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 quantum electrodynamical (QED) interactions. As a quark cannot be isolated, the intrinsic motion of the three quarks in the lowest-energy state of the QED neutron may lie predominantly in 1+1 dimensions, as in a $d$-$u$-$d$ open string. In such an 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 stability of the QED neutron in a phenomenological three-body problem in 1+1 dimensions with an effective interaction between electric charges extracted from Schwinger's exact QED solution in 1+1 dimensions. The phenomenological model in a variational calculation yields a stable QED neutron energy minimum at a mass of 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 lowest-energy QED neutron is stable against the weak decay, has a long lifetime, and is in fact a QED dark neutron. Such a QED dark neutron and its excited states may be produced following the deconfinement-to-confinement 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 of various sizes may be good candidates for a part of the primordial dark matter produced during the deconfinement-to-confinement phase transition of the quark gluon plasma in the evolution of the early Universe.