Statistics of predictions with missing higher order corrections

Abstract: Effective operators have been used extensively to understand small deviations from the Standard Model in the search for new physics. So far there has been no general method to fit for small parameters when higher order corrections in these parameters are present but unknown. We present a new technique that solves this problem, allowing for an exact p-value calculation under the assumption that higher order theoretical contributions can be treated as gaussian distributed random variables. The method we propose is general, and may be used in the analysis of any perturbative theoretical prediction, ie.~truncated power series. We illustrate this new method by performing a fit of the Standard Model Effective Field Theory parameters, which include eg.~anomalous gauge and four-fermion couplings.