Majorana CP Violation Insights from Decaying Neutrinos

TL;DR

This work shows that Majorana phases $\phi_1$ and $\phi_2$ can influence neutrino oscillation probabilities when neutrino decay renders the effective Hamiltonian non-Hermitian. Using a Cayley–Hamilton formalism, the authors derive approximate three-flavor probabilities in matter, including diagonal and off-diagonal decay terms and decay phases, and analyze their impact on CP violation and parameter degeneracies in a long-baseline setup such as DUNE. A key finding is that off-diagonal decay, together with Majorana phases, enables observable Majorana effects in $P_{\alpha\beta}$ and can modify $A^{CP}_{\alpha\beta}$ and degeneracy patterns, sometimes enhancing CP sensitivity beyond the Dirac-only case. The results suggest a new avenue to probe the Majorana nature of neutrinos via decay-induced CP-violating effects in upcoming experiments, highlighting the interplay of Dirac, Majorana, and decay phases in long-baseline phenomenology.

Abstract

It is well-known that within the standard three flavor neutrino oscillation formalism, the Majorana phases appearing in the neutrino mixing matrix cannot have any effect on neutrino oscillation probabilities thereby evading testability at neutrino oscillation experiments. We consider an effective non-Hermitian Hamiltonian describing three flavor neutrino oscillations with the possibility of neutrino decay and demonstrate that the two Majorana phases can entangle with the off-diagonal decay terms and appear at the level of oscillation probabilities. Using the Cayley-Hamilton theorem, we derive approximate analytical expressions for three flavor neutrino oscillation probabilities in the presence of neutrino decay, taking into account matter effects. In the context of a long baseline neutrino experiment, we then analyse the impact of Majorana phases on the oscillation probabilities for different channels as well as on observables related to CP violation effects in neutrino oscillations. Finally, we discuss the effect of Majorana phases on the parameter degeneracies in the neutrino oscillation framework.

Figures (10)

• Figure 1: Left panel : Comparison between analytical expression and numerical result for appearance (top) and disappearance (bottom) channels for the case of DUNE ($L = 1300$ km). The solid (dotted) line represents analytical expressions (numerical results). Right panel : the absolute error, $|\Delta P^{\textrm{error}}_{\alpha \beta}|$ (top) and $|\Delta P^{\textrm{error}}_{\alpha \alpha}|$ (bottom).
• Figure 2: The upper (lower) panel corresponds to $P^{}_{\mu e}$ ($P^{}_{\mu \mu}$) as a function of energy $E$. Different curves are shown for no decay, $P^{(0)}_{\mu e}$, no decay together with only $\gamma^{}_3$ decay, $P^{(0)}_{\mu e} +P^{(\gamma_{3})}_{\mu e}$, and for the most general case, $P^{(0)}_{\mu e} +P^{(\gamma_{3})}_{\mu e}+ P^{(\Gamma)}_{\mu e}$, using the blue, orange, and green lines, respectively, for DUNE. The left and right panels differ due to the benchmark values of the phases, as mentioned at the top of the plots.
• Figure 3: Top (bottom) panel shows $P^{}_{\mu e}$ ($\bar{P}^{}_{\mu e}$) as a function of energy E. In the top left panel, black dotted curve corresponds to $\phi^{}_{1} = \phi^{}_{2} = 0$, whereas blue (magenta) band represents $\phi^{}_{1}\in[-\pi, \pi], \phi^{}_{2}=0$ ($\phi^{}_{1} = 0, \phi^{}_{2}\in[-\pi, \pi]$). In the top right panel, the black dotted curve is for $\chi^{}_{ij} =0$, whereas the orange, green, and magenta bands correspond non-zero $\chi^{}_{12}, \chi^{}_{13},$ and $\chi^{}_{23}$, respectively. Color coding is the same for the lower and top panels.
• Figure 4: Same as Fig. \ref{['fig:pmue_band']} (top row) but for $\nu^{}_{\mu}\to\nu^{}_{\mu}$ channel.
• Figure 5: Oscillogram for $P^{}_{\mu e}$ (left panel) and $|\Delta P^{M}_{\mu e}| =|P^{\textrm{(w/ majorana)}}_{\mu e}- P^{\textrm{(w/o majorana)}}_{\mu e}|$ (right panel) in the energy $E$ versus baseline $L$ plane. The first column corresponds to probability in the presence of Majorana phases and the second column depicts the difference between the probabilities, with (w/) and without (w/o) Majorana phases for $\nu^{}_{\mu} \to \nu^{}_{e}$ channel. The value of Dirac CP phase is $\delta^{}_{} = - \pi/2$.