Can one have significant deviations from leptonic 3 $$\times $$ × 3 unitarity in the framework of type I seesaw mechanism?

We address the question of deviations from $$3\times 3$$ unitarity of the leptonic mixing matrix showing that, in the framework of type I seesaw mechanism, one may have significant deviations from unitarity that can be detected at the next round of experiments while some of the heavy neutrino masses are sufficiently low to become within experimental reach. For that purpose we introduce a specially useful parametrisation that enables to control all deviations of unitarity through a single $$3 \times 3$$ matrix, which we denote by X and which connects the mixing of the light and heavy neutrinos in the context of type I seesaw. We show that there is no need for the Yukawa couplings to be extremely suppressed. We present specific examples where deviations from $$3\times 3$$ unitarity are sufficiently small to conform to all the present stringent experimental bounds.