We calculate the m /f π ratio in the chiral and continuum limit for SU(3) gauge theory coupled to N f = 2, 3, 4, 5, 6 fermions in the fundamental representation. Keeping all systematic effects under full control we find no statistically significant N f-dependence; m /f π = 7.95(15). Assuming the KSRF-relations we conclude that 3 other low energy quantities related to the vector meson are also N f-independent within errors including the ππ coupling g ππ. If the model is thought of as a strong dynamics inspired composite Higgs model our results indicate that the experimentally most easily accessible new composite particle, the vector meson, and its properties may be robust and independent of the fermion content of the model as long as the gauge group is SU(3), provided N f-independence extends all the way to the conformal window.

In previous work, [arXiv:1905.01909], we have calculated the mϱ/fπ ratio in the chiral and continuum limit for SU(3) gauge theory coupled to Nf = 2, 3, 4, 5, 6 fermions in the fundamental representation. The main result was that this ratio displays no statistically significant Nf-dependence. In the present work we continue the study of the Nf-dependence by extending the simulations to Nf = 7, 8, 9, 10. Along the way we also study in detail the Nf-dependence of finite volume effects on low energy observables and a particular translational symmetry breaking unphysical, lattice artefact phase specific to staggered fermions.

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SU (2) gauge theory is investigated with a lattice action which is insensitive to small perturbations of the lattice gauge fields. Bare perturbation theory can not be defined for such actions at all. We compare non-perturbative continuum results with that obtained by the usual Wilson plaquette action. The compared observables span a wide range of interesting phenomena: zero temperature large volume behavior (topological susceptibility), finite temperature phase transition (critical exponents and critical temperature) and also the small volume regime (discrete β-function or step-scaling function). In the continuum limit perfect agreement is found indicating that universality holds for these topological lattice actions as well.

Should a strongly coupled composite Higgs boson scenario be realized in Nature the most easily accessible experimental signal would be new particles made up of the same ingredients as the Higgs but with different quantum numbers. The lightest of these hypothetical new particles would probably be the vector mesons. In this contribution we report results on m ρ / f π in the chiralcontinuum limit with SU(3) gauge group and N f = 2, 3, 4, 5, 6 flavors of fundamental fermions. In addition we compare m ρ / f π results from various models with different gauge groups and fermion content. The main conclusion seems to be that the experimental measurement of this vector meson mass will be able to distinguish between gauge groups but less so between the fermion content.