Chiral three-nucleon force at N4LO: Longest-range contributions

Abstract

We derive the sub-subleading two-pion exchange contributions to the three-nucleon force which appear at next-to-next-to-next-to-next-to-leading order in chiral effective field theory. In order to determine the low-energy constants, a complete analysis of pion-nucleon scattering at the subleading-loop order in the heavy-baryon expansion is carried out utilizing the power counting scheme employed in the derivation of the nuclear forces. We discuss the convergence of the chiral expansion for this particular three-nucleon force topology and give the values of the low-energy constants which provide the most realistic description of the three-nucleon force when the chiral expansion is truncated at next-to-next-to-leading order.

Chiral effective field theory for nuclear forces: Achievements and challenges

“…The loop contributions that occur at this order are obtained by replacing in the N 3 LO loops one vertex by a ∆ i = 1 vertex (with LEC c i ), which is why these loops may be more sizable than the N 3 LO loops. The 2PE topology turns out to be of modest size [56]; moreover, it can be handled in a practical way by summing it up together with the 2PE topologies at NNLO and N 3 LO [56]. The 2PE-1PE and ring topologies have also been evaluated [57].…”

Chiral dynamics of/with unstable particles

“…The πN scattering amplitude enters as a subprocess into the interactions between two and three nucleons at large distances. Thus, its detailed understanding is a necessary pre-requisite for deriving high-precision nuclear forces in chiral EFT [14,17,18].…”

“…Elastic pion-nucleon (πN) scattering certainly belongs to the the most extensively studied processes in ChPT [8][9][10][11][12][13][14][15][16]. The πN scattering amplitude enters as a subprocess into the interactions between two and three nucleons at large distances.…”

Three-nucleon reactions with chiral dynamics

“…It lowers the A y maximum and even increases the discrepancy to data. A resolution of the A y puzzle might be achieved either with the N 4 LO chiral 3NF [9] or/and using NN forces with corrected low-energy 3 P j phase-shifts.…”