DOI: 10.1140/epja/i2002-10138-1
Renormalizing the Lippmann-Schwinger equation for the one-pion exchange potential
D. Eiras and J. SotoDepartament d'Estructura i Constituents de la Matèria and IFAE, Universitat de Barcelona, Diagonal, 647, E-08028 Barcelona, Catalonia, Spain dolors@ecm.ub.es
soto@ecm.ub.es
(Received: 7 October 2002 / Revised version: 7 January 2003 / Published online: 5 May 2003)
Abstract
We address the question whether the cut-off dependence, which has to be introduced in order to properly define the Lippmann-Schwinger
equation for the one-pion exchange potential plus local (
-function) potentials, can be removed (up to inverse powers of it)
by a suitable tuning of the various (bare) coupling constants. We prove that this is indeed so both for the spin singlet and
for the spin triplet channels.
However, the latter requires, in the limit when the cut-off is taken to infinity, such a strong cut-off dependence of the
coupling constant associated to the non-local term which breaks orbital angular momentum conservation, that the renormalized
amplitude lacks from partial-wave mixing. We argue that this
is an indication that this term must be treated perturbatively.
03.65.Nk - Scattering theory.
11.10.Gh - Renormalization.
13.75.Cs - Nucleon-nucleon interactions (including antinucleons, deuterons, etc.).
21.30.Fe - Forces in hadronic systems and effective interactions.
© Società Italiana di Fisica, Springer-Verlag 2003
