Peripheral NN-scattering: role of delta-excitation, correlated two-pion and vector meson exchange

Abstract

We evaluate, within one-loop chiral perturbation theory, the two-pion exchange diagrams with single and double delta-isobar excitation contributing to elastic NN-scattering. We find that virtual ∆-excitation processes (in the static limit) produce the correct amount of isoscalar central attraction as needed in the peripheral partial waves with L ≥ 3. Furthermore we compute the two-loop diagrams involving the ππ-interaction (so-called correlated 2π-exchange). Contrary to common believe these processes lead to negligibly small and repulsive corrections to the NN-potential. The exchange of vector mesons (ρ, ω) turns out to be important for the F-wave phase shifts above T lab = 150 MeV. Without adjustable parameters we are able to reproduce the empirical NN phase shifts up to 350 MeV for L ≥ 3 and up to about (50-80) MeV for the D-waves. This is therefore the characteristic window in which the NN-interaction is basically governed by chiral symmetry. Not surprisingly, the lower partial waves require non-perturbative methods and additional short-distance parametrizations of the NN-dynamics. * Work supported in part by BMBF.

Minimally nonlocal nucleon-nucleon potentials with chiral two-pion exchange includingΔresonances

“…The LO, NLO, and N2LO terms are well known, and explicit expressions for them can be found in Refs. [39,40,[42][43][44]. The LO and NLO terms depend on the the pion decay amplitude F π , and the nucleon and N -to-∆ axial coupling constants, respectively g A and h A = 3 g A / √ 2 (this value for h A is from the large N c expansion or strong-coupling model [45], and is in good agreement with the value inferred from the empirical ∆-width).…”

Renormalization versus strong form factors for one-boson-exchange potentials

“…To our knowledge, the expectations of Ref. [53] of a large N c consistent multimeson exchange picture have not been explicitly realized for the chiral potentials without [75] and with [76] ∆-isobar contributions as they do not scale properly with N c ; one has g A ∼ N c , f π ∼ √ N c and there are terms scaling as V ChPT 2π ∼ g 4 A /f 4 π ∼ N 2 c and not as ∼ N c as found in Refs. [49,52].…”

Possible interpretation of theZb(10610) andZb(10650) in a chiral quark model

“…The chiral partner, σ-meson, is also usually introduced, although its existence is still in controversy [21]. The Hamiltonian of the ChQM used here is given as follows,…”