Endpoint behavior of the pion distribution amplitude in QCD sum rules with nonlocal condensates

TL;DR

This paper develops new sum rules for the pion distribution amplitude in QCD, focusing on its behavior near the endpoint region, and compares different models to determine their consistency with these sum rules.

Contribution

It introduces a novel sum rule for the derivatives of the pion distribution amplitude and analyzes endpoint behaviors using nonlocal condensates in QCD sum rules.

Findings

Endpoint-suppressed DAs are within the derived derivative range.

Flat-top or flat-like DAs fall outside the derivative range.

Results favor endpoint-suppressed DAs over endpoint-enhanced models.

Abstract

Starting from the QCD sum rules with nonlocal condensates for the pion distribution amplitude, we derive another sum rule for its derivative and its "integral" derivatives---defined in this work. We use this new sum rule to analyze the fine details of the pion distribution amplitude in the endpoint region $x\sim 0$. The results for endpoint-suppressed and flat-top (or flat-like) pion distribution amplitudes are compared with those we obtained with differential sum rules by employing two different models for the distribution of vacuum-quark virtualities. We determine the range of values of the derivatives of the pion distribution amplitude and show that endpoint-suppressed distribution amplitudes lie within this range, while those with endpoint enhancement---flat-type or CZ-like---yield values outside this range.