Statistics of predictions with missing higher order corrections

TL;DR

This paper introduces a novel statistical method for fitting small parameters in theoretical predictions with unknown higher order corrections, enabling exact p-value calculations assuming Gaussian distributions.

Contribution

The authors develop a general technique for accurate parameter estimation in perturbative theories with unknown higher order effects, applicable to effective field theory analyses.

Findings

Method allows exact p-value computation with Gaussian assumptions.

Applied to Standard Model Effective Field Theory parameters.

Demonstrates improved fitting accuracy in presence of higher order uncertainties.

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.