Pion observables calculated in Minkowski and Euclidean spaces with Ans\"atze for quark propagators

TL;DR

This paper develops a method to connect Euclidean and Minkowski space calculations for quark propagators using modified Wick rotation, enabling more accurate computation of pion observables from lattice QCD data.

Contribution

It introduces a modified Wick rotation technique for quark propagator Ans"atze, facilitating the calculation of pion form factors and decay constants across spacetime frameworks.

Findings

Calculated pion transition and electromagnetic form factors.

Derived pion decay constant and distribution amplitude.

Compared asymptotic behaviors with direct calculations.

Abstract

We study two quark--propagator meromorphic Ans\"atze that admit clear connection between calculations in Euclidean space and Minkowski spacetime. The connection is established through a modified Wick rotation in momentum space, where the integration contour along the imaginary axis is adequately deformed. The Ans\"atze were previously proposed in the literature and fitted to Euclidean lattice QCD data. The generalized impulse approximation is used to calculate the pion transition form factor and electromagnetic form factor, correcting an earlier result. The pion decay constant and distribution amplitude are also calculated. The latter is used to deduce the asymptotic behavior of the form factors. Such an asymptotic behavior is compared with those obtained directly from the generalized impulse approximation and the causes of differences are pointed out.