Chiral Lagrangians for spin-$\frac{1}{2}$ and spin-$\frac{3}{2}$ doubly charmed baryons

The relativistic chiral Lagrangians for both spin-$\frac{1}{2}$ and spin-$\frac{3}{2}$ doubly charmed baryons are constructed up to the order $\mathcal{O}(p^4)$. From $\mathcal{O}(p^2)$ to $\mathcal{O}(p^4)$, there are 19, 74, and 452 independent terms in the two-flavor case and 25, 112, and 864 independent terms in the three-flavor case. The chiral Lagrangians in the heavy diquark limit are also obtained. From $\mathcal{O}(p^2)$ to $\mathcal{O}(p^4)$, there are 7, 23, and 118 independent terms in the two-flavor case and 8, 31, and 189 independent terms in the three-flavor case. We present the low-energy constant relations between the relativistic case and the case in the heavy diquark limit up to the order $\mathcal{O}(p^3)$. With the heavy diquark-antiquark symmetry, the low-energy constant relations between the doubly charmed baryon case and the heavy-light meson case are also obtained up to the order $\mathcal{O}(p^3)$.