Conversion of baryonic fermions into squarks in neutron stars from supersymmetric dark matter Q-balls

The gauge-mediated model of supersymmetry breaking implies that stable nontopological solitons, Q-balls, could form in the early Universe and comprise the dark matter. It is shown that the inclusion of the effects from gravity-mediation set an upper limit on the size of Q-balls. When in a dense baryonic environment Q-balls grow until reaching this limiting size at which point they fragment into two equal-sized Q-balls. This Q-splitting process will rapidly destroy a neutron star that absorbs even one Q-ball. The new limits on Q-ball dark matter require an ultralight gravitino m3/2 < or approx. keV, naturally avoiding the gravitino overclosure problem, and providing the minimal supersymmetric standard model with a dark matter candidate where gravitino dark matter is not viable.