We present the 3-point function xi_3 and Q_3=xi_3/xi_2^2 for a spectroscopic sample of luminous red galaxies (LRG) from SDSS DR6 & DR7. We find a strong (S/N$>$6) detection of $Q_3$ on scales of 55-125 Mpc/h, with a well defined peak around 105 Mpc/h in all xi_2, xi_3 and Q_3, in excellent agreement with the predicted shape and location of the imprint of the baryon acoustic oscillations (BAO). We use very large simulations to asses and test the significance of our measurement. Models without the BAO peak are ruled out by the $Q_3$ data with 99% confidence. Our measurements show the expected shape for Q_3 as a function of the triangular configuration. This provides a first direct measurement of the non-linear mode coupling coefficients of density and velocity fluctuations which, on these large scales, are independent of cosmic time, the amplitude of fluctuations or cosmological parameters. The location of the BAO peak in the data indicates Omega_m =0.28 pm 0.05 and Omega_B=0.079 pm 0.025 (h=0.70) after marginalization over spectral index (n_s=0.8-1.2) linear b_1 and quadratic c_2 bias,which are found to be in the range: b_1=1.7-2.2 and c_2=0.75-3.55. The data allows a hierarchical contribution from primordial non-Gaussianities in the range Q_3=0.55-3.35. These constraints are independent and complementary to the ones that can be obtained using the 2-point function, which are presented in a separate paper. This is the first detection of the shape of $Q_3$ on BAO scales, but our errors are shot-noise dominated and the SDSS volume is still relatively small, so there is ample room for future improvement in this type of measurements.
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