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

Area of Science:

• High Energy Physics
• Quantum Chromodynamics
• Particle Physics

Background:

• Accurate determination of heavy quark masses is crucial for precision physics.
• Relating different heavy quark mass definitions is essential for theoretical consistency.

Purpose of the Study:

• To compute the relation between on-shell and minimal subtraction (MS) heavy quark masses.
• To achieve next-to-next-to-next-to-leading order (NNNLO) accuracy in these relations.
• To improve the precision of heavy quark mass determinations in quantum chromodynamics.

Main Methods:

• Calculation of four-loop on-shell integrals.
• Perturbative expansion of heavy quark mass relations.
• Renormalization group techniques.

Main Results:

• Presentation of results for the heavy quark mass relation to four-loop order.
• Establishment of relations between various short-distance masses and the MS quark mass.
• Achieved NNNLO accuracy for these crucial relations.

Conclusions:

• The presented four-loop results significantly enhance the accuracy of heavy quark mass determinations.
• These improved relations are vital for precise comparisons between theoretical predictions and experimental data.
• The study contributes to advancing precision calculations in quantum chromodynamics.