The MSR mass and the $ \mathcal{O}\left({\Lambda}_{\mathrm{QCD}}\right) $ renormalon sum rule
Here, 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 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 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({\Lambda}_{\mathrm{QCD}}\right) $ renormalon asymptotic behavior of the pole mass in perturbation theory. This is referred to as the $ \mathcal{O}\left({\Lambda}_{\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.