The propagation velocity of scintillation light in liquid argon $v_{g}$ at $lambda sim 128$~nm wavelength, has been measured for the first time in a dedicated experimental setup at CERN. The obtained result $frac{1}{v_{g}} = 7.46 pm 0.08$~ns/m , is then used to derive the value of the refractive index (n) and the Rayleigh scattering length ($mathcal{L}$) for liquid argon in the VUV region. For $lambda = 128$~nm we found $n= 1.358 pm 0.003$ and $mathcal{L}= 99.1 pm 2.3$~cm. The measured values are of interest for a variety of experiments searching for rare events like neutrino and dark matter interactions. The derived quantities also represent key information for theoretical models describing the propagation of scintillation light in liquid argon.
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