Pion-nucleon sigma term $\sigma_{\pi N}$ and deeply bound pionic atoms

We investigate the possibility to determine the value of the pion-nucleon sigma term $\sigma_{\pi N}$ precisely by the experimental observables of the deeply bound pionic atoms. We discuss the sensitivity of the observables to $\sigma_{\pi N}$ and take into account the typical errors of the up-to-date experiments of the deeply bound pionic atoms. We find that the gap of the binding energies and the width of the deeply bound pionic states are good observables for the $\sigma_{\pi N}$ value determination by the experimental data. We also discuss the expected difficulties for the accurate determination of the value of $\sigma_{\pi N}$ due to the correlation between the $\sigma$ term and the potential parameter in the pion-nucleus optical potential.