Context :

Aims : The \mu Ara planetary system is rather complex : It contains two already known planets , \mu Ara b with P = 640 days and \mu Ara c with P = 9.64 days , and a third companion on a wide but still poorly defined orbit .
Even with three planets in the system , the data points keep anomalously high dispersion around the fitted solution .
The high residuals are only partially due to the strong p-mode oscillations of the host star .
We have therefore studied in this paper the possible presence of a fourth planet in the system .

Methods : During the past years we have carried out additional and extremely precise radial-velocity measurements with the HARPS spectrograph .
These data turned out to be of high importance for constraining the many free parameters in a four-planet orbital fit .
Nevertheless , the search for the best solution remains difficult in this complex and multi-dimensional parameters space .
The use of the new Stakanof software and employing an optimized genetic algorithm , helped us considerably in this task and made our search extremely efficient and successful .

Results : We provide in this paper a full orbital solution of the planetary system around \mu Ara .
It turns out to be the second system known to harbor 4 planetary companions . \mu Ara b was already well known and characterized before this study .
Thanks to the new data points acquired with HARPS we can confirm the presence of \mu Ara c at P = 9.64 days , which produces a coherent RV signal over more than two years .
The new orbital fit sets the mass of \mu Ara c to 10.5 M _ { \oplus } .
Furthermore , we present the discovery of \mu Ara d , a new planet on an almost circular 310 days-period and with a mass of 0.52 M _ { Jup } .
Finally , we give completely new orbital parameters for the longest-period planet , \mu Ara e. It is the first time that this companion is constrained by radial-velocity data into a dynamical stable orbit , which leaves no doubt about its planetary nature .
We take this opportunity to discuss naming conventions for poorly characterized planets .

Conclusions :