Role of hidden-color components in the tetraquark mixing model

Abstract Multiquarks can have two-hadron components and hidden-color components in their wave functions. The presence of two-hadron components in multiquarks introduces a potential source of confusion, particularly with respect to their resemblance to hadronic molecules. On the other hand, hidden-color components are essential for distinguishing between multiquarks and hadronic molecules. In this work, we study the hidden-color components in the wave functions of the tetraquark mixing model, a model that has been proposed as a suitable framework for describing the properties of two nonets in the $$J^{P}=0^{+}$$ J P = 0 + channel: the light nonet [ $$a_{0} (980)$$ a 0 ( 980 ) , $$K_{0}^{*} (700)$$ K 0 ∗ ( 700 ) , $$f_{0} (500)$$ f 0 ( 500 ) , $$f_{0} (980)$$ f 0 ( 980 ) ] and the heavy nonet [ $$a_{0} (1450)$$ a 0 ( 1450 ) , $$K_{0}^* (1430)$$ K 0 ∗ ( 1430 ) , $$f_{0} (1370)$$ f 0 ( 1370 ) , $$f_{0} (1500)$$ f 0 ( 1500 ) ]. Our analysis reveals a substantial presence of hidden-color components within the tetraquark wave functions. To elucidate the impact of hidden-color components on physical quantities, we conduct computations of the hyperfine masses, $$\langle V_{CS}\rangle $$ ⟨ V CS ⟩ , for the two nonets, considering scenarios involving only the two-meson components and those incorporating the hidden-color components. We demonstrate that the hidden-color components constitute an important part of the hyperfine masses, such that the mass difference formula, $$\Delta M\approx \Delta \langle V_{CS}\rangle $$ Δ M ≈ Δ ⟨ V CS ⟩ , which has been successful for the two nonets, cannot be achieved without the hidden-color contributions. This can provide another evidence supporting the tetraquark nature of the two nonets.