Baryon acoustic oscillations at z = 2.34 from the correlations of Ly$alpha$ absorption in eBOSS DR14

We measure the imprint of primordial baryon acoustic oscillations (BAO) in the correlation function of Ly$alpha$ absorption in quasar spectra from the Baryon Oscillation Spectroscopic Survey (BOSS) and the extended BOSS (eBOSS) in Data Release 14 (DR14) of the Sloan Digital Sky Survey (SDSS)-IV. In addition to 179,965 spectra with absorption in the Lyman-$alpha$ (Ly$alpha$) region, we use, for the first time, Ly$alpha$ absorption in the Lyman-$beta$ region of 56,154 spectra. We measure the Hubble distance, $D_H$, and the comoving angular diameter distance, $D_M$, relative to the sound horizon at the drag epoch $r_d$ at an effective redshift $z=2.34$. Using a physical model of the correlation function outside the BAO peak, we find $D_H(2.34)/r_d=8.86pm 0.29$ and $D_M(2.34)/r_d=37.41pm 1.86$, within 1$sigma$ from the flat-$Lambda$CDM model consistent with CMB anisotropy measurements. With the addition of polynomial broadband terms, the results remain within one standard deviation of the CMB-inspired model. Combined with the quasar-Ly$alpha$ cross-correlation measurement presented in a companion paper Blomqvist19, the BAO measurements at $z=2.35$ are within 1.7$sigma$ of the predictions of this model.