Asymptotically conformal CFL quark matter within a nonlocal chiral quark model

We propose a three-flavor nonlocal NJL model of quark matter with the scalar attractive, vector repulsive and diquark pairing interaction channels. The model is treated within the separable approximation to obtain the EoS of cold quark matter. The analysis of the high density asymptotics of the model allows us to conclude about its qualitative agreement with the perturbative QCD. Particularly, a color superconducting CFL state is found to be the ground one at high densities. The conformal limit of speed of sound and dimensionless interaction measure are also shown to be reached from below and above, respectively. The model is applied to modelling NSs within the scenario of early quark deconfinement triggered by the gravitational instability of the NS matter due to the BEC of a spin-color-flavor singlet three-diquark bound state, the light sexaquark, stable against the weak and strong decays. A conservative estimate of the sexaquark mass based on the most up-to-date results from QCD sum rules and a constituent quark model assumes an early quark deconfinement with the onset mass below $1~\rm M_\odot$. The scenario is shown to be consistent with the present observational constraints on the mass-radius relation and tidal deformability of NSs. Given the fact that the proposed model by construction exhibits an asymptotically conformal behavior, we consider the question about approximately conformal quark matter in NSs. We report a non-perturbative energy density range, which is inaccessible in NSs and where the speed of sound and dimensionless interaction measure of the CFL quark matter simultaneously attain the conformal values.