Reconciling threshold and subthreshold expansions for pion–nucleon scattering. Siemens, D., Ruiz de Elvira, J., Epelbaum, E., Hoferichter, M., Krebs, H., Kubis, B., & Meißner, U. G. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics, 770:27–34, 2017.
doi  abstract   bibtex   
Heavy-baryon chiral perturbation theory (ChPT) at one loop fails in relating the pion–nucleon amplitude in the physical region and for subthreshold kinematics due to loop effects enhanced by large low-energy constants. Studying the chiral convergence of threshold and subthreshold parameters up to fourth order in the small-scale expansion, we address the question to what extent this tension can be mitigated by including the $\Delta$(1232) as an explicit degree of freedom and/or using a covariant formulation of baryon ChPT. We find that the inclusion of the $\Delta$ indeed reduces the low-energy constants to more natural values and thereby improves consistency between threshold and subthreshold kinematics. In addition, even in the $\Delta$-less theory the resummation of 1/mN corrections in the covariant scheme improves the results markedly over the heavy-baryon formulation, in line with previous observations in the single-baryon sector of ChPT that so far have evaded a profound theoretical explanation.
@article{Siemens2017,
abstract = {Heavy-baryon chiral perturbation theory (ChPT) at one loop fails in relating the pion–nucleon amplitude in the physical region and for subthreshold kinematics due to loop effects enhanced by large low-energy constants. Studying the chiral convergence of threshold and subthreshold parameters up to fourth order in the small-scale expansion, we address the question to what extent this tension can be mitigated by including the $\Delta$(1232) as an explicit degree of freedom and/or using a covariant formulation of baryon ChPT. We find that the inclusion of the $\Delta$ indeed reduces the low-energy constants to more natural values and thereby improves consistency between threshold and subthreshold kinematics. In addition, even in the $\Delta$-less theory the resummation of 1/mN corrections in the covariant scheme improves the results markedly over the heavy-baryon formulation, in line with previous observations in the single-baryon sector of ChPT that so far have evaded a profound theoretical explanation.},
archivePrefix = {arXiv},
arxivId = {1610.08978},
author = {Siemens, D. and {Ruiz de Elvira}, J. and Epelbaum, E. and Hoferichter, M. and Krebs, H. and Kubis, B. and Mei{\ss}ner, U. G.},
doi = {10.1016/j.physletb.2017.04.039},
eprint = {1610.08978},
issn = {03702693},
journal = {Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics},
keywords = {Chiral Lagrangians,Chiral symmetries,Dispersion relations,Pion–baryon interactions},
pages = {27--34},
title = {{Reconciling threshold and subthreshold expansions for pion–nucleon scattering}},
volume = {770},
year = {2017}
}

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