Transversity relations, chiral and holographic models, and pion wave functions from lattice QCD

TL;DR

This paper compares lattice QCD results with chiral and holographic models to analyze pion wave functions, revealing consistent shapes and providing a method to extract transversity information relevant for light-cone physics.

Contribution

It demonstrates how equal-time lattice QCD results can be directly related to light-cone transversity information and holographic wave functions, bridging different theoretical approaches.

Findings

Lattice QCD results match predictions of chiral quark models for pion wave functions.

Transversity information can be extracted from equal-time lattice calculations.

Holographic wave functions compare favorably with lattice results.

Abstract

We analyze the equal-time Bethe-Salpeter quark wave functions of the pion in various models. We discuss how the quenched lattice QCD results with delocalized pion interpolators can be identified with the coarse grained wave functions, typical of low-energy effective models. Actually, we find that one-loop chiral quark models predict that pseudoscalar and tensor wave functions have the same shape, while the axial component is more extended. These facts are accurately confirmed by the lattice. We also show how the transversity information, relevant for the light-cone physics, can be straightforwardly obtained from the equal-time rest-frame lattice calculations. This remarkable relation provides a way to extract, for instance, the equal-time holographic wave functions and compare them, quite favorably, to the lattice calculations.