Effective Theories for QCD-like at TeV Scale

TL;DR

This paper develops and computes effective field theories for three QCD-like models with different quark representations, providing detailed NNLO calculations of meson properties, scattering processes, and electroweak parameters relevant for lattice and phenomenological studies.

Contribution

It presents a unified approach to chiral perturbation theory for QCD-like theories with various quark representations, including comprehensive NNLO calculations of key physical quantities.

Findings

Calculated vacuum expectation values, masses, and decay constants up to NNLO.

Systematically studied meson-meson scattering channels up to NNLO.

Derived analytic expressions for the S parameter at TeV scale.

Abstract

We study the Effective Field Theory of three QCD-like theories, which can be classified by having quarks in a complex, real or pseudo-real representations of the gauge group. The Lagrangians are written in a very similar way so that the calculations can be done using techniques from Chiral Perturbation Theory (ChPT). We calculated the vacuum-expectation-value, the mass and the decay constant of pseudo-Goldstone Bosons up to next-to-next-to leading order (NNLO) \cite{Bijnens:2009qm}. The various channels of general $n$ flavour meson-meson scattering of the three theories are systematically studied and calculated up to NNLO \cite{Bijnens:2011fm}. We also calculated the vector, axial-vector, scalar, pseudo-scalar two-point functions and pseudo-scalar decay constant up NNLO order \cite{Bijnens:2011xt}. The analytic expressions of the S parameter for the three different QCD-like theories are obtained at TeV scale. Our results are useful for chiral extrapolation in lattice calculation on theory of strong dynamical and finite baryon density.