T012 $Z \to c \bar{c}\,\text{pole observables: }\,R_c, A_{FB}^{0,c}, A_c$
Z-pole charm-quark partial-width ratio and asymmetries Status REVIEWED VERIFIED High Code: NO Priority Medium
Why this constrains the RS scan
These observables constrain flavor-diagonal shifts in the left- and
right-handed \(Zc\bar c\) couplings. In anarchic warped models, the charm
coupling shifts are usually less severe than the \(Zb\bar b\) constraint
because the charm is not tied to the same custodial-protection problem as the
third-generation bottom doublet. They are still useful as a consistency check
on up-sector fermion localizations, bulk multiplet assignments, and the same
gauge-boson mixing effects that generate flavor-changing \(Z\) couplings. A
large shift in \(Zc\bar c\) would also feed the global Z-pole heavy-flavour fit
that correlates charm and bottom pseudo-observables.
What's changed since the original paper
No new LEP/SLC-style experimental average supersedes the legacy Z-pole charm
combination, so the PDG value remains data-dominated by the final LEP/SLC
heavy-flavour fit. Since arXiv:0804.1954 (
cfw\_2008\_rs\_flavor),
the RS literature has made the model dependence of ordinary \(Zf\bar f\)
couplings more explicit; the Casagrande--Goertz--Haisch--Neubert--Pfoh setup
treats the standard \(Z\) couplings, flavor-changing \(Z\) effects, and
electroweak precision constraints in a unified warped-flavor framework
(casagrande\_2008\_rs\_ewpt). On the Standard-Model side, the
fermionic electroweak two-loop calculation of Z partial widths and branching
ratios was completed in arXiv:1401.2447
(freitas\_2014\_z\_widths). Prospective FCC-ee work, including
arXiv:2107.00616 (alcaraz\_2021\_z\_lineshape\_fcc), revisits how
\(R_c\) and \(A_{\rm FB}^{c}\) could be improved with modern heavy-flavour
tagging, but those studies are not current experimental inputs.Validity and model dependence
This is a precision electroweak coupling constraint, not a flavor-changing
decay or a stand-alone RS flavor bound. It is robust as a measured Z-pole
pseudo-observable, but the translation into a bound on a 5D model is
embedding-dependent: custodial symmetry, the representation of the up-sector
quarks, brane kinetic terms, and fermion localization choices all affect the
predicted \(\delta g_{Lc}\) and \(\delta g_{Rc}\). \(R_c^0\) is mostly a width
constraint, while \(A_c\) and \(A_{\rm FB}^{0,c}\) carry chiral information and
depend on the electroweak-pole fit conventions.
Code coverage in this repo
NO. The required greps found no implementation of \(R_c\), \(A_c\),
\(A_{\rm FB}^{0,c}\), a Zcc coupling-shift calculation, or a correlated
electroweak-pole likelihood in
quarkConstraints/, qcd/,
flavorConstraints/, neutrinos/, yukawa/,
warpConfig/, solvers/, scanParams/, or
tests/. The only Z-related matches were generic \(M_Z\) support in
qcd/running.py:3, qcd/constants.py:11, and
quarkConstraints/qcd\_running.py:100; process-specific searches also
returned unrelated \(R_\chi\) hadronic helpers.
Linked evidence (opens GitHub blob at flavor-catalog-website/2026q2):
Implementation difficulty
HIGH. A live constraint would need a new electroweak-pole observable
module, LEP/SLC covariance handling for heavy-flavour pseudo-observables, and
model-specific matching from the warped spectrum to \(\delta g_{Lc}\) and
\(\delta g_{Rc}\). This is not covered by the existing \(\Delta F=2\) operator
basis or the lepton-dipole path.
Reason: A live constraint would require new electroweak-pole observable handling, LEP/SLC heavy-flavour covariance data, and model-specific matching to Z c_L and Z c_R coupling shifts; the existing $\Delta F = 2$ and lepton-dipole paths do not cover it.
Key references
pdg\_2025\_z\_boson\_charm; lepslc\_2006\_z\_resonance\_charm;
cfw\_2008\_rs\_flavor; casagrande\_2008\_rs\_ewpt;
freitas\_2014\_z\_widths; alcaraz\_2021\_z\_lineshape\_fcc.