We test the gamma-ray burst correlation between temporal variability and peak luminosity of the $gamma$-ray profile on a homogeneous sample of 36 Swift/BAT GRBs with firm redshift determination. This is the first time that this correlation can be tested on a homogeneous data sample. The correlation is confirmed, as long as the 6 GRBs with low luminosity (<5x10^{50} erg s^{-1} in the rest-frame 100-1000 keV energy band) are ignored. We confirm that the considerable scatter of the correlation already known is not due to the combination of data from different instruments with different energy bands, but it is intrinsic to the correlation itself. Thanks to the unprecedented sensitivity of Swift/BAT, the variability/peak luminosity correlation is tested on low-luminosity GRBs. Our results show that these GRBs are definite outliers.
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