Decay properties of $$P_c$$ states through the Fierz rearrangement

We systematically study hidden-charm pentaquark currents with the quark configurations $$[\bar{c} u][u d c]$$ [ c ¯ u ] [ u d c ] , $$[\bar{c} d][u u c]$$ [ c ¯ d ] [ u u c ] , and $$[\bar{c} c][u u d]$$ [ c ¯ c ] [ u u d ] . Some of their relations are derived using the Fierz rearrangement of the Dirac and color indices, and the obtained results are used to study strong decay properties of $$P_c$$ P c states as $$\bar{D}^{(*)} \varSigma _c$$ D ¯ ( ∗ ) Σ c hadronic molecules. We calculate their relative branching ratios for the $$J/\psi p$$ J / ψ p , $$\eta _c p$$ η c p , $$\chi _{c0} p$$ χ c 0 p , $$\chi _{c1} p$$ χ c 1 p , $$\bar{D}^{(*)0} \varLambda _c^+$$ D ¯ ( ∗ ) 0 Λ c + , $$\bar{D}^{0} \varSigma _c^{+}$$ D ¯ 0 Σ c + , and $$\bar{D}^{-} \varSigma _c^{++}$$ D ¯ - Σ c + + decay channels. We propose to search for the $$P_c(4312)$$ P c ( 4312 ) in the $$\eta _c p$$ η c p channel and the $$P_c(4440)/P_c(4457)$$ P c ( 4440 ) / P c ( 4457 ) in the $$\bar{D}^{0} \varLambda _c^+$$ D ¯ 0 Λ c + channel.