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Chiral effective Lagrangian for doubly charmed baryons up to $\mathcal{O}(q^4)$

The chiral effective meson-baryon Lagrangian for the description of interactions between the doubly charmed baryons and Goldstone bosons is constructed up to the order of $q^{4}$. The numbers of linearly independent invariant monomials of $\mathcal{O}(q^2)$, $\mathcal{O}(q^3)$ and $\mathcal{O}(q^4)$ are 8, 32 and 218, in order. The obtained Lagrangian can be used to study the chiral dynamics and relevant phenomenology of the doubly charmed baryons at complete one-loop level in future. For completeness, the non-relativistic reduction of the Lagrangian is also discussed.