With sufficient data, Large Hadron Collider (LHC) experiments can constrain
the selectron-smuon mass splitting through differences in the di-electron and
di-muon edges from supersymmetry (SUSY) cascade decays. We study the
sensitivity of the LHC to this mass splitting, which within mSUGRA may be
constrained down to O(10^{-4}) for 30 fb^{-1} of integrated luminosity. Over
substantial regions of SUSY breaking parameter space the fractional edge
splitting can be significantly enhanced over the fractional mass splitting.
Within models where the selectron and smuon are constrained to be universal at
a high scale, edge splittings up to a few percent may be induced by
renormalisation group effects and may be significantly discriminated from zero.
The edge splitting provides important information about high-scale SUSY
breaking terms and should be included in any fit of LHC data to high-scale
models
