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, $\hat{\xi}({\rm r},{\rm r}_L)$, where ${\rm r}_L$ is the
location of a subvolume, and the corresponding mean overdensities,
$\bar{\delta}({\rm r}_L)$. This correlation, which we call the "integrated
three-point function", $i\zeta(r)=\langle\hat{\xi}({\rm r},{\rm
r}_L)\bar{\delta}({\rm r}_L)\rangle$, 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
$i\zeta(r)$ 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 $i\zeta(r)$. 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 ($\sigma_8$ and $f$).
Combining $i\zeta(r)$ with the constraints on $b_1\sigma_8$ and $f\sigma_8$
from the global two-point correlation function and that on $\sigma_8$ 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.
