and two-meson exchange pieces. The corresponding potentials are denoted by $V^{(0)}, V^{(1)}$ and $V^{(2)}$, respectively. The contact potential $V^{(0)}$ involves all possible combinations of baryon spin operators $\vec \sigma_1,  \vec \sigma_2, \vec \sigma_3$. The one-meson exchange 3BF potential has the following generic form: $$V^{(1)}_i = \frac{1}{2f^2} \frac{\vec\sigma_1\cdot\vec q}{\vec q^{\,2}+m_i^2} (
A \vec\sigma_3+ B \, \mathrm i \vec\sigma_2\times\vec\sigma_3)\cdot\vec q
\,,$$ where the inverse squared pseudoscalar meson decay constant $f^{-2} 4.8\,$fm$^2$ determines the interaction strength. The index $i\in \{\pi^0,\pi^+,\pi^-,K^+,K^-,K^0,\bar K^0,\eta\} $ refers to the exchanged meson with mass $m_i$, carrying the momentum transfer $\vec q$. The two parameters $A$ and $B$ are combinations of low-energy constants.

![ Leading three-baryon interactions: contact term, one-meson exchange and two-meson exchange. \[fig:3BF\] ](FBBBcont "fig:")![ Leading three-baryon interactions: contact term, one-meson exchange and two-meson exchange. \[fig:3BF\] ](FBBB1ME "fig:")![ Leading three-baryon interactions: contact term, one-meson exchange and two-meson exchange. \[fig:3BF\] ](FBBB2ME2 "fig:")

On the other hand, the two-meson exchange potential (depicted in fig.\[fig:3BF\]) has following generic form: $$\begin{aligned}
V^{(2)}_{ij} ={} & -\frac{1}{4f^4} \frac{\vec\sigma_1\cdot\vec q\ ~~\vec\sigma_3\cdot\vec q'}{(\vec q^{\,2}+m_i^2)(\vec q'^{\,2}+m_j^2)} \\
&\qquad\times\Big(A' + B'\vec q\cdot\vec q' +D'\, \mathrm i\vec\sigma_2\cdot(\vec q\times\vec q')\Big) \,. {\addtocounter{equation}{1}\tag{\theequation}}\end{aligned}$$ The parameters $A',B'$ and $D'$ are combinations of low-energy constants determined in the meson-baryon subsector. The transferred 