This isn't going to be thread safe. If PolarLorentzVector only has simple types, it might work. However, if PolarLorentzVector holds a pointer (or ever was changed to hold a pointer) then if two threads are trying to change this at the same time then the pointer would get different values and the first value might already be in use by another thread when the second value changes it.

Either p4Polar_ becomes an atomic pointer or you have to make cachePolarFixed_ into a char with 3 states and do a wait.