Potential NRQCD for unequal masses and the B_c spectrum at N³LO

We determine the 1/m and 1/m² spin-independent heavy quarkonium potentials in the unequal mass case with O(α³) and O(α²) accuracy, respectively. We discuss in detail different methods to calculate the potentials, and show the equivalence among them. In particular we obtain, for the first time, the manifestly gauge invariant 1/m and 1/m² potentials in terms of Wilson loops with next-to-leading order (NLO) precision. As an application of our results we derive the theoretical expression for the B_c spectrum in the weak-coupling limit through next-to-next-to-next-to-leading order (N³LO).