Two-loop Quarkonium Hamiltonian in Non-annihilation Channel

We calculate the two-loop heavy quarkonium Hamiltonian within potential-NRQCD effective field theory in the non-annihilation channel. This calculation represents the first non-trivial step towards determining the N${}^4$LO Hamiltonian in the weak coupling regime. The large amount of computation is systematically handled by employing the $\beta$ expansion, differential equations for master integrals, and adopting a single-step matching procedure, in contrast to the conventional two-step approach.