Hyperasymptotic approximation to the top, bottom and charm pole mass

Abstract

We construct hyperasymptotic expansions for the heavy quark pole mass regulated using the principal value (PV) prescription. We apply such hyperasymptotic expansions to the $B/D$ meson masses, and $\bar{\Lambda }$ computed in the lattice. The issue of the uncertainty of the (top) pole mass is critically reexamined. The present theoretical uncertainty in the relation between ${\bar{m}}_t$, the $\overline{\mathrm{MS}}$ top mass, and $m_{t,\mathrm{PV}}$, the top pole mass regulated using the PV prescription, is numerically assessed to be $\delta m_{t,\mathrm{PV}}=28\mathrm{MeV}$ for ${\bar{m}}_t=163$ GeV.

52 pages, 27 figures; v2: 56 pages, extra clarifications, one extra appendix, added references. Journal version