IndisputableMonolith.Physics.BottomMSBarScoreCard
This module supplies RS-anchored definitions for the bottom quark mass in the MS-bar scheme at the Z scale. Precision QCD and heavy-quark phenomenologists would cite it when testing Recognition Science mass predictions against PDG data. The module assembles imported two-loop alpha_s running and mass anomalous dimension into explicit predicted and certified values.
claimThe module defines the PDG bottom mass $m_b^{\text{PDG}}$ (GeV), its uncertainty, the RS-predicted value $m_b^{\text{RS}}(M_Z)$ obtained by running the phi-ladder mass via the two-loop $\overline{\text{MS}}$ equations, and the certification predicate BottomMSBarCert asserting that the prediction lies inside the PDG band.
background
The module sits inside the Recognition Science heavy-quark closure track. It imports the RS time quantum $\tau_0=1$ tick from Constants, the two-loop beta-function running of $\alpha_s$ from TwoLoopAlphaS, and the quark-mass anomalous dimension $\gamma_m(\alpha_s)=c_0 a + c_1 a^2$ (with $C_F=4/3$) from MassAnomalousDimension. These supply the renormalization-group machinery that converts an RS-native mass (phi-ladder rung) into an $\overline{\text{MS}}$ value at the electroweak scale $M_Z$.
proof idea
this is a definition module, no proofs
why it matters in Recognition Science
The module supplies the bottom-mass scorecard that feeds into higher-level RS mass comparisons and the overall physics certification chain. It closes the heavy-quark sector by placing the RS phi-ladder prediction inside the experimental band after two-loop running, directly implementing the RS-anchored bottom mass reference stated in the module doc-comment.
scope and limits
- Does not derive the underlying RS phi-ladder mass formula.
- Does not extend the running beyond two-loop order.
- Does not treat top-quark or light-quark sectors.
- Does not incorporate lattice QCD or non-perturbative inputs.