New Types of Hydrogenlike matter Composed of Electron(s) and Meson(s)

TL;DR

The work addresses whether bound states formed by a light electron and heavier mesons can realize hydrogenlike analogs. It develops a formal framework that solves the Schrödinger equation for hydrogenlike atoms, applies Born–Oppenheimer two-center potentials for hydrogenlike molecular ions, and uses a two-electron variational approach for hydrogenlike molecules; it also scrutinizes the possible impact of strong interactions via vector-meson exchange potentials. Key findings include hydrogenic energies for Me^- atoms with $E_n=-1/(2n^2)$, a bound even-parity molecular-ion state with $E_+= -0.587$ at $R=2.003$, and a bound molecule with $E_0 = -1.139$ at $R=1.414$, with corresponding bond lengths; the strong interaction is found to be negligible in these systems. The results offer a QED-like platform to mirror heavy–flavor hadron configurations and point to possible realizations of doubly heavy triquarks and tetraquarks, motivating future high-precision experiments (e.g., at STCF) to search for such states.

Abstract

In the present work, we predict the existence of new types of hydrogenlike matter, including hydrogenlike atoms ($π^+e^-$, $K^+e^-$, $D^+e^-$), hydrogenlike molecular ions ($π^+π^+e^-$, $K^+K^+e^-$, $D^+D^+e^-$) and hydrogenlike molecules ($π^+π^+e^-e^-$, $K^+K^+e^-e^-$, $D^+D^+e^-e^-$). By solving the Schrödinger equation, the binding energy of hydrogenlike atoms is obtained as $E_n=-\frac{1}{2n^2}$. For hydrogenlike molecular ions and molecules, the variational method is employed to calculate the binding energies, i.e., $E_+=-0.587$ and $E_0=-1.139$ for hydrogenlike molecular ions and molecules, respectively. And the bond lengths for hydrogenlike molecular ions and molecules are also calculated, whose values are $2.003$ and $1.414$, respectively. Here all the quantities are in atomic units for convenience. In addition, the strong interaction between the two constituent mesons is considered in our calculations, where we find that its influence on the hydrogenlike molecular ions and molecules can be neglected. Comparisons of hydrogenlike molecular ion and molecule with the systems governed by the strong interaction are made, which suggests the possible existence of doubly heavy triquark, hidden heavy-flavor tetraquarks and doubly heavy tetraquarks. Hopefully, these types of matter would be observed in the future with the improvement of accuracy in the high energy physical experiments.

Figures (5)

• Figure 1: The Radial probability density of the 1S, 2S and 3S state with $\chi_{n0}=rR_{n0}(r)$.
• Figure 2: (color online) The electron cloud of hydrogenlike atoms and molecular ions in $xy$ plane. (a), (b), (c) and (d) corresponds to $Me^-\ (1S)$, $Me^-\ (2S)$, $Me^-\ (3S)$ and $MMe^-e^-$ with $M=\pi^+,K^+,D^+$, respectively.
• Figure 3: The line shapes of the $E_{+}$, $E_{-}$, $E_{0}$ and $E_{1}$. The variational parameter $\lambda$ is fixed as 1.238 for $E_{+}$, $E_{-}$, and as 1.166 for $E_{0}$, $E_{1}$.
• Figure 4: The Feynman diagrams of the $\pi^{+}$-$\pi^{+}$, $K^{+}$-$K^{+}$ and $D^{+}$-$D^{+}$ interactions.
• Figure 5: The strong interaction potential of $V_{\pi^{+}\pi^{+}}$, $V_{K^{+}K^{+}}$ and $V_{D^{+}D^{+}}$.