Scheming in the SMEFT. . . and a reparameterization invariance!

We explain a reparameterization invariance in the Standard Model Effective Field Theory present when considering (psi) over bar psi -> (psi) over bar psi scatterings (with psi a fermion) and how this leads to unconstrained combinations of Wilson coefficients in global data analyses restricted to these measurements. We develop a {(m) over cap (W), (m) over cap (Z), (G) over cap (F)} input parameter scheme and compare results to the case when an input parameter set {(alpha) over cap, (m) over cap (Z), (G) over cap (F)} is used to constrain this effective theory from the global data set, confirming the input parameter independence of the unconstrained combinations of Wilson coefficients, and supporting the reparameterization invariance explanation. We discuss some conceptual issues related to these degeneracies that are relevant for LHC data reporting and analysis.