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

TL;DR

This work analyzes hidden-charm-doubly-strange pentaquarks $qssc\bar{c}$ using QCD sum rules with color $\bar{\mathbf{3}}\bar{\mathbf{3}}\bar{\mathbf{3}}$ currents constructed from light quarks in two octets. By performing a full operator-product expansion up to dimension $13$ and focusing on the negative-parity channel, the authors extract masses for the states with $IJ^{P}=\frac{1}{2}{\frac{1}{2}}^-$, $\frac{1}{2}{\frac{3}{2}}^-$, and $\frac{1}{2}{\frac{5}{2}}^-$, finding masses in the broad $\sim 4.5$–$4.7$ GeV range across several current configurations. They introduce an energy-scale formula $\mu=\sqrt{M_{P}^{2}-(2{\mathbb{M}}_c)^2}-2{\mathbb{M}}_s$ to stabilize the OPE and enhance pole dominance, and conclude that the lowest pentaquark states are not simply scalar-diquark–scalar-diquark–antiquark constructions. The results motivate experimental searches in $\Xi_b$ decays, such as $\Xi_b^- \to P_{css}^-\phi \to J/\psi\Xi^-\phi$, to test these predictions and clarify the nature of hidden-charm pentaquarks with strangeness.

Abstract

In this work, we construct the color $\bar{\mathbf{3}}\bar{\mathbf{3}}\bar{\mathbf{3}}$ type local five-quark currents with the light quarks $qss$ in the flavor octet, and study the $qssc\bar{c}$ pentaquark states via the QCD sum rules in a comprehensive way, and we emphasize that we achieve two light-flavor octets. We obtain the mass spectrum of the hidden-charm-doubly-strange pentaquark states with the isospin-spin-parity $IJ^{P}=\frac{1}{2}{\frac{1}{2}}^-$, $\frac{1}{2}{\frac{3}{2}}^-$ and $\frac{1}{2}{\frac{5}{2}}^-$, which can be confronted to the experimental data in the future, especially the process $Ξ_b^- \to P_{css}^-φ\to J/ψΞ^- φ$. As a byproduct, we observe that the lowest hidden-charm pentaquark states are not of the scalar-diquark-scalar-diquark-antiquark type, it is wrong to refer the scalar and axialvector diquarks as the "good" and "bad" diquarks, respectively.

Figures (5)

• Figure 1: The $|D(n)|$ with variations of the $n$ for the central values of the input parameters, where the (I), (II) and (III) denote the spins $J=\frac{1}{2}$, $\frac{3}{2}$ and $\frac{5}{2}$ of the currents respectively, the $j=1$, $2$, $3$, $4$, $5$, $6$ and $7$ denote the series numbers of the currents.
• Figure 2: The masses with variations of the Borel parameters $T^2$ for the hidden-charm-doubly-strange pentaquark states, where the (I), (II), (III), (IV), (V) and (VI) denote the $[qs][sc]\bar{c}$ ($0$, $0$, $0$, $\frac{1}{2}$), $[qs][sc]\bar{c}$ ($0$, $1$, $1$, $\frac{1}{2}$), $[ss][qc]\bar{c}-[sq][sc]\bar{c}$ ($1$, $1$, $0$, $\frac{1}{2}$), $[ss][qc]\bar{c}-[sq][sc]\bar{c}$ ($1$, $0$, $0$, $\frac{1}{2}$), $[ss][qc]\bar{c}$ ($1$, $1$, $0$, $\frac{1}{2}$) and $[ss][qc]\bar{c}$ ($1$, $0$, $0$, $\frac{1}{2}$) pentaquark states, respectively.
• Figure 3: The masses with variations of the Borel parameters $T^2$ for the hidden-charm-doubly-strange pentaquark states, where the (I), (II), (III), (IV), (V) and (VI) denote the $[qs][sc]\bar{c}$ ($0$, $1$, $1$, $\frac{3}{2}$), $[ss][qc]\bar{c}-[sq][sc]\bar{c}$ ($1$, $0$, $1$, $\frac{3}{2}$), $[ss][qc]\bar{c}-[sq][sc]\bar{c}$ ($1$, $1$, $2$, $\frac{3}{2}$)${}_3$, $[ss][qc]\bar{c}-[sq][sc]\bar{c}$ ($1$, $1$, $2$, $\frac{3}{2}$)${}_4$, $[ss][qc]\bar{c}$ ($1$, $0$, $1$, $\frac{3}{2}$) and $[ss][qc]\bar{c}$ ($1$, $1$, $2$, $\frac{3}{2}$)${}_6$ pentaquark states, respectively.
• Figure 4: The mass with variations of the Borel parameter $T^2$ for the hidden-charm-doubly-strange pentaquark state, where the (VII) denotes the $[ss][qc]\bar{c}$ ($1$, $1$, $2$, $\frac{3}{2}$)${}_7$ pentaquark state.
• Figure 5: The masses with variations of the Borel parameters $T^2$ for the hidden-charm-doubly-strange pentaquark states, where the (I), (II), (III), (IV) and (V) denote the $[qs][sc]\bar{c}$ ($0$, $1$, $1$, $\frac{5}{2}$), $[ss][qc]\bar{c}-[qs][sc]\bar{c}$ ($1$, $0$, $1$, $\frac{5}{2}$), $[ss][qc]\bar{c}-[qs][sc]\bar{c}$ ($1$, $1$, $2$, $\frac{5}{2}$), $[qs][sc]\bar{c}$ ($1$, $0$, $1$, $\frac{5}{2}$) and $[ss][qc]\bar{c}$ ($1$, $1$, $2$, $\frac{5}{2}$) pentaquark states, respectively.