Expected Direct Search Charged Lepton Flavor Violation Sensitivity in μ⁺ and π⁺ Decays at Rest

The ability of the Mu2e experiment to probe direct Charged Lepton Flavor Violation (CLFV) μ⁺ and π⁺ decay modes is estimated. These direct modes complement the Mu2e indirect search for μ^- → e^- conversion accomplished using proposed detector validation runs. The μ⁺ validation run operates at 50% magnetic field and reduced beam intensity, to observe the e⁺ spectrum from μ⁺ decay, at and below the Michel edge Ee ≤ 53 MeV. The validation is used to correct systematic errors by mapping the theoretical Michel spectrum, known to Ο(α²), to the observed spectrum. Simultaneously, searches for two-body CLFV μ⁺ → e⁺ X decay, where Χ is a light new physics particle can be undertaken. In two weeks of data-taking, Mu2e can achieve 90% C.L. branching ratio limits of ΒR₉₀=10^-7 in the mass range 20 ≤ mX ≤ 50 MeV, improving the current experimental limit by two orders of magnitude. In the mass range m_X ≤ 20 MeV, if assuming systematic error corrections can be made, it is estimated, using two weeks of data collection, ΒR₉₀(m_X=0) = 2.3 × 10^-7, an order of magnitude improvement over the current best limit, for the case of V+A or an isotropic coupling. In addition, a two-week π⁺ validation run measuring the e⁺ in the decay π⁺ → e⁺ ν, at 76% magnetic field and introduction of a momentum degrader, allows searching for π⁺ → e⁺ N decay, where N is a spin 1/2 particle, in the mass region 20 ≤ m_N ≤ 65 MeV. A branching ratio limit at 90% C.L. of 3 × 10^-8 can be achieved, an improvement of the current search sensitivity limit by an order of magnitude.