  We present the measurements and modelling of the projected and redshift-space
clustering of CMASS galaxies in the Sloan Digital Sky Survey-III Baryon
Oscillation Spectroscopic Survey Data Release 11. For a volume-limited luminous
red galaxy sample in the redshift range of $0.48<z<0.55$, we perform halo
occupation distribution modelling of the small- and intermediate-scale
($0.1$--$60h^{-1}{\rm {Mpc}}$) projected and redshift-space two-point
correlation functions, with an accurate model built on high resolution $N$-body
simulations. To interpret the measured redshift-space distortions, the
distribution of galaxy velocities must differ from that of the dark matter
inside haloes of $\sim 10^{13}$--$10^{14}h^{-1}{\rm M_{\odot}}$, i.e. the data
require the existence of galaxy velocity bias. Most notably, central galaxies
on average are not at rest with respect to the core of their host haloes
(defined by the inner 25% of particles around the halo potential minimum), but
rather move around it with a 1D velocity dispersion of $0.22^{+0.03}_{-0.04}$
times that of the dark matter, implying a spatial offset from the centre at the
level of $\lesssim$1% of the halo virial radius. The luminous satellite
galaxies move more slowly than the dark matter, with velocities
$0.86^{+0.08}_{-0.03}$ times those of the dark matter, which suggests that the
velocity and spatial distributions of these satellites cannot both be unbiased.
The constraints mainly arise from the Fingers-of-God effect at nonlinear scales
and the smoothing to the Kaiser effect in the translinear regime; the
robustness of the results is demonstrated by a variety of tests. In addition,
no clear evidence is found for a strong luminosity dependence of the velocity
bias. We discuss the implications of the existence of galaxy velocity bias for
investigations of galaxy formation and cosmology.
