Comment on "LaMET's Asymptotic Extrapolation vs. Inverse Problem"

TL;DR

This paper critically discusses the limitations of rigid parametrizations in LaMET data extrapolation, emphasizing the importance of handling noisy lattice data with appropriate inverse problem methods and clarifying misunderstandings with prior critiques.

Contribution

The authors clarify their perspective on managing noisy lattice data in LaMET, contrasting it with Chen's approach, and correct misconceptions about their methodology.

Findings

Rigid parametrizations can introduce excessive model dependence.

Inverse problem methods better handle noisy data with proper regularization.

Clarification of methodological differences and misunderstandings.

Abstract

In arXiv:2504.17706 {Dutrieux:2025jed} we criticized the excessive model-dependence introduced by rigid few-parameter fits to extrapolate lattice data in the large momentum effective theory (LaMET) when the data are noisy and lose signal before an exponential asymptotic behavior of the space-like correlators is established. In reaction, arXiv:2505.14619 {Chen:2025cxr} claims that even when the data is of poor quality, rigid parametrizations are better than attempts at representing the uncertainty using what they call "inverse problem methods". We clarify the fundamental differences in our perspectives regarding how to meaningfully handle noisy lattice matrix elements, especially when they exhibit a strong sensitivity to the choice of regularization in the inverse problem. We additionally correct misunderstandings of {Chen:2025cxr} on our message and methods.