Effective Theories for QCD-like at TeV Scale

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) [1]. The various channels of general n flavour meson-meson scattering of the three theories are systematically studied and calculated up to NNLO [2]. We also calculated the vector, axial-vector, scalar, pseudo-scalar two-point functions and pseudo-scalar decay constant up NNLO order [3]. 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.