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A tight non-linear relation exists between the X-ray and UV emission inquasars (i.e. $L_{\rm X}\propto L_{\rm UV}^{\gamma}$), with a dispersion of$\sim$0.2~dex over $\sim$3~orders of magnitude in luminosity. Here we propose amodified version of this relation which involves the broad emission lines'full-width at half maximum, $L_{\rm X}\propto L_{\rmUV}^{\hat\gamma}\upsilon_{\rm fwhm}^{\hat\beta}$. We interpret this newrelation through a simple, {\it ad-hoc} model of accretion disc corona, derivedfrom previous works where it is assumed that reconnection and magnetic loopsabove the accretion disc can account for the production of the primary X-rayradiation. We find that the monochromatic optical-UV (2500 \AA) and X-ray (2keV) luminosities depend on the black hole mass and accretion rate as $L_{\rmUV}\propto M_{\rm BH}^{4/3} (\dot{M}/\dot{M}_{\rm Edd})^{2/3}$ and $L_{\rmX}\propto M_{\rm BH}^{19/21} (\dot{M}/\dot{M}_{\rm Edd})^{5/21}$, respectively.Assuming a broad line region size function of the disc luminosity $R_{\rmblr}\propto L_{\rm disc}^{0.5}$ we finally have that $L_{\rm X}\propto L_{\rmUV}^{4/7} \upsilon_{\rm fwhm}^{4/7}$. Such relation is remarkably consistentwith the slopes and the normalization obtained from a fit of a sample of 545optically selected quasars from SDSS DR7 cross matched with the latestXMM-Newton catalogue 3XMM-DR6. The homogeneous sample used here has adispersion of 0.21 dex, which is much lower than previous works in theliterature and suggests a tight physical relation between the accretion discand the X-ray emitting corona. The proposed new relation does not evolve withtime, and thus it can be employed as a cosmological indicator to robustlyestimate cosmological parameters.

Quasars as standard candles I: The physical relation between disc and coronal emission