EW003 $|V_{cb}|_{\,\text{inclusive}\,} \,\text{vs}\, |V_{cb}|_{\,\text{exclusive}\,}; |V_{ub}|_{\,\text{inclusive}\,} \,\text{vs}\, |V_{ub}|_{\,\text{exclusive}\,}$
$|V_{cb}|$ and $|V_{ub}|$ inclusive-exclusive semileptonic tensions Status REVIEWED VERIFIED High Code: PARTIAL Priority Low
Why this constrains the RS scan
The present scan fits CKM observables as output of anarchic quark masses, so
the inclusive--exclusive split is a diagnostic for how much CKM target choice
can move flavor predictions. In an RS extension with non-SM charged-current
operators, the same observables also set the normalization for \(b\to c\) and
\(b\to u\) semitauonic Wilson-coefficient fits.
What's changed since the original paper
Relative to arXiv:0804.1954, the main change is not a new RS formula but a
new input ecosystem. Belle, Belle II, BaBar, and LHCb now feed HFLAV averages;
inclusive \(|V_{cb}|\) uses mature kinetic and \(q^2\)-moment heavy-quark
expansion fits; and FLAG 2024 provides full-recoil lattice-plus-experiment
fits for \(B\to D^{(*)}\ell\nu\) and \(B\to\pi\ell\nu\). The same period also
turned \(R(D^{(*)})\), \(B_c\to\tau\nu\), and \(B\to(\pi,\rho,\omega)\tau\nu\)
into standard charged-current EFT interpretation channels.
Validity and model dependence
For \(e,\mu\) final states these are CKM extraction inputs, not clean
standalone BSM exclusions. Inclusive values depend on heavy-quark expansion
schemes and shape-function/model choices, while exclusive values depend on
lattice form factors, parameterization choices, and experimental correlations.
Tau-mode translations are more model dependent because vector, scalar, and
tensor operators can change both rates and templates.
Code coverage in this repo
PARTIAL. CKM target handling exists, including \(|V_{cb}|\) and
\(|V_{ub}|\) tolerances at
quarkConstraints/scan.py:42,
quarkConstraints/scan.py:46, quarkConstraints/scan.py:47,
quarkConstraints/scan.py:52, and the regression check at
tests/test\_quark\_fit.py:575. No grep hit implements inclusive or
exclusive semileptonic \(B\) rates, \(B\to D^{(*)}\ell\nu\),
\(B\to\pi\ell\nu\), or \(b\to c/u\,\tau\nu\) WET operators in
quarkConstraints/, qcd/, flavorConstraints/,
neutrinos/, yukawa/, warpConfig/,
solvers/, scanParams/, or tests/.
Linked evidence (opens GitHub blob at flavor-catalog-website/2026q2):
Implementation difficulty
HIGH. A production constraint would need a new charged-current
semileptonic likelihood, scheme handling for inclusive extractions, lattice
form-factor inputs for exclusive modes, and optional \(b\to c/u\,\tau\nu\)
Wilson operators. This is outside the existing \(\Delta F=2\) basis.
Reason: A live EW003 constraint needs a new charged-current semileptonic likelihood, inclusive-scheme handling, exclusive lattice form-factor inputs, and optional $b \to c/u \tau \nu$ WET operator matching. This is not covered by the existing $\Delta F = 2$ SLL/SLR/VLL/VRR/LR1/LR2 machinery.
Key references
pdg\_2024\_vcb\_vub;
hflav\_2023\_semileptonic\_report;
flag\_2024\_b\_semileptonic\_lattice;
iguro\_2024\_bc\_tau\_global\_fit;
bhatta\_2021\_bu\_tau\_np;
cfw\_2008\_rs\_flavor\_baseline.