Wick rotation in the light-front

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 poles in the complex momentum plane. 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 is 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 the minus component of the momentum (k∼) in the one-loop amplitude 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 other models in the literature and with the experimental data. © Copyright owned by the author(s) under the terms of the Creative Commons Attribution-NonCommercial- ShareAlike Licence.