Self Energy Analysis of Photoemission spectral function from parent cuprates, Ca$_{2}$CuO$_{2}$Cl$_{2}$

Self energy $\Sigma $ (\textbf{k},$\omega )$ is the fundamental function that describes the effects of many-body interactions on an electron in a solid. But it is very difficult to extract the self energy from experimental data, especially for non-metallic materials. In this paper we developed a new and general method with which one can extract the self energy from angle-resolved photoemission spectroscopy (ARPES) data in the full \textbf{k}-$\omega $ space. We demonstrate the validity of this method by applying it to the ARPES data from Ca$_{2}$CuO$_{2}$Cl$_{2}$ (CCOC). We find the values for the imaginary part of the self energy is compatible with the value obtained by measuring the peak width.