Chiral Lagrangians with decuplet baryons to one loop

TL;DR

This paper develops relativistic chiral Lagrangians involving decuplet baryons up to one loop order, providing a comprehensive set of terms for meson-baryon interactions and establishing relations between different formulations.

Contribution

It constructs detailed chiral Lagrangians with decuplet baryons up to order p^4, including extensive terms for various couplings, and clarifies the relation between different Lagrangian forms.

Findings

Constructed Lagrangians with 1 to 548 terms depending on order and coupling type.

Provided explicit forms for $ riangle$ and $ ext{N} riangle$ Lagrangians.

Established equivalence relations between different $ riangle$ Lagrangian formulations.

Abstract

We construct the relativistic chiral Lagrangians with decuplet baryons up to the order $\mathcal{O}(p^4)$ (one loop). For the meson-decuplet-decuplet couplings, there are 1, 13, 55, and 548 terms in the $\mathcal{O}(p^1)$-$\mathcal{O}(p^4)$ order Lagrangians, respectively. For the meson-octet-decuplet Lagrangians, the number of independent terms from $\mathcal{O}(p^1)$ to $\mathcal{O}(p^4)$ are 1, 5, 67, and 611, respectively. For convenience of applications, the $\pi\Delta\Delta$ and $\pi N\Delta$ chiral Lagrangians are picked out. This new form of $\Delta$ Lagrangians is equivalent to the original isovector-isospinor one and we establish relations between these two forms.