Publication: The MSR mass and the O(Ʌqcd) renormalon sum rule
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2018-04-02
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Springer
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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 (MS) over bar 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) over bar mass concept to renormalization scales << m(Q). 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 O(A(QCD)) renormalon asymptotic behavior of the pole mass in perturbation theory. This is referred to as the O(A(QCD)) 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.
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©The Authors.
We acknowledge partial support by the FWF Austrian Science Fund under the Doctoral Program No. W1252-N27 and the Project No. P28535-N27, the U.S. Department of Energy under the Grant No. DE-SC0011090, the Simons Foundation through the Grant 327942, the Spanish MINECO “Ram´on y Cajal” program (RYC-2014-16022), MECD grants FPA2016-78645-P, FPA2014-53375-C2-2-P and FPA2016-75654-C2-2-P, the group UPARCOS, the IFT “Centro de Excelencia Severo Ochoa” Program under Grant SEV2012-0249 and by the Ramanujan Fellowship of SERB, DST. We also thank the ErwinSchr¨odinger International Institute for Mathematics and Physics, the University of Vienna and Cultural Section of the City of Vienna (MA7) for partial support.