  Minimising the impact of stellar variability in Radial Velocity (RV)
measurements is a critical challenge in achieving the 10 cm s$^{-1}$ precision
needed to hunt for Earth twins. Since 2012, a dedicated programme has been
underway with HARPS-N, to conduct a blind RV Rocky Planets Search (RPS) around
bright stars in the Northern Hemisphere. Here we describe the results of a
comprehensive search for planetary systems in two RPS targets, HD 166620 and HD
144579. Using wavelength-domain line-profile decorrelation vectors to mitigate
the stellar activity and performing a deep search for planetary reflex motions
using a trans-dimensional nested sampler, we found no significant planetary
signals in the data sets of either of the stars. We validated the results via
data-splitting and injection recovery tests. Additionally, we obtained the 95th
percentile detection limits on the HARPS-N RVs. We found that the likelihood of
finding a low-mass planet increases noticeably across a wide period range when
the inherent stellar variability is corrected for using scalpels U-vectors. We
are able to detect planet signals with $M\sin i \leq 1$ M$_\oplus$ for orbital
periods shorter than 10 days. We demonstrate that with our decorrelation
technique, we are able to detect signals as low as 54 cm s$^{-1}$, which brings
us closer to the calibration limit of 50 cm s$^{-1}$ demonstrated by HARPS-N.
Therefore, we show that we can push down towards the RV precision required to
find Earth analogues using high-precision radial velocity data with novel
data-analysis techniques.
