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Following the idea that a stable sexaquark state with quark content (uuddss)would have gone unnoticed by experiment so far and that such a particle wouldbe a good dark matter candidate, we investigate the possible role of a stablesexaquark in the physics of compact stars given the stringent constraints onthe equation of state that stem from observations of high mass pulsars andGW170817 bounds on the compactness of intermediate mass stars. We find thatthere is a "sexaquark dilemma" (analogous to the hyperon dilemma) for which thedissociation of the sexaquark in quark matter is a viable solution fulfillingall present constraints from multi-messenger astronomy. The parameters neededto model the hybrid star including sexaquarks are in line with parameters ofpre-existing quark- and hadronic-matter models. We find that currentconstraints -- tidal deformability in accordance with GW170817 and maximum massabove the lower limit from PSR J0740+6620 -- can be satisfied two ways: withearly quark deconfinement such that neither sexaquarks nor hyperons are presentin any NS interiors, or with later deconfinement such that a neutron-sexaquarkshell surrounds the inner quark matter core.

Sexaquark dilemma in neutron stars and its solution by quark deconfinement