Abstract
We provide a detailed description and analysis of a low-scale short-distance mass scheme, called the MSR mass, that is useful for high-precision top quark mass determinations, but can be applied for any heavy quark Q. In contrast to earlier low-scale short-distance mass schemes, the MSR scheme has a direct connection to the well known overline{mathrm{MS}} mass commonly used for high-energy applications, and is determined by heavy quark on-shell self-energy Feynman diagrams. Indeed, the MSR mass scheme can be viewed as the simplest extension of the overline{mathrm{MS}} mass concept to renormalization scales ≪ mQ. The MSR mass depends on a scale R that can be chosen freely, and its renormalization group evolution has a linear dependence on R, which is known as R-evolution. Using R-evolution for the MSR mass we provide details of the derivation of an analytic expression for the normalization of the mathcal{O}left({varLambda}_{mathrm{QCD}}right) renormalon asymptotic behavior of the pole mass in perturbation theory. This is referred to as the mathcal{O}left({varLambda}_{mathrm{QCD}}right) renormalon sum rule, and can be applied to any perturbative series. The relations of the MSR mass scheme to other low-scale short-distance masses are analyzed as well.
Highlights
We provide a detailed description and analysis of a low-scale short-distance mass scheme, called the MSR mass, that is useful for high-precision top quark mass determinations, but can be applied for any heavy quark Q
It is instructive to briefly discuss what the solution of the R-evolution achieves by considering the difference of the MSR mass, mMQ SR(R0)−mMQ SR(R1), in the context of fixedorder perturbation theory (FOPT), where it is well-known that the renormalon ambiguity contained in the series for mpQole−mMQ SR(R0) and the series for mpQole−mMQ SR(R1) only cancel if one expands in αs with a common renormalization scale μ
The first aim was to give a detailed presentation of the MSR mass, which is an R-dependent short-distance mass designed for high-precision determinations of heavy quark masses from quantities where the physical scales are smaller than the quark mass, R < mQ
Summary
The MS mass mQ(μ) serves as the standard short-distance mass scheme for many highenergy applications with physical scales of the order or larger than the mass of the quark. A coherent treatment of the mass effects of lighter quarks is beyond the scope of this paper, and we use the approximation that all flavors lighter than Q are massless These mass corrections come from the insertion of massive virtual quark loops in the self-energy Feynman diagrams and start at O(αs). This is an exact mathematical statement within the context of the calculus for asymptotic series and means that we can replace the term mQ by the arbitrary scale R on the r.h.s. of eq (2.1) and use the resulting perturbative series as the definition of the R-dependent MSR mass scheme None of these short-distance masses is defined directly from the on-shell self-energy diagrams of the massive quark Q such as the MSR mass This has a number of advantages, for example when discussing heavy flavor symmetry properties in the pole-MS mass relation of different heavy quarks
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