{\mu }$ and ${\overline{\nu }}_{\mu }$. On the left it is shown the neutrino behavior and on the right antineutrino behavior, taking $n=0$ in both Case 1 and Case 7 models.

Figure 2

Contours at 95% C. L. and best fits obtained from the three models studied. Top: contours with the regions allowed to standard oscillation parameters. In this case, there are three contours for each dissipative model with $n=0$, $\pm 1$ and the same contour for the standard oscillation model. Middle: Limits on $\gamma$ as a function of $\mathrm{\Delta }{m}^2$ for the cases $n=0$, $\pm 1$. Bottom: Limits on $\gamma$ as a function of ${\sin }^2(2\theta )$ considering also $n=0$, $\pm 1$.

Figure 3

The contours obtained when $\gamma$ is fixed in its best-fit value. On the left, $\mathrm{\Delta }{m}^2$ is shown as function of ${\sin }^2\varphi$ and on the right, ${\sin }^2(2\theta )$ as a function of ${\sin }^2\varphi$. In the two situations there are contours with 1, 2 and $3\sigma$ of confidence level.