Potential NRQCD for unequal masses and the B<inf>c</inf> spectrum at N³LO

© 2016, The Author(s). Abstract: 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 Bc spectrum in the weak-coupling limit through next-to-next-to-next-to-leading order (N3LO).