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Lyman$-\alpha$ (Ly$\alpha$) emission lines are typically found to beredshifted with respect to the systemic redshifts of galaxies, likely due toresonant scattering of Ly$\alpha$ photons. Here we measure the average velocityoffset for a sample of 96 $z\approx3.3$ Ly$\alpha$ emitters (LAEs) with amedian Ly$\alpha$ flux (luminosity) of $\approx 10^{-17}~\rmerg~cm^{-2}~s^{-1}$ ($\approx10^{42}~\rm erg~s^{-1}$) and a median starformation rate (SFR) of $\approx1.3 \rm M_{\odot} yr^{-1}$ (not corrected forpossible dust extinction), detected by the Multi-Unit Spectroscopic Explorer aspart of our MUSEQuBES circumgalactic medium (CGM) survey. By postulating thatthe stacked CGM absorption profiles of these LAEs, probed by 8 backgroundquasars, must be centered on the systemic redshift, we measure an averagevelocity offset, V$_{\rm offset} = 171 \pm 8$ $\rm km s^{-1}$, between theLy$\alpha$ emission peak and the systemic redshift. The observed V$_{\rmoffset}$ is lower by factors of $\approx1.4$ and $\approx2.6$ compared to thevelocity offsets measured for narrow-band selected LAEs and Lyman breakgalaxies, respectively, which probe galaxies with higher masses and SFRs.Consistent with earlier studies based on direct measurements for individualobjects, we find that the V$_{\rm offset}$ is correlated with the full width athalf-maximum of the red peak of the Ly$\alpha$ line, and anti-correlated withthe rest-frame equivalent width. Moreover, we find that $V_{\rm offset}$ iscorrelated 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 circularvelocity of the dark matter halos hosting the LAEs.

MUSEQuBES: Calibrating the redshifts of Ly {\alpha} emitters using stacked circumgalactic medium absorption profiles