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

Abstract

In this work, we adopt the diquark model, construct the diquark-diquark-antiquark type currents with the light quarks $uus$ in two octets, and study the $uusc\bar{c}$ pentaquark states in the framework of the QCD sum rules systematically. We obtain the mass spectrum of the hidden-charm-singly-strange pentaquark states with the quantum numbers $IJ^{P}=1{\frac{1}{2}}^-$, $1{\frac{3}{2}}^-$ and $1{\frac{5}{2}}^-$. And we can search for those $P_{cs}$ states in the processes $Σ_b^+\to P_{cs}^+φ\to J/ψΣ^+ \,φ$ and $Ξ_b^0\to P_{cs}^+ K^- \to J/ψΣ^+\, K^-$.

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) represent 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 $7$ represent the series numbers of the currents.
• Figure 2: The masses with variations of the Borel parameters $T^2$ for the hidden-charm-singly-strange pentaquark states, where the (I), (II), (III), (IV), (V) and (VI) represent the $[su][uc]\bar{c}$ ($0$, $0$, $0$, $\frac{1}{2}$), $[su][uc]\bar{c}$ ($0$, $1$, $1$, $\frac{1}{2}$), $[uu][sc]\bar{c}-[us][uc]\bar{c}$ ($1$, $1$, $0$, $\frac{1}{2}$), $[uu][sc]\bar{c}-[us][uc]\bar{c}$ ($1$, $0$, $0$, $\frac{1}{2}$), $[uu][sc]\bar{c}$ ($1$, $1$, $0$, $\frac{1}{2}$) and $[uu][sc]\bar{c}$ ($1$, $0$, $0$, $\frac{1}{2}$) pentaquark states, respectively.
• Figure 3: The masses with variations of the Borel parameters $T^2$ for the hidden-charm-singly-strange pentaquark states, where the (I), (II), (III), (IV), (V) and (VI) represent the $[su][uc]\bar{c}$ ($0$, $1$, $1$, $\frac{3}{2}$), $[uu][sc]\bar{c}-[us][uc]\bar{c}$ ($1$, $0$, $1$, $\frac{3}{2}$), $[uu][sc]\bar{c}-[us][uc]\bar{c}$ ($1$, $1$, $2$, $\frac{3}{2}$)${}_3$, $[uu][sc]\bar{c}-[us][uc]\bar{c}$ ($1$, $1$, $2$, $\frac{3}{2}$)${}_4$, $[uu][sc]\bar{c}$ ($1$, $0$, $1$, $\frac{3}{2}$) and $[uu][sc]\bar{c}$ ($1$, $1$, $2$, $\frac{3}{2}$)${}_6$ pentaquark states, respectively.
• Figure 4: The mass with variations of the Borel parameter $T^2$ for the hidden-charm-singly-strange pentaquark state, where the (VII) represents the $[uu][sc]\bar{c}$ ($1$, $1$, $2$, $\frac{3}{2}$)${}_7$ pentaquark state.
• Figure 5: The masses with variations of the Borel parameters $T^2$ for the hidden-charm-singly-strange pentaquark states, where the (I), (II), (III), (IV) and (V) represent the $[su][uc]\bar{c}$ ($0$, $1$, $1$, $\frac{5}{2}$), $[uu][sc]\bar{c}-[us][uc]\bar{c}$ ($1$, $0$, $1$, $\frac{5}{2}$), $[uu][sc]\bar{c}-[us][uc]\bar{c}$ ($1$, $1$, $2$, $\frac{5}{2}$), $[su][uc]\bar{c}$ ($1$, $0$, $1$, $\frac{5}{2}$) and $[uu][sc]\bar{c}$ ($1$, $1$, $2$, $\frac{5}{2}$) pentaquark states, respectively.