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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.

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