$ΞNN$ three-baryon force from SU(3) chiral effective field theory: A femtoscopic study

TL;DR

This paper derives the $\Xi NN$ three-baryon force within SU(3) chiral EFT up to leading orders and constrains the low-energy constants via the decuplet saturation approximation. It then maps the $\Xi NN$ 3BF into the coordinate-space potential for the deuteron--$\Xi^-$ system and assesses its impact on the femtoscopy correlation function $C_{d\Xi^-}(q)$ by solving a two-body scattering problem with a distorting potential that includes the 3BF alongside two-body forces and Coulomb effects. The main finding is that the $\Xi NN$ 3BF alters the correlation function by at most about $4\%$, with the effect being suppressed by its short-range character and peripheral scattering being dominant; varying the regulator, source size, and deuteron binding energy does not qualitatively change this conclusion. This indicates limited sensitivity of the deuteron--$\Xi^-$ correlation to short-range hyperon three-baryon forces, motivating complementary approaches to probe these forces in hypernuclear and dense-matter contexts.

Abstract

Background: The development of SU(3) chiral effective field theory has opened the way to a systematic exploration of three-baryon forces (3BFs), a key ingredient in hypernuclear and dense matter physics. However, $ΞNN$ 3BF based on SU(3) chiral EFT has not been studied until now. Purpose: We apply SU(3) chiral EFT to derive $ΞNN$ potentials in momentum space. Then, we investigate how the $ΞNN$ 3BF affects the correlation function of deuteron--$Ξ^-$ pair created through heavy-ion collisions. Methods: To reduce the number of low-energy constants involved in the $ΞNN$ potentials, we employ the decuplet saturation approximation, by which only two of them remain unconstrained. The deuteron--$Ξ^-$ scattering is treated as an effective two-body problem with the $ΞNN$ 3BF incorporated into the potential between the deuteron and $Ξ^-$. Results: We found that the effect of the $ΞNN$ 3BF on the deuteron--$Ξ^-$ correlation function is at most about 4\%. This small effect is not primarily due to the loosely-bound nature of the deuteron. Instead, this is because the deuteron and $Ξ^-$ interact with each other mainly at low momentum, corresponding to peripheral scattering, where the influence of the $ΞNN$ 3BF is limited. Conclusions: Since the correlation function shows limited sensitivity to the short-range 3BF, complementary approaches may be necessary.

Figures (10)

• Figure 1: Feynman diagrams for the leading $\Xi NN$ 3BF. From left to right, they correspond to the TPE, OPE, and contact terms. The arrows specified by the indices $i$, $j$, and $k$ correspond to the initial baryons, while those with $l$, $m$, and $n$ are associated with the final ones. The dashed line represents the pion propagation.
• Figure 2: Examples of (a) three-point and (b) four-point vertices involving the coefficients $N_{B_lB_i\phi}$ and $N^f_{\phi_1\substack{m\\j}\phi_2}$, respectively. Baryons and mesons are denoted by the solid and dashed lines, respectively.
• Figure 3: Diagram of a four-baryon vertex including one meson, labeled by the coefficient $N^f_{\substack{m\\j}\substack{n\\k}\phi}$. The notation is similar to that in Fig. \ref{['fig:2meson']}.
• Figure 4: The six-baryon vertex labeled by the coefficient $\tilde{t}^{f,a} N^{f,a}_{\substack{lmn\\ijk}}$.
• Figure 5: Coordinates of the $p$--$n$--$\Xi^-$ system. The proton and neutron masses are represented by $m_2$ and $m_3$, respectively.