Abstract
We discuss the effective field theory description of bound states composed of a heavy baryon and antibaryon. This framework is a variation of the ones already developed for heavy meson-antimeson states to describe the $X(3872)$ or the $Z_c$ and $Z_b$ resonances. We consider the case of heavy baryons for which the light quark pair is in S-wave and we explore how heavy quark spin symmetry constrains the heavy baryon-antibaryon potential. The one pion exchange potential mediates the low energy dynamics of this system. We determine the relative importance of pion exchanges, in particular the tensor force. We find that in general pion exchanges are probably non-perturbative for the $\Sigma_Q \bar{\Sigma}_Q$, $\Sigma_Q^* \bar{\Sigma}_Q$ and $\Sigma_Q^* \bar{\Sigma}_Q^*$ systems, while for the $\Xi_Q' \bar{\Xi}_Q'$, $\Xi_Q^* \bar{\Xi}_Q'$ and $\Xi_Q^* \bar{\Xi}_Q^*$ cases they are perturbative If we assume that the contact-range couplings of the effective field theory are saturated by the exchange of vector mesons, we can estimate for which quantum numbers it is more probable to find a heavy baryonium state. The most probable candidates to form bound states are the isoscalar $\Lambda_Q \bar{\Lambda}_Q$, $\Sigma_Q \bar{\Sigma}_Q$, $\Sigma_Q^* \bar{\Sigma}_Q$ and $\Sigma_Q^* \bar{\Sigma}_Q^*$ and the isovector $\Lambda_Q \bar{\Sigma}_Q$ and $\Lambda_Q \bar{\Sigma}_Q^*$ systems, both in the hidden-charm and hidden-bottom sectors. Their doubly-charmed and -bottom counterparts ($\Lambda_Q {\Lambda}_Q$, $\Lambda_Q {\Sigma}_Q^{(*)}$, $\Sigma_Q^{(*)} {\Sigma}_Q^{(*)}$) are also good candidates for binding.
Highlights
Heavy hadron molecules—bound states composed of heavy hadrons—are a type of exotic hadron
We find that in general pion exchanges are probably nonperturbative for the ΣQΣ Q, ΣÃQΣ Q, and ΣÃQΣ ÃQ systems, while for the Ξ0QΞ 0Q, ΞÃQΞ 0Q, and ΞÃQΞ ÃQ cases they are perturbative
III we present the leading order effective field theory (EFT) potential for heavy baryon-antibaryon states, which consists of a series of contact four-baryon vertices plus the time-honored one pion exchange potential
Summary
Heavy hadron molecules—bound states composed of heavy hadrons—are a type of exotic hadron. A narrow resonance near the heavy baryon-baryon threshold would be an excellent candidate for a heavy baryon-antibaryon bound state Though these states have not been found yet, it is fairly straightforward to extend the available descriptions of heavy meson-antimeson molecules to them and explore the relevant dynamics behind these states. Owing to their heavy-light quark content, they are simultaneously subjected to isospin, SU(3)-flavor, chiral and heavy quark symmetry, a high degree of symmetry that can translate into a fairly regular spectrum [10,21,30–35] This spectrum will not be fully realized in nature: unless these states are shallow they will be a mixture of molecule, charmonium and other exotic components. EFT descriptions of heavy hadron molecules have been exploited successfully in the past in systems composed of heavy mesons and antimesons [31,36–38] In this manuscript we extend the heavy hadron EFT formulated in Ref.
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