Estimating Consequences of 3-Body Forces

Classifying the strengthes of three-body forces 3BFs with the condition that observables must be cut-off independent, i.e. renormalised at each order, leads to surprising results with relevance for example for thermal neutron capture on the deuteron. Details and a better bibliography in Ref. [1]. Adding 3-Body Forces (3BFs) a posteriori when theory and data disagree is untenable when predictions are required. Effective Field Theories (EFTs), see e.g. [2] for reviews, provide a model-independent way to estimate their typical strength. For systems of three identical particles in which short-range forces produce shallow two-particle bound states, and in particular for the “pion-less” EFT of Nuclear Physics EFT(π/), consistency arguments from renormalisation lead to a power-counting, namely a recipe to systematically estimate the typical size of 3BFs in all partial waves and orders, including external currents. Figure 1. Left: integral equation of nucleon-deuteron scattering. Right: generic loop correction (rectangle) at NLO. Thick line (D): NN propagator; thin line (Kl): propagator of the exchanged nucleon; ellipse: LO half off-shell amplitude. We start from the Faddeev equation, Fig. 1, in the lth partial wave of the spin doublet (λ = 1) and quartet (λ = −12) channels of nucleon-deuteron scattering at leading order LO. The NN amplitude is given by the leading term of the Effective-Range Expansion. The 3-nucleon amplitude converges for large half off-shell momenta p as p−s0−1, with s0 the solution to the algebraic equation 1 = (−1) 21−lλ √ 3π Γ [ l+s+1 2 ]