Recursive renormalization of the singlet one-pion-exchange plus point-like interactions

Abstract

The subtracted kernel approach is shown to be a powerful method to be implemented recursively in scattering equations with regular plus point-like interactions. The advantages of the method allows one to recursively renormalize the potentials, with higher derivatives of the Dirac-delta, improving previous results. The applicability of the method is verified in the calculation of the 1 S 0 nucleon-nucleon phase-shifts, when considering a potential with one-pion-exchange plus a contact interaction and its derivatives. The 1 S 0 renormalization parameters are fitted to the data. The method can in principle be extended to any derivative order of the contact interaction, to higher partial waves and to coupled channels.

Nucleon-nucleon scattering within a multiple subtractive renormalization approach

“…Instead, a subtraction point is introduced in the kernel of the LS equation [8] to reach a finite T matrix. Our research group has considered singular contact interactions in the context of nuclear [5,6,9,10], atomic, and general physics [11,12]. In such works, within specific renormalization procedures applied to few-body systems, scaling limits and correlations between low-energy observables emerge as a consequence of using singular contact (zero-range) interactions.…”

“…Indeed, the renormalization results for the observables should be independent of the specific scheme used. Our method was applied to the NN interaction with OPEP supplemented by contact interactions [5,6,10].…”

“…Renormalization of the NN interaction in chiral effective theory in LO, up to next-to-leading order (NLO), and to next-to-next-to-leading order (NNLO), in S, P , and D waves, has been done with success in coupled and uncoupled waves [5,6,10,[30][31][32][33][34]. References [30,31] apply the renormalization approach in coordinate space, while the works [5,6,10,33,34] use subtracted-resolvent two-body techniques in momentum space.…”

“…References [30,31] apply the renormalization approach in coordinate space, while the works [5,6,10,33,34] use subtracted-resolvent two-body techniques in momentum space. The subtracted renormalization procedure considered in Refs.…”

“…[33,34] is essentially different from the one applied in Refs. [5,6,10] in the way to deal with the physical inputs introduced to heal the ultraviolet divergences. In short, in the renormalization strategy of [33], one-folded subtracted equation and also a cutoff are used, implying in a window where the observables are quite independent on the cutoff.…”