Ambiguities in the up-quark mass

Area of Science:

• Theoretical particle physics
• Quantum chromodynamics

Background:

• The behavior of quark masses is crucial in understanding fundamental forces.
• Previous models assumed singularities arise when quark masses cross zero.
• The strong CP problem remains a significant puzzle in particle physics.

Purpose of the Study:

• To investigate the physical implications of adjusting the up-quark mass across positive and negative values.
• To re-evaluate the validity of solutions to the strong CP problem that rely on a vanishing lightest quark mass.

Main Methods:

• Theoretical analysis of quark mass definitions.
• Exploration of the additive ambiguity in quark mass calculations.
• Examination of the conditions under which physical singularities are avoided.

Main Results:

• No physical singularity is encountered when the up-quark mass is varied from positive to negative, provided other quarks remain massive.
• An additive ambiguity in the definition of quark mass underlies this behavior.

Conclusions:

• The assumption of singularities when quark masses change sign is not universally valid.
• Attempts to resolve the strong CP problem by setting the lightest quark mass to zero may be theoretically unsound due to this ambiguity.