Since the discovery of the charmonium-like state \mathrmX(3872) in 2003, a large number of new hadronic states have been observed in high-energy experiments (BESIII, LHCb, Belle, etc.), challenging the conventional quark-antiquark (meson) and three-quark (baryon) paradigms. Among various interpretations, hadronic molecules and diquark-antidiquark states have emerged as two important scenarios. Studies by different theory groups have shown that some of the observed tetraquark candidates can be well explained within both the molecular and the diquark-antidiquark frameworks. Therefore, we argue that in certain tetraquarks these two components should coexist with a certain proportion. Under this premise, we have recently proposed a new theoretical approach, namely, to consider the mixing effect between molecular and diquark-antidiquark states within an effective field theory framework. Specifically, based on the hidden local gauge symmetry, we introduce diquark fields and construct a complete set of interaction Lagrangians, including vertices for two light diquarks with one light meson, a heavy meson with a heavy diquark and a light diquark, and two heavy diquarks with one light meson.

Meanwhile, we apply this theory to study the following tetraquark candidates: \mathrmZ_cs(4000) , \mathrmZ_c(3900) , \mathrmX(4500) , and \mathrmT_cs0^*(2900) . By using the constructed Lagrangians, we compute the effective potentials for the coupled channels consisting of molecular and diquark-antidiquark configurations, and solve the coupled-channel Bethe-Salpeter equation in the on-shell approximation. And we obtain the following results:

For \mathrmZ_cs(4000) , the pole at (4013\pm42\mathrmi) MeV in the \mathrm\overlineD^*0D_s^*+/\overlineA_csS_cu coupled system matches the LHCb data, while a second pole at (4208\pm13\mathrmi) MeV is consistent with \mathrmZ_cs(4220) in mass but narrower in width, calling for more precise experimental measurements.

For \mathrmZ_c(3900) , the pole position lies in the range 3888–3901 MeV with a width of 17–26 MeV (depending on the cutoff), in excellent agreement with the BESIII results. The extracted effective coupling constants indicate that the diquark-antidiquark component contributes significantly, with a coupling strength about 15 GeV, nearly twice that of the molecular component.

For \mathrmX(4500) , the \mathrmD_s^*+D_s^*-/A_cq\overlineA_cq/A_cs\overlineA_cs coupled system yields a pole at (4488.0\pm\mathrmi29.6) MeV, precisely reproducing the LHCb mass and width. Notably, the \mathrmA_cs\overlineA_cs channel has the largest coupling (~10.5 GeV), indicating the importance of the diquark-antidiquark configuration.

For \mathrmT_cs0^*(2900)^++ , the \mathrmD_s^+\rho^+/D^*+K^*+/A_cu\overlineA_sd system gives a pole at (2948\pm\mathrmi48) MeV, again consistent with the LHCb measurement. The couplings of the molecular and diquark-antidiquark state channels are comparable.

Another innovative aspect of this work is the systematic construction of a color gauge-invariant effective field theory with diquark fields. By requiring gauge invariance in color space, we introduce gluon fields as gauge bosons and obtain the diquark-gluon interaction vertices. On this basis, we derive the one-gluon-exchange potential between a diquark and an antidiquark.

The theoretical approach described above can be applied not only to tetraquark systems but also, in combination with chiral quark models, to the study of baryon and pentaquark systems, thereby providing a new theoretical perspective for understanding the internal structure of tetraquarks and offering meaningful guidance for future experimental investigations.