# Relation between the $\overline{\mathrm{MS}}$ and the kinetic mass of heavy quarks

Fael, Matteo 1; Schönwald, Kay 1; Steinhauser, Matthias 1
1 Institut für Theoretische Teilchenphysik (TTP), Karlsruher Institut für Technologie (KIT)

##### Abstract:
We compute the relation between the pole mass and the kinetic mass of a heavy quark to three loops. Using the known relation between the pole and the $\overline{\mathrm{MS}}$ mass we obtain precise conversion relations between the $\overline{\mathrm{MS}}$ and kinetic masses. The kinetic mass is defined via the moments of the spectral function for the scattering involving a heavy quark close to threshold. This requires the computation of the imaginary part of a forward-scattering amplitude up to three-loop order. We discuss in detail the expansion procedure and the reduction to master integrals. For the latter analytic results are provided. We apply our result both to charm and bottom quark masses. In the latter case we compute and include finite charm quark mass effects. Furthermore, we determine the large-${\beta}_{0}$ result for the conversion formula at four-loop order. For the bottom quark we estimate the uncertainty in the conversion between the $\overline{\mathrm{MS}}$ and kinetic masses to about 15 MeV which is an improvement by a factor of 2--3 as compared to the two-loop formula. The improved precision is crucial for the extraction of the Cabibbo-Kobayashi-Maskawa matrix element $|{V}_{cb}|$ at Belle II.

 Zugehörige Institution(en) am KIT Institut für Theoretische Teilchenphysik (TTP) Publikationstyp Zeitschriftenaufsatz Publikationsdatum 08.01.2021 Sprache Englisch Identifikator ISSN: 0556-2821, 1089-4918, 1538-4500, 1550-2368, 1550-7998, 2470-0010, 2470-0029 KITopen-ID: 1000129348 Erschienen in Physical review / D Verlag American Physical Society (APS) Band 103 Heft 1 Seiten Art.-Nr.: 014005 Nachgewiesen in ScopusWeb of ScienceDimensions Relationen in KITopen Verweist aufRelation between the $\overline{\mathrm{MS}}$ and the kinetic mass of heavy quarks. Fael, Matteo; Schönwald, Kay; Steinhauser, Matthias (2020) Forschungsbericht/Preprint (1000129389)
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