Pith. sign in
def

charm

definition
show as:
module
IndisputableMonolith.Cosmology.GStarThresholds
domain
Cosmology
line
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plain-language theorem explainer

Defines the charm quark as a thermal species with mass threshold 1.27 GeV, 12 internal degrees of freedom, and fermionic statistics. Cosmology code that builds the step-function g_*(T) cites this entry when counting electroweak-sector content above the charm threshold. The body is a four-field structure literal; no proof obligations.

Claim. The charm quark is the thermal species with name $\mathrm{charm}$, mass threshold $m = 127/100\,\mathrm{GeV}$ (PDG-rounded $\approx 1.27\,\mathrm{GeV}$), $g = 12$ internal degrees of freedom, and fermionic statistics.

background

The module implements the standard instantaneous-threshold model of $g_*(T)$, the effective relativistic degrees of freedom as a function of temperature. Each species contributes its full DOF count while $T$ exceeds its mass threshold and drops out below it; the QCD crossover at $T_{\mathrm{QCD}}\approx 0.15,\mathrm{GeV}$ switches the strong sector from QGP to hadronic content.

A thermal species is a four-field record: a name string, a rational mass threshold in GeV (only order relative to $T$ matters), a natural number of internal degrees of freedom, and a Boolean flag for fermionic versus bosonic statistics. Masses are imported PDG-rounded rationals; the $\varphi$-ladder mass modules predict them independently and are not re-derived here.

Charm sits in the electroweak-sector table alongside top, Higgs, $Z$, $W$, bottom, tau, muon, and electron. The 12 DOF count is the usual SM bookkeeping for a colored Dirac quark ($2\times 2\times 3$).

proof idea

Pure definition: a structure literal packing the four Species fields. No tactics, no lemmas, no proof term beyond the constructor application $\langle\texttt{"charm"},,127/100,,12,,\mathsf{true}\rangle$.

why it matters

Feeds the electroweak species list used to evaluate the step-function $g_(T)$ as temperature falls through the charm threshold. Downstream mass-verification code also indexes the charm fermion for charge, rung, sector, and positivity of the predicted mass on the $\varphi$-ladder. The entry is imported SM content (ordering threshold only), not an RS derivation of the charm mass; RS mass modules supply that prediction separately. Closes part of the external-review gap that the repository lacked a temperature-dependent $g_(T)$.

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