Uncovering the Majorana nature through a precision measurement of the 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 ${\ensuremath{\delta}}_{CP}$ is observed at DUNE when compared with T2HK measurement due to decoherence and the 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 $\mathrm{\ensuremath{\Gamma}}=4.5(5.5)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}24}\text{ }\text{ }\mathrm{GeV}$ and a Majorana phase equal to $1.5\ensuremath{\pi}$. The latter precision is similar to the one obtained at the T2K experiment at its current Dirac $CP$ violation phase measurement.