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

Abstract

We analyze the One Boson Exchange Potential from the point of view of Renormalization theory. We show that the nucleon-meson Lagrangean while predicting the NN force does not predict the NN scattering matrix nor the deuteron properties unambiguously due to the appearance of short distance singularities. While the problem has traditionally been circumvented by introducing vertex functions via phenomenological strong form factors, we propose to impose physical renormalization conditions on the scattering amplitude at low energies. Working in the large Nc approximation with π,σ,ρ and ω mesons we show that, once these conditions are applied, results for low energy phases of proton-neutron scattering as well as deuteron properties become largely insensitive to the form factors and to the vector mesons yielding reasonable agreement with the data and for realistic values of the coupling constants.

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

“…For a free spherical P-wave u3 P (r) = pr j 1 (pr), the agreement is good using u d (r) from effective range (ER) theory [6] or from a potential [3] (POT), see Fig. 2 …”

“…Based on the LDS idea we have recently derived the sum rules for phase shifts [3,4] δ3 The previous sum rules have a parallel long distance potential analog , and are also well verified for r > 1.5fm [4]. This suggests that a coarse graining of the interaction using e.g.…”

“…The tensor force W T is singular at short distances ∼ 1/r 3 and requires renormalization (see [17] for the π case). 3 The LDS character implies relaxing the contact interaction piece not to be of the same form as the long distance…”

“…In Nuclear Physics the situation may be exactly the opposite; some symmetries such as those introduced by Wigner [1] and Serber 1 are unveiled at low energies where the wavelength becomes larger than a certain scale. For obvious reasons we call them Long Distance Symmetries (LDS) [3,4]. In the meson exchange picture this implies the presence of arbitrarily large symmetry breaking counterterms.…”

Two-photon-exchange effects in the unpolarized μp scattering within a hadronic model

“…For g σN N and m σ , their values can be found in many literatures on the nucleon-nucleon potential, and we list some of these [39][40][41][42] in the Tab. I, where we see there is about 20% difference between the values for g σN N and m σ .…”