  We propose a modified version of the observed non-linear relation between the
X-ray (2 keV) and the ultraviolet (2500 \AA) emission in quasars (i.e. $L_{\rm
X}\propto L_{\rm UV}^{\gamma}$) which involves the full width at half-maximum,
FWHM, of the broad emission line, i.e. $L_{\rm X}\propto L_{\rm
UV}^{\hat\gamma}~FWHM^{\hat\beta}$. By analysing a sample of 550 optically
selected non-jetted quasars in the redshift range of 0.36-2.23 from the Sloan
Digital Sky Survey cross matched with the XMM-Newton catalogue 3XMM-DR6, we
found that the additional dependence of the observed $L_{\rm X}-L_{\rm UV}$
correlation on the FWHM of the MgII broad emission line is statistically
significant. Our statistical analysis leads to a much tighter relation with
respect to the one neglecting FWHM, and it does not evolve with redshift. We
interpret this new relation within an accretion disc corona scenario where
reconnection and magnetic loops above the accretion disc can account for the
production of the primary X-ray radiation. For a broad line region size
depending on the disc luminosity as $R_{\rm blr}\propto L_{\rm disc}^{0.5}$, we
find that $L_{\rm X}\propto L_{\rm UV}^{4/7} ~FWHM^{4/7}$, which is in very
good agreement with the observed correlation.
