We introduce the Gauge Balance Law, a variational principle that governs the optimal convergence of gauge couplings. Defining the spread Δ (Q) =max (αᵢ^-1) −min (αᵢ^-1), we show that its minimizer Q* satisfies a second-difference balance condition on effective beta coefficients, B (Q*) =b₁^eff+b₃^eff−2b₂^eff≈0. We provide an exact 1-loop proof using the max–min functional, extend to 2-loop via local linearization, and validate numerically. Phenomenological implications for model building and collider searches are discussed. Gauge coupling unification is a central theme in high-energy physics. We propose a model-independent organizing principle based on minimizing the spread of inverse couplings.
sree Debasish Dasgupta (Thu,) studied this question.