An exotic proposal on Cooper pairing in high-$T_c$ supercondutors

We propose that a Cooper pair in a high-$T_c$ superconductor might be in fact a bound system $\mathrm{e}\mathrm{e}\mathrm{x}\bar{\mathrm{x}}$ of two electrons, a particle $\mathrm{x}$ and its antiparticle. We assume $\mathrm{e}\mathrm{e}\mathrm{x}\bar{\mathrm{x}}$ is more massive than two free electrons. We observe that $\mathrm{e}\mathrm{e}\mathrm{x}\bar{\mathrm{x}}$ should be stable in a solid if it is in a low enough state in the solid. A solid which admits such a low state for $\mathrm{e}\mathrm{e}\mathrm{x}\bar{\mathrm{x}}$ has some properties which seem closely related to the behavior of HTS materials. The interaction of the $\mathrm{x}$-particle which binds the four particles into $\mathrm{e}\mathrm{e}\mathrm{x}\bar{\mathrm{x}}$ has been discussed. We also discuss the scale of the mass excess of $\mathrm{e}\mathrm{e}\mathrm{x}\bar{\mathrm{x}}$ relative to two free electrons. An experiment designed to detect a bound system of two electrons with a mass excess has been proposed.