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Position-dependent correlation function from the SDSS-III Baryon Oscillation Spectroscopic Survey Data Release 10 CMASS Sample

We report on the first measurement of the three-point function with the position-dependent correlation function from the SDSS-III Baryon Oscillation Spectroscopic Survey (BOSS) Data Release 10 CMASS sample. This new observable measures the correlation between two-point functions of galaxy pairs within different subvolumes, $\hatξ({\rm r},{\rm r}_L)$, where ${\rm r}_L$ is the location of a subvolume, and the corresponding mean overdensities, $\barδ({\rm r}_L)$. This correlation, which we call the "integrated three-point function", $iζ(r)=\langle\hatξ({\rm r},{\rm r}_L)\barδ({\rm r}_L)\rangle$, measures a three-point function of two short- and one long-wavelength modes, and is generated by nonlinear gravitational evolution and possibly also by the physics of inflation. The $iζ(r)$ measured from the BOSS data lies within the scatter of those from the mock galaxy catalogs in redshift space, yielding a ten-percent-level determination of the amplitude of $iζ(r)$. The tree-level perturbation theory in redshift space predicts how this amplitude depends on the linear and quadratic nonlinear galaxy bias parameters ($b_1$ and $b_2$), as well as on the amplitude and linear growth rate of matter fluctuations ($σ_8$ and $f$). Combining $iζ(r)$ with the constraints on $b_1σ_8$ and $fσ_8$ from the global two-point correlation function and that on $σ_8$ from the weak lensing signal of BOSS galaxies, we measure $b_2=0.41\pm0.41$ (68% C.L.) assuming standard perturbation theory at the tree level and the local bias model.