MUSEQuBES: Calibrating the redshifts of Ly {\alpha} emitters using
  stacked circumgalactic medium absorption profiles
  Lyman$-\alpha$ (Ly$\alpha$) emission lines are typically found to be
redshifted with respect to the systemic redshifts of galaxies, likely due to
resonant scattering of Ly$\alpha$ photons. Here we measure the average velocity
offset for a sample of 96 $z\approx3.3$ Ly$\alpha$ emitters (LAEs) with a
median Ly$\alpha$ flux (luminosity) of $\approx 10^{-17}~\rm
erg~cm^{-2}~s^{-1}$ ($\approx10^{42}~\rm erg~s^{-1}$) and a median star
formation rate (SFR) of $\approx1.3 \rm M_{\odot} yr^{-1}$ (not corrected for
possible dust extinction), detected by the Multi-Unit Spectroscopic Explorer as
part of our MUSEQuBES circumgalactic medium (CGM) survey. By postulating that
the stacked CGM absorption profiles of these LAEs, probed by 8 background
quasars, must be centered on the systemic redshift, we measure an average
velocity offset, V$_{\rm offset} = 171 \pm 8$ $\rm km s^{-1}$, between the
Ly$\alpha$ emission peak and the systemic redshift. The observed V$_{\rm
offset}$ is lower by factors of $\approx1.4$ and $\approx2.6$ compared to the
velocity offsets measured for narrow-band selected LAEs and Lyman break
galaxies, respectively, which probe galaxies with higher masses and SFRs.
Consistent with earlier studies based on direct measurements for individual
objects, we find that the V$_{\rm offset}$ is correlated with the full width at
half-maximum of the red peak of the Ly$\alpha$ line, and anti-correlated with
the rest-frame equivalent width. Moreover, we find that $V_{\rm offset}$ is
correlated with SFR with a sub-linear scaling relation, V$_{\rm offset}\propto
\rm SFR^{0.16\pm0.03}$. Adopting the mass scaling for main sequence galaxies,
such a relation suggests that V$_{\rm offset}$ scales with the circular
velocity of the dark matter halos hosting the LAEs.
