We present an illustrative discussion of the physics potential of µ − -e + conversion. We point out that this process, although much less frequently studied than the related but much more popular processes of µ − -e − conversion and neutrinoless double beta decay, in fact is a promising alternative possibility to detect both lepton flavour and number violation. However, for this goal to be reached, a combined effort of experiments and theory, both in nuclear and particle physics, is necessary to advance. The aim of this paper is to be an "appetiser" to trigger such an initiative. *

We discuss how the intensity and the energy frontiers provide complementary constraints within a minimal model of neutrino mass involving just one new field beyond the Standard Model at accessible energy, namely a doubly charged scalar S ++ and its antiparticle S −− . In particular we focus on the complementarity between high-energy LHC searches and low-energy probes such as lepton flavor violation. Our setting is a prime example of how high-and low-energy physics can cross-fertilize each other.

We present a detailed discussion of the lepton flavour and number violating conversion of bound muons into positrons. This process is a viable alternative to neutrinoless double beta decay and, given that experiments on ordinary µ − -e − conversion are expected to improve their sensitivities by several orders of magnitude in the coming years, we can also assume the limit on µ − -e + conversion to improve by roughly the same factor. We discuss how new physics at a high scale can lead to short-range contributions to this conversion process and we present one explicit case in great detail (the single one for which the corresponding nuclear matrix element is presently known). The main goal of our discussion is to make the respective computation accessible to the particle physics community, so that promising models can be investigated while the nuclear physics community can simultaneously advance the computation of nuclear matrix elements. Given the progress to be expected on the experimental side, it may even be possible that lepton number violation in the eµ-sector is discovered by µ − -e + conversion before neutrinoless double beta decay can show its existence in the ee-sector.

We present a comprehensive renormalization group analysis of the littlest seesaw model involving two right-handed neutrinos and a very constrained Dirac neutrino Yukawa coupling matrix. We perform the first χ 2 analysis of the low energy masses and mixing angles, in the presence of renormalization group corrections, for various right-handed neutrino masses and mass orderings, both with and without supersymmetry. We find that the atmospheric angle, which is predicted to be near maximal in the absence of renormalization group corrections, may receive significant corrections for some nonsupersymmetric cases, bringing it into close agreement with the current best fit value in the first octant. By contrast, in the presence of supersymmetry, the renormalization group corrections are relatively small, and the prediction of a near maximal atmospheric mixing angle is maintained, for the studied cases. Forthcoming results from T2K and NOνA will decisively test these models at a precision comparable to the renormalization group corrections we have calculated.

We present the first detailed computation of the conversion of a bound muon into an electron mediated by a doubly charged SU (2) singlet scalar. Although such particles are not too exotic, up to now their contribution to µ-e conversion is unknown. We close this gap by presenting a detailed calculation, which will allow the reader not only to fully comprehend the discussion but also to generalise our results to similar cases if needed. We furthermore compare the predictions, for both the general case and for an example model featuring a neutrino mass at 2-loop level, to current experimental data and future sensitivities. We show that, depending on the explicit values of the couplings as well as on the actual future limits on the branching ratio, µ-e conversion may potentially yield a lower limit on the doubly charged singlet scalar mass which is stronger than what could be obtained by colliders. Our results considerably strengthen the case for low-energy lepton flavour violation searches being a very valuable addition to collider experiments. *