I am looking for a Java code profiler which I can use to profile my application (its a service which runs in backend) on production (so means low over head, and it must not
In general you don't (or I won't recommend) profilers that instrument your application. Instrumenting always means an uncontrollable production overhead.
What you can use is a sampling profiler. A sampling profiler makes a snapshot of the stack traces at a controllable interval. What you don't get is call counts, but, after some runtime, you get a good overview where you have hotspots. Since you can adjust the sample interval of the profiler you can influence the overhead of it.
A usable sampling profiler is shipped with the JDK, see the hprof page in the java 7 documentation. In former times there existed some graphical analysis tools for the hprof cpu traces (not the heap traces). Now they are gone. However, you can already work with the generated text file.
I took a quick look on the Java Mission Control stuff mentioned above. I think it is quite mighty and will satisfy a lot of needs, in the white paper they say it has only 2% overhead. However, it is not totally what I personally need or want. For my applications it is better to have a "light" profiling enabled all the time.