IndisputableMonolith.Physics.QCDRGE.ThresholdMatching
Module ThresholdMatching supplies the NLO matching coefficients for alpha_s and quark masses at heavy-quark thresholds in the MS-bar scheme. It is cited by calculations that evolve parameters from the Z-pole down to the charm scale. Content consists of the explicit constant c_2_alpha = 11/72 together with the matching functions and their positivity certificates.
claimThe NLO threshold matching coefficient for the strong coupling is $c_2^alpha = 11/72$ at scale $mu = m_q^{MSbar}$. The module also records the mass coefficient $d_2^m$ and the jump functions $alpha_{match}$, $m_{match}$ that enforce continuity of observables across flavor thresholds.
background
The module belongs to the QCD renormalization-group track. It imports the two-loop beta function for alpha_s from TwoLoopAlphaS and the two-loop mass anomalous dimension gamma_m(alpha_s) = c_0 alpha_s + c_1 alpha_s^2 from MassAnomalousDimension. Threshold matching is required when the number of active flavors changes at a heavy-quark MS-bar mass; the NLO coefficients supply the finite jump that keeps physical quantities continuous.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
The module supplies the threshold corrections required by CharmMSBarScoreCard. That scorecard evaluates the RS structural prediction for the charm mass at rung 15 against the PDG value m_c(m_c) = 1.27 +- 0.02 GeV after two-loop running from the Z scale. The NLO coefficients close the gap between the ladder mass formula and the measured MS-bar mass.
scope and limits
- Does not compute three-loop or higher matching coefficients.
- Does not address electroweak threshold effects.
- Does not provide numerical integration of the RGE equations.
- Does not treat non-perturbative or lattice corrections.