T014 $Z \to b\bar{s}+\bar{b}s,\ Z \to b\bar{d}+\bar{b}d,\ Z \to s\bar{d}+\bar{s}d$

Anarchic warped models naturally generate flavor-nonuniversal neutral-gauge couplings after rotating the localized fermion zero modes to the mass basis. For down-type quarks this creates off-diagonal \(Z d_i d_j\) vertices through zero-mode coupling nonuniversality, mixing with KK gauge bosons, and mixing with KK fermions. The custodial construction that protects \(Zb_L\bar b_L\) also matters for off-diagonal left-handed \(Z d_L^i\bar d_L^j\) couplings; in custodial RS, rare \(K\) and \(B\) amplitudes can instead be dominated by right-handed tree-level \(Z\) exchange. The direct on-shell \(Z\to q_iq_j\) bound is therefore a weak but conceptually clean collider diagnostic for the same effective vertices that enter \(K\), \(B_d\), and \(B_s\) rare decays and mixing. Per flavor\_catalog/PRIORITY\_TIERS.md, T014 is a this catalog wave SECONDARY entry: it provides the catalog's standalone FCNC-\(Z\) row, but has lower implementation priority than the Wave 1--7 PRIMARY constraints.

Blanke, Buras, Duling, Gemmler, and Gori 2009 is the key RS-specific update relative to the CFW era: it studies rare \(K\) and \(B\) decays in a custodial warped model and shows how tree-level \(Z\) exchange with flavor-changing down-quark couplings can dominate selected \(\Delta F=1\) amplitudes. Kamenik et al. 2024 updated the SM predictions, current direct-width bound, and future-collider reach for the \(bs\) and \(bd\) modes; those theory and projection numbers are retained in the sidecar rather than treated as T014 measured observables. The ECFA 2025 report folds this program into the Higgs/electroweak/top factory studies. Abu-Ajamieh et al. 2026 gives a dedicated quark-sector survey of flavor-violating \(Z\) couplings, translating the common direct width bound into effective-coupling conventions and comparing it with much stronger meson-oscillation constraints.

The direct \(2.9\times10^{-3}\) limit is flavor-inclusive and not a dedicated \(bs\), \(bd\), or \(sd\) analysis; it should not be treated as a powerful standalone RS exclusion. Low-energy constraints from \(K\), \(B_d\), and \(B_s\) mixing or rare decays are much stronger, but they test model-dependent linear combinations of left- and right-handed \(Z\) couplings and can be affected by correlations or cancellations with KK-gauge and other \(\Delta F=1,2\) contributions. A live implementation therefore needs an explicit convention for off-diagonal \(Z d_i d_j\) couplings and a decision on whether to impose only the weak direct width bound or the stronger low-energy-derived coupling bounds.

NO. A targeted grep for \(Z\to bs\), \(Z\to bd\), \(Z\to sd\), Zbs/Zbd/Zsd, and flavor-violating \(Z\)-coupling strings across quarkConstraints/, qcd/, flavorConstraints/, neutrinos/, yukawa/, warpConfig/, solvers/, scanParams/, and tests/ returned no hits. Broader searches find only existing \(\Delta F=2\) neutral-meson machinery (quarkConstraints/modern/phenomenology.py:23) and generic \(M_Z\)/\(\alpha_s(M_Z)\) support such as qcd/constants.py:11 and quarkConstraints/qcd\_running.py:100. There is no on-shell FCNC-\(Z\) branching-ratio likelihood or \(Z d_i d_j\) operator interface.

HIGH. Recording the external direct limit is straightforward, but a production RS constraint requires new electroweak \(\Delta F=1\) matching for off-diagonal \(Z\) couplings, custodial-embedding bookkeeping, and a policy for correlating direct \(Z\)-width information with already-implemented \(\Delta F=2\) and future rare-decay constraints. The current code only covers neutral-meson mixing and unrelated charged-lepton dipoles.

PDG2025\_Z\_hadronic\_width; ECFA2025\_FV\_Z\_decays; Kamenik2024\_FV\_Higgs\_Z\_FCCee; AbuAjamieh2026\_FV\_Z\_quark\_bounds; Eilam2002\_Rare\_Z\_decays; CsakiFalkowskiWeiler2008\_WarpedFlavor; BlankeBurasDulingGemmlerGori2009\_RareKBWarped.