The exotic double-charge exchange μ - →e + conversion in nuclei

Abstract The formalism for the neutrinoless ( μ − ,e + ) conversion is investigated in detail and the relevant nuclear matrix elements for light intermediate neutrinos in the case of 27 Al( μ − ,e + ) 27 Na are calculated. The nucleus 27 Al is going to be used as a stopping target in the MECO experiment at Brookhaven, one of the most sensitive probes expected to reach a sensitivity in the branching ratio of the order 10 −16 within the next few years. The relevant transition operators are constructed utilizing a variety of mechanisms present in current gauge theories, with emphasis on the intermediate neutrinos, both light and heavy, and heavy SUSY particles. The nuclear wave functions, both for the initial state and all excited final states are obtained in the framework of 1s–0d shell model employing the well-known and tested Wildenthal realistic interaction. In the case of the light intermediate neutrinos the transition rates to all excited final states up to 25 MeV in energy are calculated. We find that the imaginary part of the amplitude is dominant. The total rate is calculated by summing over all these partial transition strengths. We also find that the rate due to the real part of the amplitude is much smaller than the corresponding quantity found previously by the closure approximation.