Pion-nucleon scattering around the delta resonance

We develop a generalized version of heavy-baryon chiral perturbation theory to describe pion-nucleon scattering in a kinematic domain that extends continuously from threshold to the delta-isobar peak. The $P$-wave phase shifts are used to illustrate this framework.Comment: Talk given at Chiral Dynamics 2009, 8 pages and 4 figure

Heavy-particle formalism with Foldy-Wouthuysen representation

Utilizing the Foldy-Wouthuysen representation, we use a bottom-up approach to construct heavy-baryon Lagrangian terms, without employing a relativistic Lagrangian as the starting point. The couplings obtained this way feature a straightforward $1/m$ expansion, which ensures Lorentz invariance order by order in effective field theories. We illustrate possible applications with two examples in the context of chiral effective field theory: the pion-nucleon coupling, which reproduces the results in the literature, and the pion-nucleon-delta coupling, which does not employ the Rarita-Schwinger field for describing the delta isobar, and hence does not invoke any spurious degrees of freedom. In particular, we point out that one of the subleading $\pi N \Delta$ couplings used in the literature is, in fact, redundant, and discuss the implications of this. We also show that this redundant term should be dropped if one wants to use low-energy constants fitted from $\pi N$ scattering in calculations of $NN\to NN\pi$ reactions.Comment: 28 pages, 2 figures, RevTeX4, appendix added, version published in Phys. Rev.

Recent progress towards a chiral effective field theory for the NN system

Since Weinberg's proposal two decades ago, chiral effective field theory in the NN sector has been developed and applied up to order $O((Q/M_{hi})^4)$. In principle it could provide a model-independent description of nuclear force from QCD. However, in spite of its huge success, some open issues such as the renormalization group invariance and power counting, still remain to be solved. In this talk we refine the chiral effective field theory approach to the NN system based on a renormalization group analysis. Our results show that a truly model-independent description of NN system can be obtained by a new power counting which treats the subleading order corrections perturbatively.Comment: Contribution to the proceedings of the Seventh International Symposium on Chiral Symmetry in Hadrons and Nuclei, Beijing, October 2013. 4 pages, 1 figur

πN\pi N Scattering in the Δ(1232)\Delta(1232) Region in an Effective Field Theory

We develop a generalized version of heavy-baryon chiral perturbation theory to describe pion-nucleon scattering in a kinematic domain that extends continuously from threshold to the delta-isobar peak. The $P$-wave phase shifts are used to illustrate this framework. We also compare our approach with those in the literature that concern the delta resonance.Comment: 46 pages, 17 figures, version to appear in Nucl. Phys.

European Centre for Theoretical Studies in Nuclear Physics and Related Areas (ECT*)

We develop a generalized version of heavy-baryon chiral perturbation theory to describe pionnucleon scattering in a kinematic domain that extends continuously from threshold to the deltaisobar peak. The P-wave phase shifts are used to illustrate this framework. PoS(CD09)015 6th International Workshop on Chiral Dynamic