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.
Highlights
We construct hyperasymptotic expansions for the heavy quark pole mass regulated using the principal value (PV)prescription along the lines of [1]
We generalize the discussion of that reference by including possible ultraviolet renormalons
In [1] we studied observables characterized by having a large scale Q ≫ ΛQCD, and for which the operator product expansion (OPE) is believed to be a good approximation
Summary
We construct hyperasymptotic expansions for the heavy quark pole mass regulated using the principal value (PV). We generalize the discussion of that reference by including possible ultraviolet renormalons We apply such expansions to various observables. Since SPV can not be computed exactly, we obtain it approximately along an hyperasymptotic expansion (a combination of (truncated) perturbative sums and of NP corrections). This is possible if enough terms of the perturbative expansion are known, and if the divergent structure of the leading renormalons of the observable is known. In this paper we are mainly concerned in the scenario where the leading renormalon is of infrared nature and subleading renormalons can be ultraviolet and/or infrared This is the case of the pole mass. In general we will avoid to make explicit the scheme (X) and scale (μ) dependence unless necessary
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