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.
Highlights
Chiral perturbation theory (ChPT) is a useful tool to describe low-energy strong interactions of mesons [1,2,3] and baryons [4]
The interaction terms and various physical quantities in this theory are organized perturbatively by chiral dimension, the order of p=Λχ where p represents the typical scale of momentum and Λχ is the scale of chiral symmetry breaking
II, we review the building blocks for the construction of the chiral Lagrangians with the mesons, the external sources, and a part of the building blocks with baryon fields
Summary
Chiral perturbation theory (ChPT) is a useful tool to describe low-energy strong interactions of mesons [1,2,3] and baryons [4] This effective theory is based on the chiral symmetry of QCD and its spontaneous breaking. A lot of low-energy QCD problems are related to the chiral Lagrangians with decuplet states which are degenerate with the octet baryons in the large Nc limit. The lowest-order chiral Lagrangian with decuplet states is obtained [39], but we find only fragmentary results for high-order terms in the literature (see the references mentioned above) Such Lagrangians are constructed in order to focus on special problems.
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