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In a world devoid of axions, the smallness of the strong CP phase can haveimplications for leptonic CP violation being probed by neutrino experiments.For example, if nature adopted an axionless solution to the strong CP problem,the same symmetries that set the strong CP phase to zero at the tree-level, mayalso set the leptonic $CP$ phases to zero (mod \pi). This automatically happensin the left-right symmetric model when it is extended minimally to solve thestrong CP problem by imposition of both P and CP. In the Nelson Barr solutionthe needed symmetries can be assigned so that leptonic CP violation is notgenerated. In the minimal left-right symmetric model with P (and not CP), wherethe strong CP problem remains, leptonic CP phases radiatively generate thestrong CP phase in one loop, and therefore they may be absent (negligiblysmall) in large regions of parameter space. All these results motivate us toconsider a Bayesian prior for leptonic Dirac CP phase \delta_{CP} of the PMNSmatrix that has delta function like peaks at CP conserving values of 0 and \pion top of a uniform distribution. We evaluate the posterior probabilitydistribution for \delta_{CP} using the current global fit to neutrinoexperiments and find significant enhancements for the probability that\delta_{CP} is at or negligibly close to \pi. We also provide useful tables forthe posterior probability considering present and future experimentalsensitivities.

Bayesian probability for leptonic CP phase with strong CP prior