Two-loop quarkonium Hamiltonian in annihilation channel

We calculate the two-loop quarkonium Hamiltonian in the annihilation channel within the framework of potential-NRQCD effective field theory. The result agrees with the previous calculation of the corresponding four-quark operator in NRQCD for SU(N) color gauge group. We further obtain an expression with a more general color structure applicable to other gauge groups. Combined with the recently calculated two-loop Hamiltonian in the non-annihilation channel, this completes the full two-loop quarkonium Hamiltonian.