We measure and analyse the clustering of the Baryon Oscillation Spectroscopic Survey (BOSS) relative to the line-of-sight (LOS), for LOWZ and CMASS galaxy samples drawn from the final Data Release 12 (DR12). The LOWZ sample contains 361,762 galaxies with an effective redshift of $z_{rm lowz}=0.32$, and the CMASS sample 777,202 galaxies with an effective redshift of $z_{rm cmass}=0.57$. From the power spectrum monopole and quadrupole moments around the LOS, we measure the growth of structure parameter $f$ times the amplitude of dark matter density fluctuations $sigma_8$ by modeling the Redshift-Space Distortion signal. When the geometrical Alcock-Paczynski effect is also constrained from the same data, we find joint constraints on $fsigma_8$, the product of the Hubble constant and the comoving sound horizon at the baryon drag epoch $H(z)r_s(z_d)$, and the angular distance parameter divided by the sound horizon $D_A(z)/r_s(z_d)$. We find $f(z_{rm lowz})sigma_8(z_{rm lowz})=0.394pm0.062$, $D_A(z_{rm lowz})/r_s(z_d)=6.35pm0.19$, $H(z_{rm lowz})r_s(z_d)=(11.41pm 0.56),{10^3rm km}s^{-1}$ for the LOWZ sample, and $f(z_{rm cmass})sigma_8(z_{rm cmass})=0.444pm0.038$, $D_A(z_{rm cmass})/r_s(z_d)=9.42pm0.15$, $H(z_{rm cmass})r_s(z_d)=(13.92 pm 0.44), {10^3rm km}s^{-1}$ for the CMASS sample. We find general agreement with previous BOSS DR11 measurements. Assuming the Hubble parameter and angular distance parameter are fixed at fiducial $Lambda$CDM values, we find $f(z_{rm lowz})sigma_8(z_{rm lowz})=0.485pm0.044$ and $f(z_{rm cmass})sigma_8(z_{rm cmass})=0.436pm0.022$ for the LOWZ and CMASS samples, respectively.
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