Analysis of the hidden-charm pentaquark candidates in the $J/ψΛ$ mass spectrum via the QCD sum rules

TL;DR

The paper tackles the nature of hidden-charm, strangeness–bearing pentaquark candidates $P_{cs}(4338)$ and $P_{cs}(4459)$ observed in the $J/\psi\Lambda$ channel. It applies QCD sum rules with an isospin-$0$ basis of diquark–diquark–antiquark currents for the $udsc\bar{c}$ system and separates negative- from positive-parity contributions using a modified energy-scale formula $\mu=\sqrt{M_P^2-(2\mathbb{M}_c)^2}-\mathbb{M}_s$ to optimize the spectral densities. The analysis yields masses in the $M_P\approx4.33$–$4.51$ GeV range across currents, identifying a $(1,1,0,\tfrac{1}{2})$ state $M_P=4.33\pm0.11$ GeV compatible with $P_{cs}(4338)$ and other configurations near $4.37$–$4.51$ GeV that can accommodate $P_{cs}(4459)$. This approach shows that parity separation and scale-setting are crucial for robust QCD sum-rule interpretations of the $J/\psi\Lambda$ pentaquark spectrum and provides a framework for guiding future experimental tests.

Abstract

In this work, we distinguish the isospin for the first time and study the diquark-diquark-antiquark type $udsc\bar{c}$ pentaquark states with zero isospin via the QCD sum rules systematically. We distinguish contributions of the pentaquark states with negative parity from positive parity unambiguously and obtain clean QCD sum rules for the pentaquark states with negative parity. Then we adopt the modified energy scale formula to choose the optimal energy scales of the QCD spectral densities, and obtain the mass spectrum of the $udsc\bar{c}$ pentaquark states with the quantum numbers $I=0$ and $J^{P}={\frac{1}{2}}^-$, ${\frac{3}{2}}^-$, ${\frac{5}{2}}^-$, which could interpret the $P_{cs}(4338)$ and $P_{cs}(4459)$ in the $J/ψΛ$ mass spectrum naturally.

Figures (6)

• Figure 1: The diagrams contribute to the condensates $\langle\bar{q} q\rangle^2\langle\bar{q}g_s\sigma Gq\rangle$, $\langle\bar{q} q\rangle \langle\bar{q}g_s\sigma Gq\rangle^2$, $\langle \bar{q}q\rangle^3\langle \frac{\alpha_s}{\pi}GG\rangle$, where $q=u$, $d$ or $s$. Other diagrams obtained by interchanging of the $c$ quark lines (dashed lines) or light quark lines (solid lines) are implied.
• Figure 2: The contributions of the vacuum condensates $D(n)$ with variations of the Borel parameter $T^2$ for the $[ud][sc]\bar{c}$ ($0$, $0$, $0$, $\frac{1}{2}$) pentaquark state.
• Figure 3: The masses with variations of the Borel parameters $T^2$ for the hidden-charm pentaquark states, where the (I), (II), (III) and (IV) denote the $[ud][sc]\bar{c}$ ($0$, $0$, $0$, $\frac{1}{2}$), $[ud][sc]\bar{c}$ ($0$, $1$, $1$, $\frac{1}{2}$), $[us][dc]\bar{c}-[ds][uc]\bar{c}$ ($1$, $1$, $0$, $\frac{1}{2}$) and $[us][dc]\bar{c}-[ds][uc]\bar{c}$ ($1$, $0$, $0$, $\frac{1}{2}$) pentaquark states, respectively.
• Figure 4: The masses with variations of the Borel parameters $T^2$ for the hidden-charm pentaquark states, where the (I), (II), (III), (IV) and (V) denote the $[ud][sc]\bar{c}$ ($0$, $1$, $1$, $\frac{3}{2}$), $[us][dc]\bar{c}-[ds][uc]\bar{c}$ ($0$, $1$, $1$, $\frac{3}{2}$), $[us][dc]\bar{c}-[ds][uc]\bar{c}$ ($1$, $0$, $1$, $\frac{3}{2}$), $[us][dc]\bar{c}-[ds][uc]\bar{c}$ ($1$, $1$, $2$, $\frac{3}{2}$)${}_4$ and $[us][dc]\bar{c}-[ds][uc]\bar{c}$ ($1$, $1$, $2$, $\frac{3}{2}$)${}_5$ pentaquark states, respectively.
• Figure 5: The masses with variations of the Borel parameters $T^2$ for the hidden-charm pentaquark states, where the (I) and (II) denote the $[ud][sc]\bar{c}$ ($0$, $1$, $1$, $\frac{5}{2}$) and $[us][dc]\bar{c}-[ds][uc]\bar{c}$ ($1$, $1$, $2$, $\frac{5}{2}$) pentaquark states, respectively.