Abstract 

   We study the relationship between X-ray luminosity and the star formation rate (SFR) for a sample of dusty active galactic nuclei (AGNs) at 0.04 < z < 3.3. Our sample consists of dusty AGNs detected in both X-ray and far-Infrared by XMM and Herschel in the XMM-LSS field. All of the selected targets have spectroscopic redshifts and broad band photometry that allows black hole mass and spectral energy distribution (SED) analysis. We compare their X-ray and AGN-removed infrared luminosities, and study the dependence of the observed relation on luminosity, obscuration, supermassive black hole mass, Eddington ratio, and the fraction of AGN contribution to infrared luminosity. We find a positive correlation between L_X and SFR up to z=3. This is consistent with the secular evolution scenario, in which the nucleus and galaxy are fueled by the same gas supply at a relatively constant ratio. We also investigate the effect of binning choices on the observed trend. Comparing our results to those in the literature, we propose a unified physical scenario that explains the observed L_X-SFR connection once sample selection bias is accounted for.