Can μ – e Conversion in Nuclei be a Good Probe for Lepton - Number Violating Higgs Couplings ?

Motivated by the improving sensitivity, R, of experiments on μ T i → e T i and the enhanced Higgs nucleon interaction, we study this lepton number violating process induced by Higgs exchange. Taking the possible sensitivity, R ≃ 10, we obtain the constraint on the Higgs-muon-electron vertex, κμe, to be less than 2.4×10−7 if the masses of the Higgs scalar and W gauge boson are the same. κμe is also calculated for some models. In this paper we report on a study of direct muon-electron conversion in nuclei as a probe of new physics represented by an effective μ−e−S vertex where S is a neutral scalar particle. For example, the scalar S can be the Higgs scalars in a one doublet model with an extended fermion sector, or linear combinations of scalar particles in some extended Higgs models such as the supersymmetric standard model. Previous discussion of μ−e conversion concentrated mostly on the effects of virtual photon and Z–boson exchanges [1]. Effects of an extra Z– boson has also been considered recently [2]. Scalar and pseudoscalar effects were outlined in Ref. [1] where the details of the nuclear effects were emphasized. If the Higgs coupling to nucleon is taken to be proportional to the current masses of the u– and d–quarks, then the effect would be very small. Here, we treat the scalar-nucleon-nucleon via the approach of Shifman, et. al. [3], which increase the coupling strength to that of 2 27 mN where mN is the mass of the nucleon. This is approximately one order of magnitude enhancement over the use of the current quark masses. A second enhancement of the S−N −N coupling can arise in extended Higgs model where it is multiplied by ratios of vacuum expectation values of scalars fields. In supersymmetry, the ratio tan β ≥ 10 is certainly acceptable. The third factor comes from the fact that scalar exchange in μ− e is coherent 1 over the nuclei [4]. In this respect, it is similar to photon and Z exchange. On the experimental side, we are encouraged by the on going experiment at PSI [5] of μ T i → e T i which will achieve a sensitivity R(T i) = Γ(μT i → eT i)/Γ(μT i → νμT i) ≃ 3× 10 and prospects of lowering this limit to the level of 10 − 10 being considered at INS Moscow [6] and TRIUMF [7]. This motivated us to reexamine μ− e conversion and focus on it as a probe of the non-standard μ − e − S vertex. Comparison with μ → e γ and/or μ → 3e where they appliy are also given. At the quark level, the effective interaction Lagrangian induced by an exchange of a Such is not the case for pseudoscalar and axial vector exchanges and henceforth we shall ignore them