Wick Rotation in the Light-Front

TL;DR

This paper introduces a Wick-rotation method in light-front dynamics to study electroweak properties of mesons, enabling analysis of form factors and decay constants with various Bethe-Salpeter models, and compares results with experimental data.

Contribution

It presents a novel Wick-rotation technique in light-front calculations that avoids complex plane cuts, allowing flexible modeling of meson structures and testing QCD asymptotic behaviors.

Findings

Successfully applied Wick-rotation to analyze meson form factors.

Demonstrated compatibility of models with experimental data.

Explored the impact of regulator powers on asymptotic behavior.

Abstract

We study the electroweak properties of pseudo-scalar mesons in the light and heavy-light sectors. In particular, we address the electromagnetic form factors and decay constants of the pion, kaon and D mesons. The structure of composite systems are given by the Bethe-Salpeter (BS) amplitude of a meson formed by a confined pair of constituent quark and antiquark, which in our work is written in terms of Pauli-Villars regulators. The analytical structure contains single poles in the complex momentum space. The BS amplitude takes into account poles due to the regulator parameters, while the quark-antiquark cut is avoided, implying in confined quarks with the property that the sum of the constituents masses can be larger than the mass of the meson. The one-loop expressions of the electroweak transition amplitudes are conveniently written in terms of light-front momentum. Technically, we introduce a Wick-rotation of he minus component of the momentum (k-minus) in the one-loop amplitudes allowing to avoid the cuts in the complex plane of this momentum variable without crossing them. This is particularly useful as we can study the electroweak properties with several models of the BS amplitude with different powers of Pauli-Villars regulators. The possibility to change the power of the BS amplitude is interesting in order to test the asymptotic behavior of the electromagnetic form factors searching for a suitable form that incorporates the expected QCD decaying power-law form. The results are compared with others models in the literature and with the experimental data.