The theory behind is well explained in Francis Halzen, Quarks and Leptons 6.7 & 11.1
Because the charge of the charm quark is 2/3, this cross section is 4/3 times that for annihilation into a pair muon anti muon which in turn is 4/3 * pi * (alpha)^2 /s where s is 4 times the squared energy of the beams and alpha is the fine structure constant about 1/137.
If possible, please give me the PDG value for this process.. What you have said Juan, is only about the e- m process.. But that annihilation can be happen via weak interaction too right..?? Then what will be the total cross section?