Faddeev calculation of ${}_{\mathrm{\Lambda }}^3\mathrm{H}$ incorporating the $2\pi$-exchange $\mathrm{\Lambda }NN$ interaction

Faddeev calculations of hypertriton (${}_{\mathrm{\Lambda }}^3\mathrm{H}$) separation energy are performed, incorporating $2\pi$-exchange $\mathrm{\Lambda }NN$ three-baryon force. Repulsive contributions of the three-baryon force in the order of 20 keV are found, depending on the $NN$ interactions employed. The effect is not negligible compared with the small separation energy of ${}_{\mathrm{\Lambda }}^3\mathrm{H}$.

Figure 1

Diagram of $2\pi$-exchange $\mathrm{\Lambda }NN$ 3BF in momentum space. The small filled circle denotes the $NN\pi$ vertex with the coupling constant $g_A/f_0^2$, and the large filled circle denotes the $NN\pi \pi$ vertex specified by the coupling constants $3b_0+b_D$ and $2b_2+3b_4$ in Eq. (9).

Figure 2

$\mathrm{\Lambda }$-deuteron folding potential with ${\ell }_{\mathrm{\Lambda }}=0$ from $2\pi$-exchange $\mathrm{\Lambda }NN$ 3BF. The deuteron is described by the semilocal $N^3\mathrm{LO}$ ChEFT interaction [11] with the cutoff scale of 550 MeV. The contribution of the deuteron $s$-state pair is shown.

Figure 3

Results of Faddeev calculations with and without $2\pi$-exchange $\mathrm{\Lambda }NN$ 3BF using $S=-1 YN$ interactions of NLO13, NLO19, and NSC89. Various $NN$ potentials parametrized in ChEFT are employed. The shaded band indicates the average in experimental data of $148\pm 40$ keV by the Mainz group [8]. Repulsive contributions of the 3BF are separately shown in the lower panel.