The study aims to establish a unique self-consistency identity in quantum chromodynamics (QCD) characterized by the equation β₀ = Y.
Identified relationships among β₀, n_f, and D_M in the context of QCD.
Solving for the variable Y and analyzing its implications within SU(3).
Calculated the strong coupling constant α_s(m_Z) and its error margin.
Derived a unique solution Y = 7 for SU(3).
Found α_s(m_Z) = 0.1176 with only a 0.21% error margin.
Demonstrated that this identity does not hold for other gauge groups SU(N).
Abstract
Self-consistency in QCD: β₀ = Y, nf = Y − 1, DM = Y + 4. Unique solution Y = 7. Only occurs for SU (3) among all SU (N). Yields αₛ (mZ) = 0. 1176 (0. 21% error). Companion paper to Turbulence Exponents.