  We present an analysis of the lowest-lying decuplet baryon masses in the
covariant baryon chiral perturbation theory with the extended-on-mass-shell
scheme up to next-to-next-to-next-to-leading order. In order to determine the
$14$ low-energy constants, we perform a simultaneous fit of the $n_f=2+1$
lattice QCD data from the PACS-CS, QCDSF-UKQCD, and HSC Collaborations, taking
finite-volume corrections into account self-consistently. We show that up to
next-to-next-to-next-to-leading order one can achieve a good description of the
lattice QCD and experimental data. Surprisingly, we note that the current
lattice decuplet baryon masses can be fitted rather well by the next-to-leading
order baryon chiral perturbation theory, which, however, misses the
experimental data a little bit. Furthermore, we predict the pion- and
strangeness-sigma terms of the decuplet baryons by use of the Feynman-Hellmann
theorem.
