We analyse the properties of the CIV broad emission line in connection with the X-ray emission of 30 bright SDSS quasars at z~3.0-3.3 with pointed XMM-Newton observations, which were selected to test the suitability of AGN as cosmological tools. In our previous work, we found that a large fraction (~25%) of the quasars in this sample are X-ray underluminous by factors of >3-10. As absorbing columns of >10$^{23}$ cm$^{-2}$ can be safely ruled out, their weakness is most likely intrinsic. Here we explore possible correlations between the UV and X-ray features of these sources to investigate the origin of X-ray weakness. We fit their UV SDSS spectra and analyse their CIV properties (e.g., equivalent width, EW; line peak velocity, $upsilon_{rm peak}$) as a function of the X-ray photon index and 2-10 keV flux. We confirm the trends of CIV $upsilon_{rm peak}$ and EW with UV luminosity at 2500 angstrom for both X-ray weak and X-ray normal quasars, as well as the correlation between X-ray weakness and CIV EW. In contrast to some recent work, we do not observe any clear relation between the 2-10 keV luminosity and $upsilon_{rm peak}$. We find a correlation between the hard X-ray flux and the integrated CIV flux for X-ray normal quasars, whilst X-ray weak quasars deviate from the main trend by more than 0.5 dex. We argue that X-ray weakness might be interpreted in a starved X-ray corona picture associated with an ongoing disc-wind phase. If the wind is ejected in the vicinity of the black hole, the extreme-UV radiation that reaches the corona will be depleted, depriving the corona of seeds photons and generating an X-ray weak quasar. Yet, at the largest UV luminosities (>10$^{47}$ erg s$^{-1}$), there will still be an ample reservoir of ionising photons that can explain the excess CIV emission observed in the X-ray weak quasars with respect to normal sources of similar X-ray luminosities.
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