T010 $Z \to b \bar{b}\,\text{pole observables: }\,R_b, A_{FB}^{0,b}, A_b$
Z-pole bottom-quark partial-width ratio and asymmetries Status SUBTLETY-ADDED VERIFIED High Code: NO Priority High
Why this constrains the RS scan
In warped models with anarchic five-dimensional Yukawas, the third-generation
left-handed doublet is typically localized closer to the IR brane to account
for the top mass. That same localization makes the \(Z b_L\bar b_L\) coupling
sensitive to gauge-boson and fermion mixing with Kaluza-Klein states. \(R_b\)
mostly constrains the total \(Z\to b\bar b\) partial width, while \(A_b\) and
\(A_{\rm FB}^{0,b}\) test the chiral balance of the bottom coupling. Custodial
extensions, especially protections of \(Z b_L\bar b_L\), are therefore not a
minor detail; they determine whether this observable is a leading bound or a
diagnostic cross-check.
What's changed since the original paper
There has not been a new LEP/SLC-style experimental average superseding the
Z-pole combination, so the PDG value remains legacy-data dominated. The
post-CFW theory story did change: Casagrande et al. gave a detailed RS
electroweak-precision treatment including Zbb couplings, while later SM work
completed the fermionic two-loop description of Z partial widths and branching
ratios (
freitas\_2014\_z\_widths). Future-collider studies now
revisit the experimental systematics of \(R_b\) and \(A_{\rm FB}^b\); the
FCC-ee projection quotes relative uncertainties of order \(0.01\%\), but it is
a prospective reference rather than a current constraint
(fcc\_ee\_2025\_zbb\_projection.txt).Validity and model dependence
This is a precision electroweak coupling constraint, not a flavor-changing
amplitude by itself. It is highly relevant for RS flavor because the same
fermion localizations and custodial choices that control flavor violation also
set the tree-level Z-bottom coupling shifts. Its interpretation is therefore
model-dependent: minimal bulk RS, custodial RS, brane kinetic terms, and
different embeddings of the bottom multiplet can move the constraint
substantially. \(A_{\rm FB}^{0,b}\) also contains the initial-state leptonic
asymmetry input, so \(A_b\) is the cleaner bottom-coupling handle.
In custodial RS, reduced \(Z b_L b_L\) pressure can make this observable
relatively less direct as a mass setter or more diagnostic of embeddings;
quote RS bounds only after specifying custodial protection, fermion embeddings,
and brane kinetic terms.
Code coverage in this repo
NO. The required greps found no implementation of \(R_b\), \(A_b\),
\(A_{\rm FB}^{0,b}\), or a Zbb electroweak-pole likelihood in
quarkConstraints/, flavorConstraints/, neutrinos/,
yukawa/, qcd/, 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.Implementation difficulty
HIGH. A catalog-only record is straightforward, but a live constraint would
need a new electroweak-pole observable module, a correlated treatment of the
LEP/SLC pseudo-observables, and model-specific matching from the 5D spectrum to
\(\delta g_{Lb}\) and \(\delta g_{Rb}\). The largest blocker is not lattice
input or QCD running; it is the RS electroweak matching and custodial-symmetry
bookkeeping.
Reason: A live constraint would require new electroweak-pole observable handling plus RS matching for shifts in Z b_L and Z b_R couplings, including custodial-protection model dependence and LEP/SLC correlations.
Key references
pdg\_2025\_z\_boson; lepslc\_2006\_z\_resonance;
cfw\_2008\_rs\_flavor; casagrande\_2008\_rs\_ewpt;
freitas\_2014\_z\_widths; fcc\_ee\_2025\_zbb\_projection.