We present new XMM-Newton observations of two luminous and high accretion-rate radio-quiet active galactic nuclei (AGNs) at z~2. Together with archival X-ray and rest-frame optical spectra of three sources with similar properties as well as 25 moderate-luminosity radio-quiet AGNs at z<0.5, we investigate, for the first time, the dependence of the hard (>~2 keV) X-ray power-law photon index on the broad H_beta emission-line width and on the accretion rate across ~3 orders of magnitude in AGN luminosity. Provided the accretion rates of the five luminous sources can be estimated by extrapolating the well-known broad-line region size-luminosity relation to high luminosities, we find that the photon indices of these sources, while consistent with those expected from their accretion rates, are significantly higher than expected from the widths of their H_beta lines. We argue that, within the limits of our sample, the hard-X-ray photon index depends primarily on the accretion rate.
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