Bag versus NJL models for colour-flavour-locked strange quark matter

We compare the mass-radius relationship of strange stars obtained in two theoretical frameworks describing the colour-flavour-locking state of dense quark matter: the semi-empirical MIT bag model and a self-consistent approach using the Nambu-Jona-Lasinio (NJL) model. In the simplest MIT model extended to include pairing, one can make the equation of state stiffer by increasing the gap parameter so that larger maximum masses for these objects can be reached. In the NJL model, however, such an effect is not possible. To increase the gap parameter within the NJL model to values comparable to those considered in the MIT case, a noticeable increase of the diquark-coupling-constant strength is needed, but this in turn softens the equation of state producing a lower maximum star mass. This behaviour is interpreted as signalling the system crossover at high diquark coupling from a Bardeen-Cooper-Schrieffer regime to a Bose-Einstein condensate one, a process that cannot be reproduced within the simple MIT prescription.