Appendix E: Muon-to-electron conversion in nuclei
With the discovery of neutrino masses and mixings we have learned that neutral lepton flavor quantum numbers are violated in nature. An immediate question arises: "Does lepton flavor violation also occur at an appreciable rate with the charged leptons?" While the Standard Model predicts negligible rates for charged lepton flavor violation, many models, including various versions of supersymmetry, predict CLFV at an appreciable and potentially observable rate. Searches for CLFV are the most powerful and promising probes for new physics at and above the TeV scale.
Rare muon processes provide the deepest CLFV probes due to the copious production of muons in proton fixed-target collisions. SNuMI and Project X are capable of extending the current sensitivity by many orders of magnitude. Current experiments have been able to rule out, at the 90 percent confidence level, μ→eγ with branching ratios above 1.1×10-11, μ→eee with branching ratios above 1.0×10-12, while the rate for μ+48Ti→e+48Ti normalized to the capture rate (μ→e conversion in titanium) is constrained to be less than 4.3×10-12. Various scenarios for new physics at the TeV scale predict these processes to occur with rates that are close to these current bounds. In fact, searches for CLFV in muon processes already provide the most stringent constraints on some new physics scenarios. The bounds on many scenarios became even more stringent with the discovery that neutrinos have nonzero masses and large mixing angles.
One can estimate the new physics expectations for the rates for different muon CLFV processes in a model independent way. For concreteness, consider the effect of adding to the Standard Model the following CLFV effective Lagrangian:
Here Λ sets the scale of new physics and κ interpolates between a pure transition magnetic-moment-type operator (κ<<1) and a pure four-fermion interaction (κ>>1). This effective Lagrangian describes both μ→eγ and μ→e conversion (and, at a less significant level, μ→eee, which will not be discussed). It qualitatively captures the predictions of most new physics scenarios containing CLFV. The potential experimental sensitivity to Λ and κ is depicted in the figure. Overall, an experiment sensitive to μ→e conversion rates larger than 10-17 is probing a fundamental new physics scale Λ up to several thousands of TeV, regardless of the value of κ.
For κ<<1, the normalized μ→e conversion rate is at least several times 10-3 times the branching ratio for μ→eγ, while for κ>>1 the branching ratio for μ→eγ is many orders of magnitude smaller than the normalized capture rate for μ→e conversion. A μ→e conversion experiment at the 10-17 level is at least as sensitive to new physics as a μ→eγ experiment at the 10-14 level. Hence, a μ→e conversion experiment associated with Project X could probe CLFV physics beyond the reach of the Muon-to-Electron-Gamma experiment, which will start taking data at the Paul Scherrer Institute soon and aims at being sensitive to μ→eγ if its branching ratio is above 10-13.
In the case of a confirmed signal, combined results from different CLFV searches would provide detailed information regarding the underlying new physics. In particular a versatile μ→e conversion experimental set-up has the unique capability of being able to distinguish the underlying effective operators responsible for CLFV (in the example above, this means measuring κ as well as Λ) by observing the conversion rate on different nuclear targets.