Sigma terms are the quark mass contributions to the mass of a given baryon. We study the sigma terms of the full baryon octet (nucleon, lambda, sigma, xi) which has by far not been studied as much as the nucleon sigma term separately. This allows us to investigate flavour symmetry breaking in the octet. Using similar methods as for the nucleon the sigma terms are determined on CLS gauge field ensembles employing the Lüscher-Weisz gluon action and the Sheikholeslami-Wohlert fermion action with $N_\mathrm{f} = 2 + 1$. The ensembles analysed here have pion masses ranging from ${410}\,\mathrm{MeV}$ down to ${216}\,\mathrm{MeV}$ and lattice spacings covering a range between
${0.039}\,\mathrm{fm}$ and ${0.098}\,\mathrm{fm}$.
To tackle the well-known problem of excited state contamination we have studied the effect of different multi-state fits on the sigma terms.
In order to investigate the systematic error arising from the varied treatment of the excited states we carry out the full analysis for different choices of multi-state fits. In the end, the sigma terms of the baryon octet are simultaneously extrapolated to the physical point taking the quark mass dependence, lattice spacing and finite volume effects into account.
Notably SU(3) low energy constants (LECs) from Baryon Chiral Perturbation Theory are also fitted that quantify flavour-symmetry breaking effects.