Neglecting correlations leads to misestimated model errors in EFT predictions

TL;DR

This paper investigates how neglecting correlations between EFT truncation errors and low-energy constants leads to overestimating uncertainties in predictions, highlighting the importance of accounting for these correlations.

Contribution

It demonstrates the impact of correlations on EFT uncertainty estimates using a toy model, revealing that ignoring them can misestimate the true predictive uncertainty.

Findings

Correlations reduce overall EFT prediction uncertainties.

Neglecting correlations overestimates uncertainties.

Proper accounting improves EFT predictive accuracy.

Abstract

Bayesian analyses of the convergence pattern of Effective Field Theories (EFTs) enable estimation of the uncertainty induced by a truncated expansion. When an EFT that has been calibrated to data is used to make a prediction this truncation uncertainty enters the posterior predictive distribution twice: directly from the finite-order calculation of the predicted quantity and indirectly through the posterior probability distributions of the EFT low-energy constants (LECs) determined by the calibration. In this work, we focus on the interplay of these two sources of uncertainty. We do this in the context of a toy EFT that we fit to pseudodata and use to make predictions. Direct EFT truncation uncertainty and LEC uncertainty are correlated in predictions when the predicted quantity is correlated with the observables used to fit the LECs. Here this results in the overall theoretical uncertainty in the EFT prediction being smaller than either the uncertainty induced by the truncation error or that stemming from the LECs alone.