Fair scans of the seesaw. Consequences for predictions on LFV processes

Abstract

We give a straightforward procedure to scan the seesaw parameter-space, using the common “R-parametrization”, in a complete way. This includes a very simple rule to incorporate the perturbativity requirement as a condition for the entries of the R-matrix. As a relevant application, we show that the somewhat propagated belief that BR(μ → e, γ) in supersymmetric seesaw models depends strongly on the value of θ 13 is an “optical effect” produced by incomplete scans, and does not hold after a careful analytical and numerical study. When the complete scan is done, BR(μ → e, γ) gets very insensitive to θ 13. This holds even if the right-handed neutrino masses are kept constant or under control (as is required for succesful leptogenesis). In most cases the values of BR(μ → e, γ) are larger than the experimental upper bound. Including (unflavoured) leptogenesis does not introduce any further dependence on θ 13, although decreases the typical value of BR(μ → e, γ).