Narrow Results

In this paper, we present an explanation for the ΔI = 1/2 rule in K-decays based on the premise of an infrared fixed point α_IR in the running coupling α_s of quantum chromodynamics (QCD) for three light quarks u, d, s. At the fixed point, the quark condensate spontaneously breaks scale and chiral SU(3)_L×SU(3)_R symmetry. Consequently, the low-lying spectrum contains nine Nambu–Goldstone bosons: π, K, η and a QCD dilaton σ. We identify σ as the f₀(500) resonance and construct a chiral-scale perturbation theory χPT_σ for low-energy amplitudes expanded in α_s about α_IR. The ΔI = 1/2 rule emerges in the leading order of χPT_σ through a σ-pole term K_S→σ→ππ, with a g_KSσ coupling fixed by data on γγ→π⁰π⁰ and K_S→γγ. We also determine R_IR ≈5 for the nonperturbative Drell–Yan ratio at α_IR.

The dynamics with an infrared stable fixed point in the conformal window in QCD like theories with a relatively large number of fermion flavors is reviewed. The emphasis is on the description of a clear signature for the conformal window, which in particular can be useful for lattice computer simulations of these gauge theories.

We performed the renormalization group analysis of scalar models exhibiting spontaneous symmetry breaking. It is shown that an infrared fixed point appears in the broken symmetric phase of the models, which induces a dynamical scale, that can be identified with the correlation length. This enables one to identify the type of the phase transition which shows similarity to the one appearing in the crossover scale. The critical exponent ν of the correlation length also proved to be equal in the crossover and the infrared scaling regimes.

The novel idea is that the undergoing accelerated expansion of the universe happens due to infrared quantum gravity modifications at intermediate astrophysical scales of galaxies or galaxy clusters, within the framework of Asymptotically Safe gravity. The reason is that structures of matter are associated with a scale-dependent positive cosmological constant of quantum origin. In this context, no extra unproven energy scales or fine-tuning are used. Furthermore, this model was confronted with the most recent observational data from a variety of probes, and with the aid of Bayesian analysis, the most probable values of the free parameters were extracted. Finally, the model proved to be statistically equivalent with $\mathrm{\Lambda }$CDM, and thus being able to resolve naturally the concept of dark energy and its associated cosmic coincidence problem.

The dynamics with an infrared stable fixed point in the conformal window in QCD like theories with a relatively large number of fermion flavors is reviewed. The emphasis is on the description of a clear signature for the conformal window, which in particular can be useful for lattice computer simulations of these gauge theories.