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Baryon chiral perturbation theory with Wilson fermions up to $\mathcal{O}(a^2)$ and discretization effects of latest $n_f=2+1$ LQCD octet baryon masses

We construct the chiral Lagrangians relevant in studies of the ground-state octet baryon masses up to $\mathcal{O}(a^2)$ by taking into account discretization effects and calculate the masses up to $\mathcal{O}(p^4)$ in the extended-on-mass-shell scheme. As an application, we study the latest $n_f=2+1$ LQCD data on the ground-state octet baryon masses from the PACS-CS, QCDSF-UKQCD, HSC, and NPLQCD Collaborations. It is shown that the discretization effects for the studied LQCD simulations are at the order of one to two percent for lattice spacings up to $0.15$ fm and the pion mass up to 500 MeV.