Open string QED meson description of the X17 particle and dark matter

Abstract: As a quark and an antiquark cannot be isolated, the intrinsic motion of a composite $q \bar q$ system in its lowest-energy states lies predominantly in 1+1 dimensions, as in an open string with the quark and the antiquark at its two ends. Accordingly, we study the lowest-energy states of an open string $q\bar q$ system in QCD and QED in 1+1 dimensions. We show that $\pi^0, \eta$, and $\eta'$ can be adequately described as open string $q\bar q$ QCD mesons. By extrapolating into the $q\bar q$ QED sector in which a quark and an antiquark interact with the QED interaction, we find an open string isoscalar $I(J^\pi)$=$0(0^-)$ QED meson state at 17.9$\pm$1.5 MeV and an isovector $(I(J^\pi)$=$1(0^-), I_3$=0) QED meson state at 36.4$\pm$3.8 MeV. The predicted masses of the isoscalar and isovector QED mesons are close to the masses of the hypothetical X17 and E38 particles observed recently, making them good candidates for these particles. The decay products of QED mesons may show up as excess $e^+e^-$ and $\gamma \gamma$ pairs in the anomalous soft photon phenomenon associated with hadron productions in high-energy hadron-proton collisions and $e^+$-$e^-$ annihilations. Measurements of the invariant masses of excess $e^+e^-$ and $\gamma \gamma$ pairs will provide tests for the existence of the open string $q\bar q$ QED mesons. An assembly of gravitating QED mesons are expected to emit electron-positron pairs and/or gamma rays and their decay energies and lifetimes will be modified by their gravitational binding energies. Consequently, a self-gravitating isoscalar QED meson assembly whose mass $M$ and radius $R$ satisfy $(M/M_\odot)/(R/R_\odot) \gtrsim 4.71 \times 10^5$ will not produce electron-positron pairs nor gamma rays and may be a good candidate for the primordial dark matter.