In this paper , we explore whether or not quark deconfinement may occur in high-mass neutron stars such as J1614-2230 ( 1.97 \pm 0.04 M _ { \odot } ) and J0348+0432 ( 2.01 \pm 0.04 M _ { \odot } ) .
Our study is based on a non-local extension of the SU ( 3 ) Nambu Jona-Lasinio ( n3NJL ) model with repulsive vector interactions among the quarks .
This model goes beyond the frequently used local version of the Nambu Jona-Lasinio ( NJL ) model by accounting for several key features of QCD which are not part of the local model .
Confined hadronic matter is treated in the framework of non-linear relativistic mean field theory .
We find that both the local as well as the non-local NJL model predict the existence of extended regions of mixed quark-hadron ( quark-hybrid ) matter in high-mass neutron stars with masses of 2.1 to 2.4 M _ { \odot } .
Pure quark matter in the cores of neutron stars is obtained for certain parametrizations of the hadronic lagrangian and choices of the vector repulsion among quarks .
The radii of high-mass neutron stars with quark-hybrid matter and/or pure quark matter cores in their centers are found to lie in the canonical range of 12 to 13 km .