Abstract
In this article, we construct both the axialvector-diquark-axialvector-diquark-antiquark type and axialvector-diquark-scalar-diquark-antiquark type interpolating currents, then calculate the contributions of the vacuum condensates up to dimension-10 in the operator product expansion, and study the masses and pole residues of the $J^P={\frac{1}{2}}^\pm$ hidden-charm pentaquark states with the QCD sum rules in a systematic way. In calculations, we use the formula $\mu=\sqrt{M^2_{P}-(2{\mathbb{M}}_c)^2}$ to determine the energy scales of the QCD spectral densities. We take into account the $SU(3)$ breaking effects of the light quarks, and obtain the masses of the hidden charm pentaquark states with the strangeness $S=0,\,-1,\,-2,\,-3$, which can be confronted with the experimental data in the future.
Highlights
The LHCb collaboration studied the 0 b →J/ψ K − p decays, and one observed two pentaquark candidates Pc(4380) and Pc(4450) in the J/ψ p mass spectrum with the significances of more than 9 σ [1]
Scalar-diquark–antiquark type interpolating currents, which are supposed to couple potentially to the lowest pentaquark states according to the light scalar-diquark constituent [32], calculate the contributions of the vacuum condensates up to dimension 10 in the operator product expansion and study the masses and pole residues of 1± 2 hidden-charm pentaquark states with the QCD sum rules
(2Mc )2 to determine the energy scales of the QCD spectral densities, the resulting pole contributions are about (40–60) %, and the contributions of the vacuum condensates of dimension 10 are less than 5 %, the two criteria of the conventional QCD sum rules can be satisfied
Summary
J/ψ K − p decays, and one observed two pentaquark candidates Pc(4380) and Pc(4450) in the J/ψ p mass spectrum with the significances of more than 9 σ [1]. Scalar-diquark–antiquark type interpolating currents, which are supposed to couple potentially to the lowest pentaquark states according to the light scalar-diquark constituent [32], calculate the contributions of the vacuum condensates up to dimension 10 in the operator product expansion and study the masses and pole residues of. We calculate the vacuum condensate up to dimension 10 in the operator product expansion, and study the masses and pole residues of the lowest pentaquark states in a systematic way. The article is arranged as follows: we derive the QCD sum rules for the masses and pole residues of the pentaquark states in Sect. After isolating the pole terms of the lowest states of the hidden-charm pentaquark states, we obtain the following results: λ−P p M. where the M± are the masses of the lowest pentaquark states with the parity ±, respectively. We obtain the masses through fractions, see Eqs. (36)–(37), the effects of the gluon condensates can be safely absorbed into the pole residues λ±P and tiny effects on the masses can be safely neglected
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