V. Baru, E. Epelbaum, C. Hanhart, M. Hoferichter, A. E. Kudryavtsev, D. R. Phillips
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 ($\chi$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 $\chi$PT expansion for that quantity. This
demonstrates unequivocally that $\chi$PT cannot be applied to compute $V(r)$
for distances smaller than $r \sim 1$ 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.
View original:
http://arxiv.org/abs/1202.0208
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