# Four-loop relation between the $\bar{\rm MS}$ and on-shell quark mass

@inproceedings{Marquard2016FourloopRB,
title={Four-loop relation between the \$\bar\{\rm MS\}\$ and on-shell quark mass},
author={Peter Marquard and Alexander Valeryevich Smirnov and Vladimir A. Smirnov and Matthias Steinhauser},
year={2016}
}
• Published 14 January 2016
• Physics
In this contribution we discuss the four-loop relation between the on-shell and $\bar{\rm MS}$ definition of heavy quark masses which is applied to the top, bottom and charm case. We also present relations between the $\bar{\rm MS}$ quark mass and various threshold mass definitions and discuss the uncertainty at next-to-next-to-next-to-leading order.

## References

SHOWING 1-10 OF 31 REFERENCES

### Quark mass relations to four-loop order in perturbative QCD.

• Physics
Physical review letters
• 2015
Results are presented for the relation between a heavy quark mass defined in the on-shell and minimal subtraction (MS[over ¯]) scheme to four-loop order and the new results are used to establish relations between various short-distance masses and the MS[ over ¯] quarks mass to next-to-next- to-next to-leading order accuracy.

### Charm and bottom quark masses: An update

• Physics
• 2009
Using new four-loop results for the heavy quark vacuum polarization and new data for bottom quark production in electron-positron annihilation, an update on the determination of charm- and

### First combination of Tevatron and LHC measurements of the top-quark mass

• Physics
• 2014
We present a combination of measurements of the mass of the top quark, $m_{\rm top}$, performed by the CDF and D0 experiments at the Tevatron collider and the ATLAS and CMS experiments at the Large

### Next-to-Next-to-Next-to-Leading Order QCD Prediction for the Top Antitop S-Wave Pair Production Cross Section Near Threshold in e(+)e(-) Annihilation.

• Physics
Physical review letters
• 2015
We present the third-order QCD prediction for the production of top antitop quark pairs in electron-positron collisions close to the threshold in the dominant S-wave state. We observe a significant

### The toolbox of modern multi-loop calculations: novel analytic and semi-analytic techniques

An algorithm to derive the canonical form of an arbitrary Feynman integral in order to facilitate their identification is discussed and a practical solution to the problem of multi-loop analytical tensor reduction is presented.

### Phys

• Rev. Lett. 82
• 1999