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

Abstract In this work, we distinguish the isospin for the first time and study the diquark–diquark–antiquark type $$udsc\bar{c}$$ u d s c c ¯ pentaquark states with zero isospin via the QCD sum rules systematically. We distinguish contributions of the pentaquark states with negative parity from positive parity unambiguously and obtain clean QCD sum rules for the pentaquark states with negative parity. Then we adopt the modified energy scale formula to choose the optimal energy scales of the QCD spectral densities, and obtain the mass spectrum of the $$udsc\bar{c}$$ u d s c c ¯ pentaquark states with the quantum numbers $$I=0$$ I = 0 and $$J^{P}={\frac{1}{2}}^-$$ J P = 1 2 - , $${\frac{3}{2}}^-$$ 3 2 - , $${\frac{5}{2}}^-$$ 5 2 - , which could interpret the $$P_{cs}(4338)$$ P cs ( 4338 ) and $$P_{cs}(4459)$$ P cs ( 4459 ) in the $$J/\psi \Lambda $$ J / ψ Λ mass spectrum naturally.