Eur. Phys. J. C (2006) 48: 169-178
https://doi.org/10.1140/epjc/s10052-006-0004-x

Theoretical Physics

More on the infrared renormalization group limit cycle in QCD

¹ Theory Division, Jefferson Laboratory, Newport News, VA, 23606, USA
² Helmholtz-Institut für Strahlen- und Kernphysik (Theorie), Universität Bonn, Nußallee 14–16, 53115, Bonn, Germany
³ Institut für Kernphysik (Theorie), Forschungszentrum Jülich, 52425, Jülich, Germany

^* e-mail: hammer@itkp.uni-bonn.de

Received: 1 March 2006
Revised: 9 May 2006
Published online: 29 September 2006

Abstract

We present a detailed study of the recently conjectured infrared renormalization group limit cycle in QCD using chiral effective field theory. It was conjectured that small increases in the up and down quark masses can move QCD to the critical trajectory for an infrared limit cycle in the three-nucleon system. At the critical quark masses, the binding energies of the deuteron and its spin-singlet partner are tuned to zero and the triton has infinitely many excited states with an accumulation point at the three-nucleon threshold. We exemplify three parameter sets where this effect occurs at next-to-leading order in the chiral counting. For one of them, we study the structure of the three-nucleon system in detail using both chiral and contact effective field theories. Furthermore, we investigate the matching of the chiral and contact theories in the critical region and calculate the influence of the limit cycle on three-nucleon scattering observables.