https://doi.org/10.1140/epja/i2012-12069-6
Regular Article - Theoretical Physics
The multiple-scattering series in pion-deuteron scattering and the nucleon-nucleon potential: perspectives from effective field theory
1
Institut für Theoretische Physik II, Ruhr-Universität Bochum, D-44780, Bochum, Germany
2
Institute for Theoretical and Experimental Physics, B. Cheremushinskaya 25, 117218, Moscow, Russia
3
Institut für Kernphysik and Jülich Center for Hadron Physics, Forschungszentrum Jülich, D-52425, Jülich, Germany
4
Institute for Advanced Simulation, Forschungszentrum Jülich, D-52425, Jülich, Germany
5
Helmholtz-Institut für Strahlen- und Kernphysik and Bethe Center for Theoretical Physics, Universität Bonn, D-53115, Bonn, Germany
6
Institute of Nuclear and Particle Physics and Department of Physics and Astronomy, Ohio University, 45701, Athens, OH, USA
* e-mail: v.baru@fz-juelich.de
Received:
6
February
2012
Accepted:
28
March
2012
Published online:
18
May
2012
Important contributions to meson-nucleus scattering are produced by terms in the multiple-scattering series, which is defined as the sum of all diagrams where the meson scatters back and forth between a pair of static nucleons before leaving the nucleus. In particular, the sum of this series is needed for an accurate description of kaon-deuteron scattering, and appears as part of the nucleon-nucleon potential. In this article we present some effective-field-theory (EFT)-based insights into this series in the case of two-nucleon systems. In particular, we discuss the fact that, if meson-nucleon scattering is approximated by the scattering-length term, individual terms of the series are divergent, and enhanced with respect to the straightforward expectation from chiral perturbation theory (
PT). This apparently indicates the presence of similarly enhanced counterterms. However, we show that when the series is resummed the divergences cancel, such that no additional information on short-range interactions is needed to obtain predictions for observables after resummation. We discuss the conditions under which this resummation is justified. We show that the same issues arise in the NN potential, where the resummed series produces poles whose appearance indicates the breakdown scale of the PT expansion for that quantity. This demonstrates unequivocally that PT cannot be applied to compute V(r) for distances smaller than 
fm --at least in the theory without explicit Delta(1232) degrees of freedom. We briefly discuss whether this bound can be lowered if the Delta resonance is included in the EFT as an explicit degree of freedom.
© SIF, Springer-Verlag Berlin Heidelberg, 2012
