K018 $K_{l3}: K \to \pi e \nu \,\text{ and }\, K \to \pi \mu \nu; |V_{us}| f_+(0)$
Kaon semileptonic decays and source-level $V_{us}$ input Status REVIEWED VERIFIED High Code: PARTIAL Priority Low
Why this constrains the RS scan
This is a tree-level charged-current process, not a neutral-meson
\(\Delta F=2\) observable. In the current quark scan it is relevant mainly
as the semileptonic source behind the fitted \(|V_{us}|\) target and the
EW002 first-row unitarity test. Nonminimal warped models with modified
\(W\)-quark couplings, vector-like fermion mixing, lepton nonuniversality, or
right-handed charged currents could shift the extracted \(V_{us}\) or the
\(K_{\mu3}/K_{e3}\) consistency test, but a minimal KK-gluon flavor analysis
does not map this measurement into the existing operator basis.
What's changed since the original paper
The 2008 RS-flavor baseline
CsakiFalkowskiWeiler:RSFlavor2008
centered on flavor-changing neutral constraints, so the post-2008 K018 story
is precision charged-current consolidation. The sidecar entries
FlaviaNet2010:K018:average\_fplus\_vus and
FlaviaNet2010:K018:r\_mue record the 2010 FlaviaNet average
\(|V_{us}|f_+(0)=0.2163(5)\) and \(K_{\mu3}/K_{e3}\) universality ratio
\(r_{\mu e}=1.002(5)\). The 2025 PDG update keeps the same source-level
convention while tightening the average to \(0.21656(35)\). FLAG 2024 supplies
the auxiliary lattice normalization, \(f_+(0)=0.9698(17)\), and the derived
\(|V_{us}|=0.22328(58)\), which feed the CKM-unitarity entry rather than
replacing the measured K018 product.Validity and model dependence
The measured \(|V_{us}|f_+(0)\) product is experimentally robust but depends
on consistent radiative, isospin, and phase-space conventions. The derived
\(|V_{us}|\) additionally depends on the lattice \(f_+(0)\) average. As an
RS constraint, K018 is model-dependent: it is a charged-current CKM and
lepton-universality diagnostic, not a standalone FCNC bound unless the model
specifies nonstandard \(W\), scalar, tensor, or right-handed-current effects.
Code coverage in this repo
PARTIAL. The repo has a generic CKM target containing \(|V_{us}|\):
quarkConstraints/scan.py:43 documents the PDG-derived CKM averages,
quarkConstraints/scan.py:247 labels the reduced CKM observable as
Vus, and tests/test\_quark\_fit.py:587 anchors the target
against PDG 2024. The coverage grep found no \(K_{\ell3}\) decay-rate,
\(|V_{us}|f_+(0)\), \(f_+(0)\), \(K_{e3}\), or \(K_{\mu3}\) implementation.
The modern flavor surface is still limited to \(\varepsilon_K\), \(K\),
\(B_d\), \(B_s\), and \(D0\) systems at
quarkConstraints/modern/phenomenology.py:23.
Linked evidence (opens GitHub blob at flavor-catalog-website/2026q2):
Implementation difficulty
HIGH. A live K018 constraint would need a charged-current
semileptonic likelihood or EFT wrapper, radiative/isospin convention
bookkeeping, lattice \(f_+(0)\) provenance, and a decision about whether it is
implemented as a direct \(V_{us}\) target, an EW002 sub-input, or a BSM
charged-current operator constraint. The existing \(\Delta F=2\)
SLL/SLR/VLL/VRR/LR machinery does not cover it.
Reason: A live K018 constraint requires a new charged-current semileptonic observable or EW002 sub-likelihood, radiative/isospin and phase-space conventions, lattice f_+(0) provenance, and BSM charged-current matching. Existing $\Delta F = 2$ operators do not cover it.
Key references
PDG2025:K018Kl3: PDG 2025 \(K_{\ell3}\) product average and mode values.FLAG2024:K018KaonSemileptonic: lattice \(f_+(0)\) normalization and derived \(|V_{us}|\).FlaviaNet:K018Kaon2010: post-2008 \(K_{\ell3}\) consolidation and \(r_{\mu e}\).CsakiFalkowskiWeiler:RSFlavor2008: 2008 warped-flavor context.