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Unlike the Dirac CP-phase $\delta$, the Majorana CP-phases $\alpha,\beta$ do not appear in the formula of neutrino flavour oscillation probability. Hence, they cannot be measured from oscillation experiments.

However, unlike the unphysical phases (which can always be absorbed into the definition of fields) of the PMNS mixing matrix, the Majorana phases are physical (cannot be absorbed into the definition of fields, if neutrinos are of Majorana type) i.e., are in principle, measurable.

But how can one possibly measure the Majorana phases, at least in principle?

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  • $\begingroup$ In principle? Scattering matrix elements typically depend on all the physical parameters. In some cases you can find cross-sections that are insensitive to some parameter to tree level, but if you consider complicated enough processes, and sufficiently high loop order, predictions will depend on all Standard Model parameters. $\endgroup$ – AccidentalFourierTransform Mar 13 '18 at 20:18
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Indeed, oscillation experiments (even including matter effects) are not sensitive to Majorana phases. The matrix element for $0\nu\beta\beta$ decay involves one Majorana phase difference $\alpha$ (see, for example, here) $$ |m_{ββ} | \simeq sin (2 θ_{12})\sqrt{Δm^{2}_{12}} + e^{ 2i α} sin( 2 θ_{13}) \sqrt{Δm^2_{23}} . $$ The second Majorana phase is of course measurable in principle (using some other lepton number violating process), but I am not aware of a practical way to do it.

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