Δ-excitations and the three-nucleon force

We study the three-nucleon force in chiral effective field theory with explicit Δ-resonance degrees of freedom. We show that up to next-to-next-to-leading order, the only contribution to the isospin symmetric three-nucleon force involving the spin-3/2 degrees of freedom is given by the two-pion-exchange diagram with an intermediate delta, frequently called the Fujita–Miyazawa force. We also analyze the leading isospin-breaking corrections due to the delta. For that, we give the first quantitative analysis of the delta quartet mass splittings in chiral effective field theory including the leading electromagnetic corrections. The charge-symmetry breaking three-nucleon force due to an intermediate delta excitation is small, of the order of a few keV.