I got a hint: the UserTransaction is bound as "UserTransaction" and not as "java:comp/UserTransaction". So I renamed the hibernate service to use UserTransaction and it works.
I tried to figure out a solution where I don't have to change this name (and use java:comp/UserTransaction inside Schedule) but I can't. I tried to use an alias, but it gives me a problem in my web-app.
The problem seem to be solved for now.