# Precise Relation Between Quark Masses in Different Renormalization Schemes

**Principal Investigator:** Matthias Steinhauser, Institut für Theoretische Teilchenphysik, Karlsruhe Institute of Technology/KIT (Germany)

**HPC Platform: **Hornet and Hermit of HLRS

**Date Published: S**eptember 2015

**HLRS Project ID: **NumFeyn

The Standard Model of particle physics describes the fundamental interaction of elementary particles. From the mathematical point of view it is a relativistic quantum field theory which contains couplings and masses as free parameters. The meaning of these parameters is fixed once a so-called renormalization scheme is chosen. Researchers of the Karlsruhe Institute of Technology, the Deutsches Elektronen-Synchrotron (DESY), and the Moscow State University have computed a precise relation between heavy quark masses defined in the two most commonly used renormalization schemes, the minimal subtraction (MS) and on-shell scheme.

The basis of the calculation is perturbative quantum field theory which requires the evaluation of multi-loop integrals. The latter can be represented by so-called Feynman diagrams. A typical representative is shown in Fig.1.

Copyright: Institut für Theoretische Teilchenphysik, Karlsruhe Institute of Technology (KIT)

In the calculation applied at this project the researchers obtain analytical expressions of the mass relation which depends on about 350 multidimensional integrals. If possible the latter have to be computed analytically. For the other cases the physicists aim for an evaluation with highest possible precision using numerical methods.

For the calculations the high performance computing (HPC) systems of the High Performance Computing Center Stuttgart (HLRS) of the University of Stuttgart were used, which enabled the researchers to obtain the required precision of their calculations by respecting the CPU time limit granted for the research project.

To illustrate the result, numerical results for the heaviest quark, the top quark, are provided. The correction term between the MS and on-shell mass at first, second, and third order in perturbation theory read 7.5 GeV, 1.6 GeV and 0.5 GeV. The researchers’s new correction term amounts to 0.2 GeV which, on the one hand, shows that perturbation theory converges well and, on the other hand, significantly reduces the uncertainty from the conversion between the two mass definitions.

**Reference: **P. Marquard, A.V. Smirnov, V.A. Smirnov and M. Steinhauser, “Quark Mass Relations to Four-Loop Order in Perturbative QCD,” Phys. Rev. Lett. 114 (2015) 14, 142002

**Scientific contact:**

Prof. Matthias Steinhauser

Institut für Theoretische Teilchenphysik

Karlsruhe Institute of Technology (KIT)

76128 Karlsruhe

e-mail: matthias.steinhauser@kit.edu

*September 2015*