Chiral Lagrangians with decuplet baryons to one loop

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 $\pi \mathrm{\Delta }\mathrm{\Delta }$ and $\pi N\mathrm{\Delta }$ chiral Lagrangians are picked out. This new form of $\mathrm{\Delta }$ Lagrangians is equivalent to the original isovector-isospinor one and we establish relations between these two forms.