Naive Dimensional Analysis for Three-Body Forces Without Pions

Abstract

For systems of three identical particles in which short-range forces produce shallow two-particle bound states, and in particular for the ``pion-less'' Effective Field Theory of Nuclear Physics, I extend and systematise the power-counting of three-body forces to all partial-waves and orders, including external currents. With low-energy observables independent of the details of short-distance dynamics, the typical strength of a three-body force is determined from the superficial degree of divergence of the three-body diagrams which contain only two-body forces. This naïve dimensional analysis must be amended as the asymptotic solution to the leading-order Faddeev equation depends for large off-shell momenta crucially on the partial wave and spin-combination of the system. It is shown by analytic construction to be weaker in most channels with angular momentum smaller than 3 than expected. This demotes many three-nucleon forces to high orders. Observables like the quartet-S-scattering length are less sensitive to three-nucleon forces than guessed. I also comment on the Efimov effect and limit-cycle for non-zero angular momentum.

31 pages LaTeX2e, including 8 figures in 13 .eps files, embedded with includegraphicx; linguistic corrections only, version to appear in Nucl Phys A

References in corpus (5)

• Improved Convergence in the Three-Nucleon System at Very Low Energies
• Cutoff schemes in chiral perturbation theory and the quark mass expansion of the nucleon mass
• $Nd\to {}^{3}H\gamma$ with Effective Field Theory
• The three-body problem with short-range forces: renormalized equations and regulator-independent results
• Effective theories of scattering with an attractive inverse-square potential and the three-body problem

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