Pion-mass dependence of three-nucleon observables

Abstract

We use an effective field theory (EFT) which contains only short-range interactions to study the dependence of a variety of three-nucleon observables on the pion mass. The pion-mass dependence of input quantities in our “pionless” EFT is obtained from a recent chiral EFT calculation. To the order we work at, these quantities are the 1 S 0 scattering length and effective range, the deuteron binding energy, the 3 S 1 effective range, and the binding energy of one three-nucleon bound state. The chiral EFT input we use has the inverse 3 S 1 and 1 S 0 scattering lengths vanishing at m π crit = 197.8577 MeV. At this “critical” pion mass, the triton has infinitely many excited states with an accumulation point at the three-nucleon threshold. We compute the binding energies of these states up to next-to-next-to-leading order in the pionless EFT and study the convergence pattern of the EFT in the vicinity of the critical pion mass. Furthermore, we use the pionless EFT to predict how doublet and quartet nd scattering lengths depend on m π in the region between the physical pion mass and m π = m π crit .