Possible primordial e+e− production of a collisionless X particle as a dark matter candidate

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In a previous work the author proposed a phenomenological particle-based model of dark matter capable of reproducing the observed flat rotation curves of spiral galaxies. The model was compared with observational data from three galaxies and was found to provide a consistent description of the transition from the baryon-dominated inner regions to the asymptotically flat outer  regime. The model is based on the hypothetical existence of a neutral particle X, stable on cosmological  timescales and effectively collisionless on galactic scales, with a mass assumed to be of the order of the neutron mass. In the proposed scenario, the production of the dark-matter particle X is assumed to occur through two distinct intermediate channels. The first is mediated by the ordinary virtual photon, e⁺e⁻→γ∗→XXˉ  while the second proceeds through a dark-photon mediating the interaction between the Standard Model sector. e⁺e⁻→A′→XXˉ. The two channels are not assumed to be mutually exclusive. On the contrary, both amplitudes are assumed to contribute simultaneously to the production process. The quantum interference between the virtual-photon and dark-photon channels plays a central role in the generation of the primordial particle–antiparticle asymmetry. The analysis is developed in several steps. First, the relativistic kinematic conditions required for the production of X–Xˉ pairs are derived. Second, the reaction cross section and the corresponding production rate are analysed within a simplified relativistic framework. The production rate is then compared with the cosmological expansion rate in order to determine whether the process could occur efficiently during the primordial thermal epoch. The possible role of quantum interference between virtual-photon and dark-photon intermediate states is subsequently examined as a mechanism for generating a small primordial X–Xˉ asymmetry. Finally, the cosmological evolution of the surviving particle population is investigated in order to evaluate whether the resulting relic abundance is compatible with the dark matter density inferred from present observations