Role of hidden-color components in the tetraquark mixing model

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 JP=0⁺ JP=0+ channel: the light nonet [ a₀ (980) a0(980) , K₀* (700) K0∗(700) , f₀ (500) f0(500) , f₀ (980) f0(980) ] and the heavy nonet [ a₀ (1450) a0(1450) , K₀^* (1430) K0∗(1430) , f₀ (1370) f0(1370) , f₀ (1500) f0(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, VCS ⟨VCS⟩ , 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, Δ M≈ Δ VCS ΔM≈Δ⟨VCS⟩ , 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.