Sexaquark dilemma in neutron stars and its solution by quark deconfinement

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 would be a good dark matter candidate, we investigate the possible role of a stable sexaquark in the physics of compact stars given the stringent constraints on the equation of state that stem from observations of high mass pulsars and GW170817 bounds on the compactness of intermediate mass stars. We find that there is a "sexaquark dilemma" (analogous to the hyperon dilemma) for which the dissociation of the sexaquark in quark matter is a viable solution fulfilling all present constraints from multi-messenger astronomy. The parameters needed to model the hybrid star including sexaquarks are in line with parameters of pre-existing quark- and hadronic-matter models. We find that current constraints -- tidal deformability in accordance with GW170817 and maximum mass above the lower limit from PSR J0740+6620 -- can be satisfied two ways: with early quark deconfinement such that neither sexaquarks nor hyperons are present in any NS interiors, or with later deconfinement such that a neutron-sexaquark shell surrounds the inner quark matter core.