Old nuclear symmetries and large N as long distance symmetries in the two nucleon system

Abstract

Wigner and Serber symmetries for the two-nucleon system provide unique examples of long distance symmetries in Nuclear Physics, i.e. symmetries of the meson exchange forces broken only at arbitrarily small distances. We analyze the large N c picture as a key ingredient to understand these, so far accidental, symmetries from a more fundamental viewpoint. A set of sum rules for NN phase-shifts, NN potentials and coarse grained V lowk NN potentials can be derived showing Wigner SU(4) and Serber symmetries not to be fully compatible everywhere. The symmetry breaking pattern found from the partial wave analysis data, high quality potentials in coordinate space at long distances and their V lowk relatives is analyzed on the light of large N c contracted SU(4) C symmetry. Our results suggest using large N c potentials as long distance ones for the two-nucleon system where the meson exchange potential picture is justified and known to be consistent with large N c counting rules. We also show that potentials based on chiral expansions do not embody the Wigner and Serber symmetries nor do they scale properly with N c . We implement the One Boson Exchange potential realization saturated with their leading N c contributions due to π, σ , ρ and ω mesons. The short distance 1/r 3 singularities stemming from the tensor force can be handled by renormalization of the Schrödinger equation. A good description of deuteron properties and deuteron electromagnetic form factors in the impulse approximation for realistic values of the meson-nucleon couplings is achieved. International Workshop on Effective Field Theories: from the pion to the upsilon

Low Scale Saturation of Effective NN Interactions and Their Symmetries

“…[41]. The strong dependence observed at larger Λ values just reflects the inadequacy of the second order truncation in Equation (27). This also reflects in the 25%-50% inaccuracy off the exact V lowk of the Ds themselves despite showing plateaus, and thus will not be discussed any further.…”

“…lower panel) as a function of the momentum scale Λ (in fm −1 ). Cs from Equation (27) solving Equation (8) including the Ds using just the low energy threshold parameters from Ref. [41] (thick solid).…”

“…A further objection to attempt the separation explicitly concerns the long distance pionic physics (see also [25][26][27][28]). Actually, we may separate the pionic contributions as follows:…”

“…If this d exists, one can replace the zero energy scattering problem by the truncated original potential, which, following [25][26][27], we denote as the V highr potential. The corresponding reduced potential, U highr (r) = MV highr (r), reads…”

“…Once we have the V highr interaction, we can compute the integrals and compare Equation (3) with the low momentum expansion, Equation (27) for p = p,…”