Potential NRQCD for unequal masses and the $B_c$ spectrum at NNNLO

TL;DR

This paper derives high-precision, gauge-invariant heavy quarkonium potentials for unequal masses using Wilson loops and applies these results to predict the $B_c$ meson spectrum at NNNLO accuracy.

Contribution

It introduces the first gauge-invariant expressions for $1/m$ and $1/m^2$ potentials in unequal mass quarkonium and applies them to compute the $B_c$ spectrum at NNNLO.

Findings

Derived gauge-invariant $1/m$ and $1/m^2$ potentials at NLO.

Established equivalence of different calculation methods.

Predicted the $B_c$ spectrum at NNNLO accuracy.

Abstract

We determine the $1/m$ and $1/m^2$ spin-independent heavy quarkonium potentials in the unequal mass case with $\mathcal O(\alpha^3)$ and $\mathcal O(\alpha^2)$ 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 $1/m^2$ 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 (N$^3$LO).