Uncovering Majorana nature through a precision measurement of $CP$ phase

We show the possibility to discover the neutrino nature by measuring the Majorana CP phase at the DUNE experiment. This phase is turned on by a decoherence environment, possibly originated by physics at the Planck scale. A sizable distortion in the measurement of the Dirac CP violation phase $\delta_{\mathrm{CP}}$ is observed at DUNE when compared with T2HK measurement due to decoherence and non-null Majorana phase. Being that, when the measurement of the Majorana phase is performed at DUNE, it reaches a precision of 23 (21) $\%$ for a decoherence parameter $\Gamma=4.5(5.5)\times 10^{-24} \mathrm{GeV}$ and a Majorana phase equal to $1.5 \pi$. The latter precision is similar to the one obtained at the T2K experiment at its current Dirac CP violation phase measurement.