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The current and upcoming high precision photometric surveys such as TESS,CHEOPS, and PLATO will provide the community with thousands of new exoplanetcandidates. As a consequence, the presence of such a correlation is crucial inselecting the targets with the lowest RV jitter for efficient RV follow-up ofexoplanetary candidates. Studies of this type are also crucial to designoptimized observational strategies to mitigate RV jitter when searching forEarth-mass exoplanets. Our goal is to assess the correlation betweenhigh-precision photometric variability measurements and high-precision RVjitter over different time scales. We analyze 171 G, K, and M stars withavailable TESS high precision photometric time-series and HARPS precise RVs. Wederived the stellar parameters for the stars in our sample and measured the RVjitter and photometric variability. We also estimated chromospheric Ca II H$\&$ K activity indicator $log(R' _{HK})$, $\textit{v sin i}$, and the stellarrotational period. Finally, we evaluate how different stellar parameters and aRV sampling subset can have an impact on the potential correlations. We find avarying correlation between the photometric variability and RV jitter asfunction of time intervals between the TESS photometric observation and HARPSRV. As the time intervals of the observations considered for the analysisincreases, the correlation value and significance becomes smaller and weaker,to the point that it becomes negligible. We also find that for stars with aphotometric variability above 6.5 ppt the correlation is significantlystronger. We show that such a result can be due to the transition between thespot-dominated and the faculae-dominated regime. We quantified the correlationsand updated the relationship between chromospheric Ca II H $\&$ K activityindicator $log(R' _{HK})$ and RV jitter.

The correlation between photometric variability and radial velocity jitter, based on TESS and HARPS observations