Phenomenology of the right-handed lepton mixings at the LHC in LR symmetric theory and the Time-Reversal symmetry violation in the µ --> eϒ decay and µ --> e conversion process

We study how the elements of the leptonic right-handed mixing matrix can be determined at the LHC in the minimal Left-Right symmetric extension of the standard model. We do it by explicitly relating them with physical quantities of the Keung-Senjanovi\'c process and the lepton number violating decays of the right doubly charged scalar. We also point out that the left and right doubly charged scalars can be distinguished at the LHC, without measuring the polarization of the final state leptons coming from their decays. Then we study time reversal symmetry violation in the $\mu\rightarrow e\gamma $ decay and the $\mu\rightarrow e$ conversion process and compute a T-odd triple vector correlation for the $\mu\rightarrow e\gamma $ decay and the $\mu\rightarrow e$ conversion process, finding simple results in terms of the CP violating phases of the effective Hamiltonians. Finally we focus on the minimal Left-Right symmetric extension of the Standard Model, which is a complete model of neutrino masses that can lead to an appreciable correlation. We show that under rather general assumptions, this correlation can be used to discriminate between Parity or Charge-conjugation as the discrete Left-Right symmetry.