Abstract
The experimental sensitivity to μ→e conversion on nuclei is set to improve by four orders of magnitude in coming years. However, various operator coefficients add coherently in the amplitude for μ→econversion, weighted by nucleus-dependent functions, and therefore in the event of a detection, identifying the relevant new physics scenarios could be difficult. Using a representation of the nuclear targets as vectors in coefficient space, whose components are the weighting functions, we quantify the expectation that different nuclear targets could give different constraints. We show that all but two combinations of the 10 Spin-Independent (SI) coefficients could be constrained by future measurements, but discriminating among the axial, tensor and pseudoscalar operators that contribute to the Spin-Dependent (SD) process would require dedicated nuclear calculations. We anticipate that μ→econversion could constrain 10 to 14 combinations of coefficients; if μ→eγ and μ→ee¯e constrain eight more, that leaves 60 to 64 “flat directions” in the basis of QED × QCD-invariant operators which describe μ→e flavour change below mW.
Highlights
The observation of neutrino mixing and masses implies that flavour cannot be conserved among charged leptons
The PRISM/PRIME proposal [6] aims to probe ∼ 10−18, and at the same time enables to use heavy μ → e conversion targets with shorter lifetimes of their muonic atoms, thanks to its designed pure muon beam with no pion contamination.1. This enhanced sensitivity and broader selection of μ → e conversion targets motivate our interest in lowenergy μ ↔ e flavour change
This letter studies the selection of targets for μ→e conversion, with the aim that they probe independent combinations of μ → e flavour-changing parameters, while including the theoretical uncertainties of the calculation
Summary
The observation of neutrino mixing and masses implies that flavour cannot be conserved among charged leptons. The tensor and axial vector contributions were estimated in References [19,11] for light ( Z 20) nuclei, where the muon wavefunction is wider than the radius of the nucleus, and the electron can be approximated as a plane wave In this limit, where the muon wavefunction can be factored out of the nuclear spin-expectation-value, the nuclear calculation of SD WIMP scattering on the quark axial current can be used for μ→e conversion. Where is the proton spin expectation value in isotope at zero momentum transfer, and S I (mμ)/S I (0) is a finite momentum transfer correction, which has been calculated for the axial current in some nuclei (see e.g. References [21,22] for Aluminium; this factor includes the derivative operators O(DNeNr,)X ).
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