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We compile 23 Gamma-ray Bursts (GRBs) and 21 blazars with estimated Dopplerfactors, and the Doppler factors of GRBs are estimated from their Lorentzfactors by assuming their jet viewing angles \theta->0 degree. Using theconventional assumption that the prompt emission of GRBs is dominated by thesynchrotron radiation, we calculate the synchrotron luminosity of GRBs fromtheir total isotropic energy and burst duration. Intriguingly, we discover auniform correlation between the synchrotron luminosity and Doppler factor,L_syn \propto D^3.1, for GRBs and blazars, which suggests that they may sharesome similar jet physics. One possible reason is that GRBs and blazars have,more or less, similar intrinsic synchrotron luminosities and both of them arestrongly enhanced by the beaming effect. After Doppler and redshift-correction,we find that the intrinsic peak energy of the GRBs ranges from 0.1 to 3 keVwith a typical value of 1 keV. We further correct the beaming effect for theobserved luminosity of GRBs and find that there exists a positive correlationbetween the intrinsic synchrotron luminosity and peak energy for GRBs, which issimilar to that of blazars. Our results suggest that both the intrinsicpositive correlation and the beaming effect may be responsible for the observedtight correlation between the isotropic energy and the peak energy in GRBs (socalled "Amati" relation).

A Uniform Correlation between Synchrotron Luminosity and Doppler Factor in Gamma-ray Bursts and Blazars: hint of similar intrinsic luminosities?