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19 April 2024 |
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On the convergence of nuclear effective field theory with perturbative pions | | David B. Kaplan
; | | Date: |
17 May 2019 | | Abstract: | The classic paper by Fleming, Mehen and Stewart (FMS) found problems for the
convergence of spin-triplet nucleon-nucleon partial wave scattering amplitudes
when following the proposal of Kaplan, Savage and Wise to construct nuclear
effective field theory around the unitary fermion limit with perturbative pion
exchange. FMS identified the subclass of iterated one-pion exchange potential
graphs as the cause of this poor convergence, which they showed persisted in
the chiral limit. Here we develop theoretical tools to analytically compute
these Feynman graphs to high order in all angular momentum channels
simultaneously, examining the amplitudes computed to seven loops in the $L=J$
channels, and three loops in the coupled $L=Jpm1$ channels. We find that there
is nothing pathological about the perturbative expansion of a $1/r^3$ potential
in general, and that the expansion converges satisfactorily in all partial
waves except ${}^3P_0$ and the coupled ${}^3S_1-{}^3D_1$ channels; for those
partial waves we do see convergence issues, and suggest a possible way to
improve it. | | Source: | arXiv, 1905.7485 | | Services: | Forum | Review | PDF | Favorites | |
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