Leading three-baryon forces from SU(3) chiral effective field theory

Leading three-baryon forces are derived within SU(3) chiral effective field theory. Three classes of irreducible diagrams contribute: three-baryon contact terms, one-meson exchange, and two-meson exchange diagrams. We provide the minimal nonrelativistic terms of the chiral Lagrangian that contribute to these diagrams. SU(3) relations are given for the strangeness $S=0$ and $-1$ sectors. In the strangeness-zero sector we recover the well-known three-nucleon forces from chiral effective field theory. Explicit expressions for the $\mathrm{\Lambda }NN$ chiral potential in isospin space are presented.

Figure 1

Leading three-baryon interactions: (from left to right) contact term, one-meson exchange, and two-meson exchange. Solid circles and solid dots denote vertices with ${\mathrm{\Delta }}_i=1$ and ${\mathrm{\Delta }}_i=0$, respectively.

Figure 2

Generic one-meson exchange diagram. The wiggly line symbolized the four-baryon contact vertex, to illustrate the baryon bilinears.

Figure 3

Feynman diagrams contributing to the one-meson exchange three-body potential for $B_1{B}_2{B}_3\to B_4{B}_5{B}_6$.

Figure 4

Generic two-meson exchange diagram.

Figure 5

Feynman diagrams contributing to the two-meson exchange three-body potential for $B_1{B}_2{B}_3\to B_4{B}_5{B}_6$.