Hyperasymptotic approximation to the top, bottom and charm pole mass

TL;DR

This paper develops hyperasymptotic expansions for heavy quark pole masses, applies them to meson masses and lattice calculations, and critically reassesses the theoretical uncertainty in the top quark pole mass.

Contribution

It introduces hyperasymptotic expansions for heavy quark pole masses and evaluates the associated uncertainties, providing new insights into mass relations and precision.

Findings

Hyperasymptotic expansions improve mass calculations.

Uncertainty in top pole mass is estimated at 28 MeV.

Application to B/D meson masses and lattice results.

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 $\bar{\rm MS}$ top mass, and $m_{t, \rm PV}$, the top pole mass regulated using the PV prescription, is numerically assessed to be $\delta m_{t,\rm PV}= 28\;{\rm MeV}$ for ${\bar m}_t =163$ GeV.