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We present a measurement of baryon acoustic oscillations (BAO) in thecross-correlation of quasars with the Ly$\alpha$-forest flux-transmission at amean redshift $z=2.40$. The measurement uses the complete SDSS-III data sample:168,889 forests and 234,367 quasars from the SDSS Data Release DR12. Inaddition to the statistical improvement on our previous study using DR11, wehave implemented numerous improvements at the analysis level allowing a moreaccurate measurement of this cross-correlation. We also developed the firstsimulations of the cross-correlation allowing us to test different aspects ofour data analysis and to search for potential systematic errors in thedetermination of the BAO peak position. We measure the two ratios$D_{H}(z=2.40)/r_{d} = 9.01 \pm 0.36$ and $D_{M}(z=2.40)/r_{d} = 35.7 \pm 1.7$,where the errors include marginalization over the non-linear velocity ofquasars and the metal - quasar cross-correlation contribution, among othereffects. These results are within $1.8\sigma$ of the prediction of theflat-$\Lambda$CDM model describing the observed CMB anisotropies. We combinethis study with the Ly$\alpha$-forest auto-correlation function[2017A&A...603A..12B], yielding $D_{H}(z=2.40)/r_{d} = 8.94 \pm 0.22$ and$D_{M}(z=2.40)/r_{d} = 36.6 \pm 1.2$, within $2.3\sigma$ of the sameflat-$\Lambda$CDM model.

Baryon acoustic oscillations from the complete SDSS-III Ly$\alpha$-quasar cross-correlation function at $z=2.4$