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We construct the relativistic chiral Lagrangians with decuplet baryons up to the order Ϭ(p4) (one loop). For the meson-decuplet-decuplet couplings, there are 1, 13, 55, and 548 terms in the Ϭ(p¹)-Ϭ(p4) order Lagrangians, respectively. For the meson-octet-decuplet Lagrangians, the number of independent terms from Ϭ(p¹) to Ϭ(p4) is 1, 5, 67, and 611, respectively. For convenience of application, the πΔΔ and πNΔ chiral Lagrangians are picked out. This new form of Δ Lagrangians is equivalent to the original isovector-isospinor one, and we establish relations between these two forms. [ABSTRACT FROM AUTHOR]

We construct the Lorentz-invariant chiral Lagrangians up to the order O(p4) by including Δ(1232) as an explicit degree of freedom. A full one-loop investigation on processes involving Δ(1232) can be performed with them. For the pΔΔ Lagrangian, one obtains 38 independent terms at the order O(p³) and 318 independent terms at the order O(p4). For the πNΔ Lagrangian, we get 33 independent terms at the order O(p³) and 218 independent terms at the order O(p4). The heavy baryon projection is also briefly discussed. [ABSTRACT FROM AUTHOR]