Mu2e Run I Sensitivity Projections for the Neutrinoless μ⁻ → e⁻ Conversion Search in Aluminum

The Mu2e experiment at Fermilab will search for the neutrinoless ${\mu }^{-}\to e^{-}$ conversion in the field of an aluminum nucleus. The Mu2e data-taking plan assumes two running periods, Run I and Run II, separated by an approximately two-year-long shutdown. This paper presents an estimate of the expected Mu2e Run I search sensitivity and includes a detailed discussion of the background sources, uncertainties of their prediction, analysis procedures, and the optimization of the experimental sensitivity. The expected Run I $5\sigma$ discovery sensitivity is $R_{\mu e}=1.2\times {10}^{-15}$, with a total expected background of $0.11\pm 0.03$ events. In the absence of a signal, the expected upper limit is $R_{\mu e}<6.2\times {10}^{-16}$ at 90% CL. This represents a three order of magnitude improvement over the current experimental limit of $R_{\mu e}<7\times {10}^{-13}$ at 90% CL set by the SINDRUM II experiment.