Context : The precision of radial velocity ( RV ) measurements to detect indirectly planetary companions of nearby stars has improved to enable the discovery of extrasolar planets in the Neptune and Super-Earth mass range .
Detections of extremely low mass planets , even as small as 1 Earth mass or below , in short-period orbits now appears conceivable in ongoing RV planet searches .
Discoveries of these Earth-like planets by means of ground-based RV programs will help to determine the parameter \eta _ { \oplus } , the frequency of potentially habitable planets around other stars .

Aims : In search of low-mass planetary companions we monitored Proxima Centauri ( M5V ) as part of our M dwarf program .
In the absence of a significant detection , we use these data to demonstrate the general capability of the RV method in finding terrestrial planets .
For late M dwarfs the classic liquid surface water habitable zone ( HZ ) is located close to the star , in which circumstances the RV method is most effective .
We want to demonstrate that late M dwarfs are ideal targets for the search of terrestrial planets with the RV technique .

Methods : Using the iodine cell technique we obtained differential RV measurements of Proxima Cen over a time span of 7 years with the UVES spectrograph at the ESO VLT .
We determine upper limits to the masses of companions in circular orbits by means of numerical simulations .

Results : The RV data of Proxima Cen have a total rms scatter of 3.1 ~ { } { m s } ^ { -1 } and a period search does not reveal any significant signals .
In contrast to our earlier results for Barnard ’ s star , the RV results for the active M dwarf Proxima Cen are only weakly correlated with H _ { \alpha } line index measurements .
As a result of our companion limit calculations , we find that we successfully recover all test signals with RV amplitudes corresponding to planets with m \sin i \geq 2 - 3 ~ { } M _ { \oplus } residing inside the HZ of Proxima Cen with a statistical significance of > 99 \% .
Over the same period range , we can recover 50 % of the test planets with masses of m \sin i \geq 1.5 - 2.5 ~ { } M _ { \oplus } .
Based on our simulations , we exclude the presence of any planet in a circular orbit with m \sin i \geq 1 ~ { } M _ { Neptune } at separations of a \leq 1 AU .

Conclusions :