Context : The discovery of Proxima b marked one of the most important milestones in exoplanetary science in recent years .
Yet the limited precision of the available radial velocity data and the difficulty in modelling the stellar activity calls for a confirmation of the Earth-mass planet .

Aims : We aim to confirm the presence of Proxima b using independent measurements obtained with the new ESPRESSO spectrograph , and refine the planetary parameters taking advantage of its improved precision .

Methods : We analysed 63 spectroscopic ESPRESSO observations of Proxima ( Gl 551 ) taken during 2019 .
We obtained radial velocity measurements with a typical radial velocity photon noise of 26 cm \cdot s ^ { -1 } .
We combined these data with archival spectroscopic observations and newly obtained photometric measurements to model the stellar activity signals and disentangle them from planetary signals in the radial velocity ( RV ) data .
We ran a joint Markov chain Monte Carlo analysis on the time series of the RV and full width half maximum of the cross-correlation function to model the planetary and stellar signals present in the data , applying Gaussian process regression to deal with the stellar activity signals .

Results : We confirm the presence of Proxima b independently in the ESPRESSO data and in the combined ESPRESSO+HARPS+UVES dataset .
The ESPRESSO data on its own shows Proxima b at a period of 11.218 \pm 0.029 days , with a minimum mass of 1.29 \pm 0.13 M _ { \oplus } .
In the combined dataset we measure a period of 11.18427 \pm 0.00070 days with a minimum mass of 1.173 \pm 0.086 M _ { \oplus } .
We get a clear measurement of the stellar rotation period ( 87 \pm 12 d ) and its induced RV signal , but no evidence of stellar activity as a potential cause for the 11.2 days signal .
We find some evidence for the presence of a second short-period signal , at 5.15 days with a semi-amplitude of only 40 cm \cdot s ^ { -1 } .
If caused by a planetary companion , it would correspond to a minimum mass of 0.29 \pm 0.08 M _ { \oplus } .
We find that for the case of Proxima , the full width half maximum of the cross-correlation function can be used as a proxy for the brightness changes and that its gradient with time can be used to successfully detrend the RV data from part of the influence of stellar activity .
The activity-induced RV signal in the ESPRESSO data shows a trend in amplitude towards redder wavelengths .
Velocities measured using the red end of the spectrograph are less affected by activity , suggesting that the stellar activity is spot dominated .
This could be used to create differential RVs that are activity dominated and can be used to disentangle activity-induced and planetary-induced signals .
The data collected excludes the presence of extra companions with masses above 0.6 M _ { \oplus } at periods shorter than 50 days .

Conclusions :