The radio luminosity, black hole mass and Eddington ratio for quasars   from the Sloan Digital Sky Survey
  We investigate the $\mbh- \sigma_*$ relation for radio-loud quasars with redshift $z<0.83$ in Data Release 3 of the Sloan Digital Sky Survey (SDSS). The sample consists of 3772 quasars with better model of H$\beta$ and \oiii lines and available radio luminosity, including 306 radio-loud quasars, 3466 radio-quiet quasars with measured radio luminosity or upper-limit of radio luminosity (181 radio-quiet quasars with measured radio luminosity). The virial supermassive black hole mass (\mbh) is calculated from the broad \hb line, the host stellar velocity dispersion ($\sigma_*$) is traced by the core \oiii gaseous velocity dispersion, and the radio luminosity and the radio loudness are derived from the FIRST catalog. Our results are follows: (1) For radio-quiet quasars, we confirm that there is no obvious deviation from the $\mbh- \sigma_*$ relation defined in inactive galaxies when \mbh uncertainties and luminosity bias are concerned. (2) We find that radio-loud quasars deviate much from the $\mbh- \sigma_*$ relation respect to that for radio-quiet quasars. This deviation is only partly due to the possible cosmology evolution of the $\mbh- \sigma_*$ relation and the luminosity bias. (3) The radio luminosity is proportional to $\mbh^{1.28^{+0.23}_{-0.16}}(\lb/\ledd)^{1.29^{+0.31}_{-0.24}}$ for radio-quiet quasars and $\mbh^{3.10^{+0.60}_{-0.70}}(\lb/\ledd)^{4.18^{+1.40}_{-1.10}}$ for radio-loud quasars. The weaker correlation of the radio luminosity dependence upon the mass and the Eddington ratio for radio-loud quasars shows that other physical effects would account for their radio luminosities, such as the black hole spin. 
Wei-Hao. Bian (IHEP, NJNU), Yan-Mei. Chen (IHEP), Chen. Hu (IHEP),   Kai. Huang (NJNU), and Yan. Xu (NJNU)