Probing the three-body force in hadronic systems with specific charge parity

TL;DR

This paper investigates the role of three-body forces in specific three-hadron systems with definite charge parity, finding they are crucial for binding in one system but minor in another, highlighting their importance in hadronic physics.

Contribution

It demonstrates that three-body forces are essential for binding in certain three-hadron systems with specific charge parity, using contact-range potentials constrained by scattering data and charge symmetry.

Findings

Three-body forces are minor in binding the $ar{D}_sDK$ system.

Three-body forces are crucial for binding the $ar{D}^*D ext{eta}$ system.

The $ar{D}^*D ext{eta}$ system is a promising candidate to explore three-body forces.

Abstract

Three-body forces, a type of non-perturbative strong interaction, 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, $\bar{D}_sDK$ and $\bar{D}^*D\eta$, 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 $I(J^{PC})=0(0^{--})$ $\bar{D}_sDK$ system, but a crucial one in binding the $I(J^{PC})=0(1^{-+})$ $\bar{D}^*D\eta$ system. In fact, three-body forces determine whether $\bar{D} ^*D\eta$ forms a bound state, making this system a promising candidate for exploring three-body forces in hadronic physics.