Selecting μ → e conversion targets to distinguish lepton flavour-changing operators

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 → e conversion, 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 → e conversion could constrain 10 to 14 combinations of coefficients; if µ → eγ and µ → eēe 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 § Another interesting observable at these experiments is the µ − e − → e − e − in a muonic atom. This process could have not only photonic dipole but also contact interactions, and the atomic number dependence of its reaction rate makes possible to discriminate the type of relevant CLFV interactions [7,8,9]. * * Since the current MEG bound on the dipole coefficients constrains them to be below the sensitivity of the current µ → e conversion bounds, the dipole overlap integral was set to zero in obtaining this Figure.

Bounds on lepton flavor violating physics and decays of neutral mesons from τ(μ)→3ℓ , ℓγγDib1, Gutsche2, Kovalenko3 et al. 2019Phys. Rev. D90160View full textAdd to dashboardCite

“…Appendix C: Q 2 dependence of meson propagators and form factors Let us note that in Eqs. (9), (10), (16), (22), and (23), we neglected the squared momentum transfer Q 2 -dependence of the meson propagator and the form factorsg M 1 2 (Q 2 ). For most of the processes of our current interest, this Q 2dependence results in a less than 5% deviation from the approximate formulae that we use, which for our purposes is more than sufficient.…”

“…From Eqs. (15), (16), (22) and (23), we deduce upper limits for the branching ratios of the two-body LFV decays M (Z) → 1 2 of neutral vector and pseudoscalar mesons and Z-boson, using the existing data (1)-(3) for three-body LFV decays τ (µ) → 3 . We present our results in the second column of Table I and compare them with the limits derived from the study of lepton conversion [2] and available experimental data [1].…”

“…(7), and the meson-lepton couplings, g M , from (8), which are shown in Appendix D. Using these relations in the decay rate formulas for Γ(M → l 1 l 2 ) from Appendix A and substituting them into Eqs. (15), (16), (22) and (23), we set upper limits on the coefficients C/Λ 2 of the effective operators (7) from the experimental data on τ (µ) → 3 . There are several operators contributing simultaneously to each of these processes, and therefore the data impose upper limits on linear combinations of the corresponding Wilson coefficients shown in Appendix E. In practice, it is useful to have individual upper limits for these coefficients under certain reasonable assumptions.…”

“…[3]- [9] and further used in a series of papers (see, e.g., Refs. [10]- [22]). In particular, in Refs.…”

Low-energy lepton physics in the MRSSM: (g − 2)μ, μ→eγ and μ→e conversion

“…We remark that in parallel to model specific studies there has been significant recent progress on model-independent effective field theoretical (EFT) approaches to CLFV: loop corrections to µ → eγ have been evaluated in an EFT with dimension-6 operators [39,40]; higher-order corrections to µ → eγ, µ → eee and µ → e from running below the weak scale have been evaluated [41][42][43] and disentanglement of different Wilson coefficients by experimental observables has been studied [44,45].…”