The chiral Lagrangian with three flavors and large-Nc sum rules

TL;DR

This paper systematically analyzes the low-energy constants in the three-flavor baryon chiral Lagrangian, applying large-Nc sum rules to relate and constrain these constants at different chiral orders, with implications for baryon axial and decay properties.

Contribution

It provides a comprehensive large-Nc sum rule analysis for the baryon chiral Lagrangian at next-to-leading order, reducing the number of independent low-energy constants.

Findings

Identifies 4 LEC at leading order and 23 at subleading order.

Derives 3 and 18 sum rules at leading order for different LECs.

Reduces the number of sum rules to 2 and 8 at next-to-leading order.

Abstract

We reconsider the chiral Lagrangian with three-flavor baryon fields. A systematic analysis of all LEC that contribute to the axial-vector and pseudoscalar currents in the baryon octet and decuplet fields at next-to-leading order is performed. While there are 4 LEC relevant at leading order, the number of relevant LEC at subleading chiral order is 23. For those a leading order large-$N_c$ analysis predicts 3 and 18 sum rules respectively. At the next accuracy level the number of sum rules is reduced to 2 and 8. Our results are illustrated by a tree-level analysis of available axial-vector coupling constants and strong decay widths of the baryon decuplet states.