Strange Pentaquark Molecules in QCD Sum Rules

TL;DR

The paper addresses the spectroscopy of hidden- and open-strange pentaquark states by formulating them as hadronic molecules built from a baryon octet plus an $s\bar{s}$ pair. Using QCD sum rules, it constructs 21 interpolating currents with $J^P = 1/2^-$ and $3/2^-$, computes two-point correlators, and executes an operator-product expansion up to dimension-11 with a Borel transformation to extract masses via $M_H^2 = \frac{\int ds\, s\, \rho_i^{QCD}(s) e^{-s/M_B^2}}{\int ds\, \rho_i^{QCD}(s) e^{-s/M_B^2}}$. The results show no bound states for $J^P = 1/2^-$, but three bound states in the $J^P = 3/2^-$ sector matching $\\Lambda(2050)3/2^-$, $\\Xi(2250)$, and $N(2120)3/2^-$ as $\\Lambda\\phi$, $\\Xi\\phi$, and $\\Sigma K^*$ molecular states, respectively; several near-threshold excitations align with PDG resonances and suggest multiplet partner relations, such as $\\Lambda(2050)3/2^-$ with $\\Xi(2250)$ and $N\\eta_s$ with $\\Lambda\\eta_s$. The work supports the hadronic-molecular interpretation in the strange sector and provides predictive structure for future searches, while highlighting the need for broader current bases to uncover additional states.

Abstract

In this article, we systematically construct hidden- and open-strange pentaquarks in the hadronic molecular picture to search for possible partners of hadronic molecular state multiplets in the strange quark sector using QCD sum rules. Within this picture, 21 distinct currents are constructed with $J^P = 1/2^-$ and $3/2^-$. There is no bound state found from $J^P = 1/2^-$ currents, while three of them from $J^P = 3/2^-$ currents are bound-state solutions consistent with the $Λ(2050)3/2^-$, $Ξ(2250)$, and $N(2120)3/2^-$ states, which can be identified as $Λφ$, $Ξφ$, and $ΣK^\ast$ hadronic molecular states, respectively. Other constructions are interpreted as hadronic molecular states composed of excited states with the same quantum numbers, and some of these exhibit mass values that align with known resonances listed in the RPP(PDG). Our numerical results indicate that $Λ(2050)3/2^-$ and $Ξ(2250)$ should be the multiplet partner of each other. Additionally, although $ΣK^\ast$ bound state was identified under this framework, no corresponding partner states were found within the context of the currents we constructed. Alternative constructions may offer new possibilities for identifying such states.

Figures (2)

• Figure 1: The pole contribution and the OPE convergence with respect to the Borel parameter $M_B^2$ with different threshold parameter $\sqrt{s_0}$.
• Figure 2: The mass with respect to the Borel parameter $M_B^2$ with different threshold parameter $\sqrt{s_0}$.