Analysis of the

In this article, we construct both the axialvector-diquark–axialvector-diquark–antiquark type and the 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 we 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 $$\mathrm{SU}(3)$$ breaking effects of the light quarks, and we 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