On the stability of the open-string QED neutron and dark matter

We study the stability of a hypothetical QED neutron, which consists of a color-singlet system of two $d$ quarks and a $u$ quark interacting with the QED interaction. As a quark cannot be isolated, the intrinsic motion of the three quarks in the lowest-energy state may lie predominantly in 1+1 dimensions, as in a $d$-$u$-$d$ open string. The attractive $d$-$u$ and $u$-$d$ QED interactions may overcome the weaker repulsive $d$-$d$ QED interaction to bind the three quarks together. We examine the QED neutron in a phenomenological three-body problem in 1+1 dimensions with an effective interaction extracted from Schwinger's exact QED solution in 1+1 dimensions. The phenomenological model in a variational calculation yields a stable QED neutron at 44.5 MeV. The analogous QED proton with two $u$ quarks and a $d$ quark has been found to be too repulsive to be stable and does not have a bound or continuum state, onto which the QED neutron can decay via the weak interaction. Consequently, the QED neutron is stable against the weak decay, has a long lifetime, and is in fact a QED dark neutron. It may be produced following the deconfinement-to-confinement phase transition of the quark gluon plasma in high-energy heavy-ion collisions. Because of the long lifetime of the QED dark neutron, self-gravitating assemblies of QED dark neutrons or dark antineutrons may be good candidates for a part of the primordial dark matter produced during the phase transition of the quark gluon plasma in the evolution of the early Universe.