B016 $B \to K \ell^+ \ell^-$

This is a \(\Delta B=1\) flavor-changing neutral-current probe of the same down-sector flavor structure that appears in \(B_s\) mixing, but it tests semileptonic and dipole operators rather than four-quark \(\Delta F=2\) operators. In warped or anarchic-flavor models, flavor-changing \(Z\) or KK electroweak-gauge couplings and loop dipoles can feed \(C_7\), \(C_9\), \(C_{10}\), and primed semileptonic coefficients. The branching fractions are therefore useful diagnostics of \(b\to s\ell\ell\) structure, while the LFU ratios and \(K^*\) angular program carry related but distinct information.

Since the arXiv:0804.1954 RS-flavor baseline, source key CsakiFalkowskiWeiler2008:CompositeFlavor, this channel moved from sparse \(B\)-factory evidence into precision rare-\(B\) phenomenology. BaBar provided early post-baseline \(B\to K^{(*)}\ell^+\ell^-\) asymmetry inputs (BaBar2009:BtoKllAsymmetries). LHCb measured differential \(B\to K^{(*)}\mu^+\mu^-\) branching fractions and isospin asymmetries with hadron-collider data (LHCb2014:BtoKmumuDifferential), and Belle measured both electron and muon \(B\to K\ell\ell\) modes together with \(R_K\) (Belle2021:BtoKllLFU). HFLAV now provides current charged and neutral exclusive-\(K\) branching-fraction averages, while the separate \(R_K\) updates shifted the clean LFU-anomaly interpretation toward correlated semileptonic-Wilson-coefficient and hadronic-systematics questions.

The HFLAV branching fractions are measured observables and are appropriate for cataloging, but using them as hard RS cuts is model-dependent. A faithful constraint must specify the dilepton \(q^2\) regions, charmonium vetoes, form-factor inputs, nonlocal charm treatment, correlations with \(C_7\) from \(b\to s\gamma\), and correlations with \(R_K\) and \(B\to K^*\ell\ell\). The entry is therefore a semileptonic \(\Delta B=1\) constraint seed, not a drop-in replacement for a global \(b\to s\ell\ell\) fit.

NO. The modern phenomenology surface lists only \(\epsilon_K\), \(K\), \(B_d\), \(B_s\), and \(D^0\) systems at quarkConstraints/modern/phenomenology.py:23. The only live lepton-flavor module is \(\mu\to e\gamma\), implemented at flavorConstraints/muToEGamma.py:75. Required greps over the implementation directories found no \(B\to K\ell\ell\), \(b\to s\ell\ell\), \(C_9\), \(C_{10}\), or \(R_K\) backend.

HIGH. Integration would require a new \(\Delta B=1\) semileptonic Hamiltonian, matching to \(C_7\), \(C_9\), \(C_{10}\), and primed operators, \(q^2\)-bin handling, form factors, nonlocal-charm uncertainties, and experimental covariance support. The existing \(\Delta F=2\) basis is not enough.

Process-local snapshots: HFLAV2025Dec:BplusToKplusll, HFLAV2025Dec:B0ToK0ll, Belle2021:BtoKllLFU, LHCb2014:BtoKmumuDifferential, BaBar2009:BtoKllAsymmetries, and CsakiFalkowskiWeiler2008:CompositeFlavor.