QCD sum rule study of hidden-charm pentaquarks

Hua-Xing Chen,Er-Liang Cui,Shi-Lin Zhu,Xiang Liu,T G Steele,Wei Chen

doi:10.1140/epjc/s10052-016-4438-5

Abstract

We study the mass spectra of hidden-charm pentaquarks having spin $J = {1\over2}/{3\over2}/{5\over2}$ and quark contents $uud c \bar c$. We systematically construct all the relevant local hidden-charm pentaquark currents, and select some of them to perform QCD sum rule analyses. We find that the $P_c(4380)$ and $P_c(4450)$ can be identified as hidden-charm pentaquark states composed of an anti-charmed meson and a charmed baryon. Besides them, we also find a) the lowest-lying hidden-charm pentaquark state of $J^P = 1/2^-$ has the mass $4.33^{+0.17}_{-0.13}$ GeV, while the one of $J^P = 1/2^+$ is significantly higher, that is around $4.7-4.9$ GeV; b) the lowest-lying hidden-charm pentaquark state of $J^P = 3/2^-$ has the mass $4.37^{+0.18}_{-0.13}$ GeV, consistent with the $P_c(4380)$ of $J^P = 3/2^-$, while the one of $J^P = 3/2^+$ is also significantly higher, that is above $4.6$ GeV; c) the hidden-charm pentaquark state of $J^P = 5/2^-$ has a mass around $4.5-4.6$ GeV, slightly larger than the $P_c(4450)$ of $J^P = 5/2^+$.

Highlights

The detailed relations between [cd cd ][ abcqaqbqc] and [cd qd ][ abccaqbqc] cannot be obtained
We construct the currents of the color configuration [cd cd ][ abcuadbuc]
We find the following currents having J P = 1/2+ and quark contents uudcc: ξ40 = [ abc(uaT Cσμν γ5db)γ5cc][cd σμν γ5ud ], ξ41

Summary

A short summary

We systematically construct all local pentaquark interpolating currents having J P = 1/2+ and quark contents uudcc. One may wonder that there are altogether 71 independent currents. Some of these currents can be related by applying the color rearrangement in. Considering there are 71 currents in all, it will be too complicate to perform thorough transformation one by one. We can give an estimation that at least one third of these 71 currents are not independent and can be expressed by other currents. QCD sum rule analyses using the currents selected as well as those selected in Appendices A and B

QCD sum rules analyses

Numerical analysis

3.94 GeV2 value used

Results and discussions