Mixing angle and phase correlations from A5 with generalised CP and their prospects for discovery

The observed leptonic mixing pattern could be explained by the presence of a discrete flavour symmetry broken into residual subgroups at low energies. In this scenario, a residual generalised CP symmetry allows the parameters of the PMNS matrix, including Majorana phases, to be predicted in terms of a small set of input parameters. In this article, we study the mixing parameter correlations arising from the symmetry group A5 including generalised CP subsequently broken into all of its possible residual symmetries. Focusing on those patterns which satisfy present experimental bounds, we then provide a detailed analysis of the measurable signatures accessible to the planned reactor, superbeam and neutrinoless double beta decay experiments. We also discuss the role which could be played by high-precision measurements from longer term projects such as the Neutrino Factory. This work provides a concrete example of how the synergies of the upcoming experimental programme allow flavour symmetric models to be thoroughly investigated. Indeed, thanks to the rich tapestry of observable correlations, we find that each step of the experimental programme can make important contributions to the assessment of such flavour-symmetric patterns, and ultimately all patterns that we have identified can be excluded, or strong evidence found for their continued relevance.