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 $J^P=0^{+}$ channel: the light nonet [$a_0(980)$, $K_0^{\ast }(700)$, $f_0(500)$, $f_0(980)$] and the heavy nonet [$a_0(1450)$, $K_0^{\ast }(1430)$, $f_0(1370)$, $f_0(1500)$]. 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, $⟨V_{CS}⟩$, 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, $\Delta M\approx \Delta ⟨V_{CS}⟩$, 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.

Comments: 10 pages, no figure. The version accepted for publication in EPJC