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Abstract

We propose a complex extension of mixed $\ensuremath{\mu}\ensuremath{\tau}$ antisymmetry in the neutrino Majorana mass matrix ${M}_{\ensuremath{\nu}}$. This can be implemented in the Lagrangian by a generalized $CP$ transformation (labeled by a mixing parameter $\ensuremath{\theta}$) on the left-chiral flavor neutrino fields. We investigate its implications for leptonic $CP$ violation and neutrino phenomenology in general. Interestingly, the $\ensuremath{\mu}\ensuremath{\tau}$ mixing parameter $\ensuremath{\theta}$ gets correlated with the Dirac $CP$ phase $\ensuremath{\delta}$ and the atmospheric mixing angle ${\ensuremath{\theta}}_{23}$ through an analytical relation. In general, for arbitrary $\ensuremath{\theta}$, both ${\ensuremath{\theta}}_{23}$ and $\ensuremath{\delta}$ are nonmaximal. We discuss the corresponding results for the $CP$ asymmetry parameter ${A}_{\ensuremath{\mu}e}$ in neutrino oscillation experiments. For a nonmaximal $\ensuremath{\delta}$, one of the two Majorana phases is different from 0 or $\ensuremath{\pi}$, thereby leading to nonvanishing Majorana $CP$ violation with observable consequences for the neutrinoless double-beta ($\ensuremath{\beta}\ensuremath{\beta}0\ensuremath{\nu}$) decay process. We numerically work out in detail the predictions for that process in relation to various ongoing and forthcoming experiments. We also work out the predictions of our scheme on flavor flux ratios at neutrino telescopes. While exact $CP$-transformed $\ensuremath{\mu}\ensuremath{\tau}$ interchange antisymmetry ($\ensuremath{\theta}=\ensuremath{\pi}/2$) leads to an exact equality among those ratios, taking the value 0.5, a tiny deviation can cause a drastic change in them. Careful measurements of these flux ratios in the future will further constrain the parameter $\ensuremath{\theta}$.

CPtransformed mixedμτantisymmetry for neutrinos and its consequences

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Abstract

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