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The Long and Short of Nuclear Effective Field Theory Expansions
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Nonperturbative effective field theory calculations for NN scattering seem to break down at rather low momenta. By examining several toy models, we clarify how effective field theory expansions can in general be used to properly separate long- and short-range effects. We find that one-pion exchange has a large effect on the scattering phase shift near poles in the amplitude, but otherwise can be treated perturbatively. Analysis of a toy model that reproduces 1S0 NN scattering data rather well suggests that failures of effective field theories for momenta above the pion mass can be due to short-range physics rather than the treatment of pion exchange. We discuss the implications this has for extending the applicability of effective field theories.
Forward citations
Cited by 2 Pith papers
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A short review on the compositeness of the $X(3872)$
Radiative decays and the LHCb line-shape data are incompatible with a purely molecular X(3872) and favor a compact or partially composite state, with a proposed molecular-amplitude fit for a decisive test.
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Isosinglet-isotriplet mixing and the $X(3872)$ lineshape
A phenomenological model mixing compact isosinglet and molecular isotriplet components for the X(3872) qualitatively reproduces interference-enhanced charged DD* decays and structures in J/psi pi pi lineshapes.
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