Three-body forces, a type of nonperturbative strong interactions, are widely studied in nuclear physics. However, whether their inclusion is necessary in nuclear systems remains a topic of intense debate. In this Letter, we propose that the existence of three-body forces in certain three-body hadronic systems with definite $C$ parity is certain. Such systems consist of two components whose interactions are mediated by three-body forces—a mechanism not easily realized in conventional three-nucleon systems. We investigate two specific three-body hadronic systems, ${\overline{D}}_{s}DK$ and ${\overline{D}}^{*}D\eta$, using contact-range potentials. The two-body hadron-hadron interactions are constrained by reproducing their scattering lengths, while the three-body couplings are constrained by charge symmetry. Our results indicate that three-body forces play a minor role in binding the $I(J^{PC})=0(0^{--}){\overline{D}}_{s}DK$ system, but a crucial one in binding the $I(J^{PC})=0(1^{-+}){\overline{D}}^{*}D\eta$ system. In fact, three-body forces determine whether ${\overline{D}}^{*}D\eta$ forms a bound state, making this system a promising candidate for exploring three-body forces in hadronic physics.

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• Color confinement
• Effective field theory
• Multiquark bound states
• Particle interactions