Eur. Phys. J. A (2015) 51: 26
https://doi.org/10.1140/epja/i2015-15026-y

Regular Article - Theoretical Physics

Three-nucleon force at large distances: Insights from chiral effective field theory and the large-N_c expansion

¹ Institut für Theoretische Physik II, Ruhr-Universität Bochum, D-44780, Bochum, Germany
² SSC RF ITEP, Bolshaya Cheremushkinskaya 25, 117218, Moscow, Russia
³ Departamento de Física, FCEyN, Universidad de Buenos Aires and IFIBA, CONICET, Ciudad Universitaria, Pab. 1, 1428, Buenos Aires, Argentina

^* e-mail: hermann.krebs@rub.de

Received: 22 December 2014
Accepted: 3 February 2015
Published online: 3 March 2015

Abstract

We confirm the claim of Phillips and Schat (Phys. Rev. C 88, 034002 (2013)) that 20 operators are sufficient to represent the most general local isospin-invariant three-nucleon force and derive explicit relations between the two sets of operators suggested in the above-mentioned work and that by Krebs et al. (Phys. Rev. C 87, 054007 (2013)). We use the set of 20 operators to discuss the chiral expansion of the long- and intermediate-range parts of the three-nucleon force up to next-to-next-to-next-to-next-to-leading order in the standard formulation without explicit Δ(1232) degrees of freedom. We also address implications of the large-N _c expansion in QCD for the size of the various three-nucleon force contributions.