Determine whether exponential correlator decay produces a genuine linear power correction

Determine whether the exponential large-separation decay of the renormalized equal-time correlator induces a genuine linear correction to the leading-power quasi-distribution matching relation, given the differing proposed origins of the decay mass parameter.

Background

The paper argues that, beyond leading power, a physical hadron correlator may decay at large spatial separation as exp(-mz), which produces momentum-space smearing over a width of order m/P^z and can populate the exterior region |x|>1. Such smearing appears to generate a linear power correction, although standard factorization corrections are usually quadratic in inverse momentum.

The authors note that the interpretation depends on the origin of the mass parameter m. Two cited studies identify that origin differently, so whether the apparent linear correction is genuine remains unresolved.