Analysis of the ${\frac{1}{2}}^{\pm }$ pentaquark states in the diquark-diquark-antiquark model with QCD sum rules

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 $\mu =\sqrt{M_P^2-(2{\mathbb{M}}_c{)}^2}$ 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.

Comments: 34 pages, 16 figures. arXiv admin note: substantial text overlap with arXiv:1508.04189