Canonical Constraints on Leptonic Cp Violation using UHCR neutrino fluxes

It is shown that one can in principle constrain the CP-violating parameter delta from measurements of four independant |V_{ij}|^2, or three of them and a ratio, in the leptonic sector. To quantify our approach, using unitarity, we derive simple expressions in terms of four independant |V_{ij}|^2 for cos(delta) and an expression for sin^2(delta) from J^2. Thus, depending on the values of |V_{ij}| and their accuracy, we can set meaningful limits on |delta|. To illustrate numerically, if |V_{u1}|^2 is close to 0.1 with a 10% precision, and if |V_{e3}^2 is larger than 0.005 and for values of |V_{e2}|^2 and |V_{u3}|^2 that stay within +-0.1 of the current experimental data leads to a bound pi/2 < |delta| < pi. Alternatively, a certain combination of parameters with values of |V_{e3}|^2 larger than 0.01 leads to a closed bound of 73 < |delta| < 103. In general, we find that it is better to use |V_{u1}|^2 or |V_{t1}|^2 as the fourth independant |V_{ij}|^2 and that over most of the parameter space, delta is least sensitive to |V_{e3}|^2. With just three independant measurements (solar, atmospheric and reactor) it is impossible to set limits on the CP phase. In this respect, we study the use of ultra high energy cosmic (UHCR) neutrino fluxes as the additional fourth information. We find that within the SM, neutrino fluxes of all three flavours will be very similar but that pushing current neutrino data to their extreme values still allowed, ratios of cosmic neutrino fluxes can differ by up to 20%; such large discrepancies could imply negligibly small CP-violation. We also study a non radiative neutrino decay model and find that the neutrino fluxes can differ by a factor of up to 3 within this model and that an accuracy of 10% on the neutrino fluxes is sufficient to set interestin limits on delta.Comment: 8 pages, 2 figures, 5 table