The relation between the and the on-shell quark mass at order αs3

1999/11/30 by K.G. Chetyrkin, K. G. Chetyrkin, M. Steinhauser · 5 citations
Physics and Astronomy · #Bottom quark #Conformal map #Limit (mathematics) #Momentum (technical analysis) #Particle physics theoretical and experimental studies #Quantum Chromodynamics and Particle Interactions #Quantum and Classical Electrodynamics #Quark #Scalar (mathematics) #Top quark #Top quark condensate #hep-ph

paper · pdf · doi:10.1016/s0550-3213(99)00784-1

published as Nucl.Phys.B573:617-651,2000 · 38 pages, misprint in eq.(22) fixed, few references updated and a note added about a recent confirmation of our main results by Melnikov and van Ritbergen (hep-ph/9912391)

openalex publication_date 2000/05/01 · arxiv created 2000/06/06 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

The relation between the on-shell and \rm MS mass can be expressed through scalar and vector part of the quark propagator. In principle these two-point functions have to be evaluated on-shell which is a non-trivial task at three-loop order. Instead, we evaluate the quark self energy in the limit of large and small external momentum and use conformal mapping in combination with Padé improvement in order to construct a numerical approximation for the relation [1]. The errors of our final result are conservatively estimated to be below 3%. The numerical implications of the results are discussed in particular in view of top and bottom quark production near threshold. We show that the knowledge of new \cal O(α_s³) correction leads to a significant reduction of the theoretical uncertainty in the determination of the quark masses.

Citations

• Heavy quark current correlators to (αs2
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• Massive 3-loop Feynman diagrams reducible to SC ^* primitives of algebras of the sixth root of unity
• Integration by parts: The algorithm to calculate β-functions in 4 loops
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• Top quark threshold production in γγ collision in the next-to-leading order
• bquark low-scale running mass fromΥsum rules
• Two-loop QCD corrections of the massive fermion propagator
• Recurrence relations for three-loop prototypes of bubble diagrams with a mass
• The Nielsen identities for the two-point functions of QED and QCD
• Bdecays in the upsilon expansion

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