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The [CII] 158$~\mu$m emission line represents so far one of the mostprofitable tools for the investigation of the high-redshift galaxies in theearly Universe. Being one of the brightest cooling lines in the rest-framefar-infrared regime of star-forming galaxies, it has been successfullyexploited as a tracer of star-formation rate (SFR) in local sources. Thepicture is more complex at higher redshifts, where its usability in thiscontext is still under investigation. Recent results from the ALMA LargeProgram to INvestigate [CII] at Early times (ALPINE) survey suggest that thereis no (or weak) evolution of the L$\mathrm{_{[CII]}}$-SFR relation up to$z\sim6$ but their reliability is hampered by the presence of a largepopulation of [CII] non-detected galaxies. In this work, we characterize thepopulation of [CII] non-detections in ALPINE. By stacking their ALMA spectra,we obtain a signal detected at $\sim5.1\sigma$, resulting in a [CII] luminosityof $\mathrm{log(L_\mathrm{[CII]}}/\mathrm{L_{\odot}})$ $\sim7.8$. Whencombining this value with those from the [CII] detections, we find a$\mathrm{L_{[CII]}}$-SFR relation with a slope $b=1.14\pm0.11$, in agreementwithin the uncertainties both with the linear relation found in the localUniverse, and with the previous findings from ALPINE at $z\sim5$. This suggeststhat the [CII] line can be considered a good tracer of star formation up to thedistant Universe. Finally, we show that the galaxies of our sample that mostdeviate from the observed L$_\mathrm{[CII]}$-SFR relation could suffer from aless precise redshift estimation, perhaps artificially reducing their [CII]luminosity. In this respect, we claim that there is no evidence in favour of adeficit of [CII] content in high-z galaxies, in contrast with earlier studies.

The ALPINE-ALMA [CII] Survey: the population of [CII]-undetected galaxies and their role in the $\mathrm{L_{[CII]}}$-SFR relation