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

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, $\Xi NN$ 3BF based on SU(3) chiral EFT has not been studied until now. Purpose: We apply SU(3) chiral EFT to derive $\Xi NN$ potentials in momentum space. Then, we investigate how the $\Xi NN$ 3BF affects the correlation function of deuteron--$\Xi^-$ pair created through heavy-ion collisions. Methods: To reduce the number of low-energy constants involved in the $\Xi NN$ potentials, we employ the decuplet saturation approximation, by which only two of them remain unconstrained. The deuteron--$\Xi^-$ scattering is treated as an effective two-body problem with the $\Xi NN$ 3BF incorporated into the potential between the deuteron and $\Xi^-$. Results: We found that the effect of the $\Xi NN$ 3BF on the deuteron--$\Xi^-$ 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 $\Xi^-$ interact with each other mainly at low momentum, corresponding to peripheral scattering, where the influence of the $\Xi NN$ 3BF is limited. Conclusions: Since the correlation function shows limited sensitivity to the short-range 3BF, complementary approaches may be necessary.