Three-nucleon forces from chiral effective field theory

We perform the first fully consistent analysis of $\mathrm{nd}$ scattering at next-to-next-to-leading order in chiral effective field theory including the corresponding three-nucleon force and extending our previous work, where only the two-nucleon interaction has been taken into account. The three-nucleon force appears first at this order in the chiral expansion and depends on two unknown parameters. These two parameters are determined from the triton binding energy and $\mathrm{nd}$ doublet scattering length. We find an improved description of various scattering observables in relation to the next-to-leading order results especially at moderate energies ${(E}_{\mathrm{lab}}=65\mathrm{}\mathrm{MeV}).\mathrm{}$ It is demonstrated that the long-standing $A_y$ problem in $\mathrm{nd}$ elastic scattering is still not solved by the leading 3NF, although some visible improvement is observed. We discuss possibilities of solving this puzzle. The predicted binding energy for the $\alpha$ particle agrees with the empirical value.

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