Coherent μ − e Conversion at Next - to - Leading Order

We analyze next-to-leading order (NLO) corrections and uncertainties for coherent μ − e conversion . The analysis is general but numerical results focus on 27Al, which will be used in the Mu2E experiment. We obtain a simple expression for the branching ratio in terms of Wilson coefficients associated with possible physics beyond the Standard Model and a set of model-independent parameters determined solely by Standard Model dynamics. For scalar-mediated conversion, we find that NLO two-nucleon contributions can significantly decrease the branching ratio, potentially reducing the rate by as much as 50%. The pion-nucleon σ-term and quark masses give the dominant sources of parametric uncertainty in this case. For vectormediated conversion, the impact of NLO contributions is considerably less severe, while the present theoretical uncertainties are comparable to parametric uncertainties.