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 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 Revolution. Using Revolution for the MSR mass we provide details of the derivation of an analytic expression for the normalization of the O(Λ QCD) renormalon asymptotic behavior of the pole mass in perturbation theory. This is referred to as the O(Λ 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.

We provide a systematic renormalization group formalism for the mass effects in the relation of the pole mass m pole Q and short-distance masses such as the MS mass m Q of a heavy quark Q, coming from virtual loop insertions of massive quarks lighter than Q. The formalism reflects the constraints from heavy quark symmetry and entails a combined matching and evolution procedure that allows to disentangle and successively integrate out the corrections coming from the lighter massive quarks and the momentum regions between them and to precisely control the large order asymptotic behavior. With the formalism we systematically sum logarithms of ratios of the lighter quark masses and m Q , relate the QCD corrections for different external heavy quarks to each other, predict the O(α 4 s ) virtual quark mass corrections in the pole-MS mass relation, calculate the pole mass differences for the top, bottom and charm quarks with a precision of around 20 MeV and analyze the decoupling of the lighter massive quark flavors at large orders. The summation of logarithms is most relevant for the top quark pole mass m pole t , where the hierarchy to the bottom and charm quarks is large. We determine the ambiguity of the pole mass for top, bottom and charm quarks in different scenarios with massive or massless bottom and charm quarks in a way consistent with heavy quark symmetry, and we find that it is 250 MeV. The ambiguity is larger than current projections for the precision of top quark mass measurements in the high-luminosity phase of the LHC.

We provide a general method to effectively compute differential and cumulative event-shape distributions to O(α s ) precision for massive quarks produced primarily at an e + e − collider. In particular, we show that at this order, due to the screening of collinear singularities by the quark mass, for all event shapes linearly sensitive to soft dynamics, there appear only two distributions at threshold: a Dirac delta function and a plus distribution. Furthermore, we show that the coefficient of the latter is universal for any infra-red and collinear safe event shape, and provide an analytic expression for it. Likewise, we compute a general formula for the coefficient of the Dirac delta function, which depends only on the event-shape measurement function in the soft limit. Finally, we present an efficient algorithm to compute the differential and cumulative distributions, which does not rely on Monte Carlo methods, therefore achieving a priory arbitrary precision even in the extreme dijet region. We implement this algorithm in a numeric code and show that it agrees with analytic results on the distribution for 2-jettiness, heavy jet mass and a massive generalization of C-parameter.

We calculate the O(α 2 s ) corrections to the primary massive quark jet functions in Soft-Collinear Effective Theory (SCET). They are an important ingredient in factorized predictions for inclusive jet mass cross sections initiated by massive quarks emerging from a hard interaction with smooth quark mass dependence. Due to the effects coming from the secondary production of massive quark-antiquark pairs there are two options to define the SCET jet function, which we call universal and mass mode jet functions. They are related to whether or not a soft mass mode (zero) bin subtraction is applied for the secondary massive quark contributions and differ in particular concerning the infrared behavior for vanishing quark mass. We advocate that a useful alternative to the common zero-bin subtraction concept is to define the SCET jet functions through subtractions related to collinear-soft matrix elements. This avoids the need to impose additional power counting arguments as required for zero-bin subtractions. We demonstrate how the two SCET jet function definitions may be used in the context of two recently developed factorization approaches to treat secondary massive quark effects. We clarify the relation between these approaches and in which way they are equivalent. Our two-loop calculation involves interesting technical subtleties related to spurious rapidity divergences and infrared regularization in the presence of massive quarks.

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