Nuclear $\mu -e$ conversion via Lorentz and CPT violation

One of the three common experimental channels searching for charged lepton flavor violation (CLFV) via $\mu -e$ conversion involves first capturing the muon on a nuclear target. This channel provides a unique opportunity to constrain four-point quark-lepton operators that may contribute to CLFV, in addition to the electromagnetic operators that can also be accessed in the other channels. We investigate the leading Lorentz- and CPT-violating contributions for nuclear $\mu -e$ conversion experiments within the Standard-Model Extension and obtain the first bounds on the relevant quark-lepton operators using the results of the SINDRUM II experiment; we also consider possibilities for improved constraints from upcoming experiments.