Abstract
We present a simple and physically compelling boundary condition regularization scheme in the framework of effective field theory as applied to nucleon–nucleon interaction. It is free of off-shell ambiguities and ultraviolet divergences and provides finite results at any step of the calculation. Low-energy constants and their non-perturbative evolution can directly be obtained from experimental threshold parameters in a completely unique, one-valued and model independent way when the long range explicit pion effects are removed. This allows to compute scattering phase shifts which are, by construction consistent with effective range expansion to a given order in the CM momentum and are free from finite cut-off artifacts. We illustrate how the method works in the 1S0 channel for the one pion exchange potential.
Highlights
Effective field theories (EFT) are a powerful tool to deal with non-perturbative low energy physics
The first order differential equation satisfied by the boundary condition of the problem defined in the interval R < r < ∞ as a function of the boundary radius was very helpful, since the whole problem could be mapped into a variable phase equation [35] of a truncated potential in the region 0 < r ≤ R with a non-trivial initial condition at the origin, encoding the short distance physics
See, the effect of introducing pions always improves the results. This can be fully appreciated at NNLO, where effective range expansion (ERE) does a poor job above CM momenta ∼ 100MeV, but explicit One Pion Exchange (OPE) effects enlarge the energy range up to about ∼ 140MeV ∼ mπ. where we expect explicit two pion exchange contributions to start playing a role
Summary
Effective field theories (EFT) are a powerful tool to deal with non-perturbative low energy physics. The first order differential equation satisfied by the boundary condition of the problem defined in the interval R < r < ∞ as a function of the boundary radius was very helpful, since the whole problem could be mapped into a variable phase equation [35] of a truncated potential in the region 0 < r ≤ R with a non-trivial initial condition at the origin, encoding the short distance physics In this way, the long range pions could be eliminated and the evolution of the threshold parameters as a function of the boundary radius could be determined non-perturbatively. The boundary condition admits a simple physical interpretation: it can be mapped into a variable phase shift problem [35] with a truncated potential This interpretation directly provides the non-perturbative renormalization flow of low energy parameters and a quite transparent analysis of both infrared as well as ultraviolet fixed points and limit cycles [38]. VII we present some final remarks, conclusions and perspectives for future work
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