We use 211 galaxy spectra from our survey for Lyman break galaxies (LBGs) associated with 11 damped Lyα systems (DLAs) to measure the three-dimensional LBG autocorrelation and DLA-LBG cross-correlation functions with the primary goal of inferring the mass of DLAs at z ~ 3. From every measurement and test in this work, we find evidence for an overdensity of LBGs near DLAs that is very similar to that of LBGs near other LBGs. Conventional binning of the data while varying both r0 and γ parameters of the fiducial model of the correlation function ξ(r) = (r/r0)-γ resulted in the best-fit values and 1 σ uncertainties of r0 = 2.65 ± 0.48, γ = 1.55 ± 0.40 for the LBG autocorrelation, and r0 = 3.32 ± 1.25, γ = 1.74 ± 0.36 for the DLA-LBG cross-correlation function. To circumvent shortcomings found in binning small data sets, we perform a maximum likelihood analysis based on Poisson statistics. The best-fit values and 1 σ confidence levels were found to be r0 = 2.91, γ = 1.21 for the LBG autocorrelation, and r0 = 2.81, γ = 2.11 for the DLA-LBG cross-correlation function. We report a redshift spike of five LBGs with Δz = 0.015 of the z = 2.936 DLA in the PSS 0808+5215 field; the DLA-LBG clustering signal survives when omitting this field from the analysis. Using the correlation function measurements and uncertainties, we compute the z ~ 3 LBG galaxy bias bLBG to be 1.5 bLBG 3, corresponding to an average halo mass of 109.7 MLBG 1011.6 M☉, and the z ~ 3 DLA galaxy bias bDLA to be 1.3 bDLA 4, corresponding to an average halo mass of 109 MLBG 1012 M☉. Finally, two of the six QSOs discovered were found to lie within Δz = 0.0125 of two of the survey DLAs. We estimate that the probability of this occurring by chance is 1 in 940, indicating a possible relationship between the distribution of QSOs and DLAs at z ~ 3.
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