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

TL;DR

Problem: determine the role of three-body forces in hadronic three-body systems with definite charge parity. Approach: apply $\pi$onless EFT and the Gaussian Expansion Method to two systems, $J^{PC}=0^{--}$ in $\bar{D}_sDK$ and $J^{PC}=1^{-+}$ in $\bar{D}^*D\eta$, fixing two-body couplings from scattering data and the three-body coupling $C_3$ by charge symmetry. Key results: the three-body force is minor for $\bar{D}_sDK$ but essential for binding $\bar{D}^*D\eta$, with binding occurring only when $C_3$ is sufficiently attractive; the energy partition shows the three-body contribution can reach ~18\% of the total in some cases and radii lie in the $1$–$4$ fm range. Significance: identifies $\bar{D}^*D\eta$ as a promising candidate to probe three-body forces in hadronic physics and points to experimental observables such as momentum-correlation lineshapes and invariant-mass distributions, e.g., in $B$ decays.

Abstract

Three-body forces, as a type of non-perturbative strong interaction, are widely discussed in studies of nuclear properties. 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 $\bar{D}^*Dη$, 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 $J^{PC}=0^{--}$ $\bar{D}_sDK$ system, but a crucial one in binding the $J^{PC}=1^{-+}$ $\bar{D}^*Dη$ system. In fact, three-body forces determine whether $\bar{D} ^*Dη$ forms a bound state, making this system a promising candidate for exploring three-body forces in hadronic physics.

Figures (5)

• Figure 1: Contact term in the $\bar{D}^*D\eta$ system.
• Figure 2: Three Jacobi channels of the $\bar{D}^*D\eta$ system.
• Figure 3: Binding energy and rms radii $\langle r_{\bar{D}_s K} \rangle$ and $\langle r_{D K} \rangle$ of the $J^{PC}=0^{--}$$\bar{D}_sDK$ three-body system as functions of the three-body potential strength $C_3$, shown for different choices of the cutoffs $b_2$ and $b_3$.
• Figure 4: Binding energy and rms radii $\langle r_{D\eta} \rangle$ and $\langle r_{\bar{D}^*D} \rangle$ of the $J^{PC}=1^{-+}$$\bar{D}^*D\eta$ three-body system as functions of the three-body potential strength $C_3$ for $b_2=0.5$ fm.
• Figure 5: Binding energy and rms radii $\langle r_{D\eta} \rangle$ and $\langle r_{\bar{D}^*D} \rangle$ of the $J^{PC}=1^{-+}$$\bar{D}^*D\eta$ three-body system as functions of the three-body potential strength $C_3$ for $b_2=1.0$ fm.