IndisputableMonolith.Physics.QCDRGE.AlphaRunning
AlphaRunning defines the one-loop beta coefficient beta0 and the explicit running formula alpha_s_running for the strong coupling from its value at the Z boson mass. QCD phenomenologists extending one-loop results to two-loop or lattice matching would cite these objects. The module assembles N_c, N_f_Z and the boundary condition alpha_s_MZ into the standard logarithmic running expression without further derivation.
claimThe one-loop coefficient $b_0 = (11/3)N_c - (2/3)N_f$ and the running coupling $a_s(Q) = a_s(M_Z) / (1 + b_0 a_s(M_Z) log(Q^2/M_Z^2)/(4 pi))$, with $N_c=3$, $N_f$ evaluated at the Z scale, and $a_s(M_Z)$ taken from the strong-force boundary condition.
background
The module operates inside the QCD renormalization-group track of Recognition Science. It imports the RS time quantum tau_0 from Constants and the T15 strong-force derivation from StrongForce, which obtains alpha_s(M_Z) from planar edge geometry of the ledger. Sibling definitions introduce N_c, N_f_Z, beta0, alpha_s_MZ and the function alpha_s_running that implements the one-loop flow.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
AlphaRunning supplies the one-loop running that TwoLoopAlphaS imports and extends by adding the second beta coefficient b1 to reach the standard MS-bar two-loop formula. It therefore completes the base layer of the QCD RGE chain that begins from the T15 strong-force hypothesis.
scope and limits
- Does not include two-loop or higher-order beta-function coefficients.
- Does not derive the boundary value alpha_s(M_Z) from first principles.
- Does not incorporate quark-mass threshold corrections.
- Does not perform numerical integration or experimental fitting.