Reconciling threshold and subthreshold expansions for pion–nucleon scattering

Siemens, D.; Ruiz de Elvira Carrascal, Jacobo; Epelbaum, E.; Hoferichter, M.; Krebs, H.; Kubis, B.; Meißner, U.-G. (2017). Reconciling threshold and subthreshold expansions for pion–nucleon scattering. Physics letters. B, 770, pp. 27-34. Elsevier 10.1016/j.physletb.2017.04.039

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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 Δ (1232) as an explicit degree of freedom and/or using a covariant formulation of baryon ChPT. We find that the inclusion of the Δ indeed reduces the low-energy constants to more natural values and thereby improves consistency between threshold and subthreshold kinematics. In addition, even in the -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.

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