Catalog · Beauty · B019

B019 $R_{K^*}$

Lepton-flavor universality ratio in B0 $ \to K*0 \ell^+ \ell^-$

Status SUBTLETY-ADDED VERIFIED High Code: NO Priority Medium

Why this constrains the RS scan

$R_{K^*}$ probes $\Delta B=1$ semileptonic FCNC amplitudes in $b\to s\ell^+\ell^-$. In RS/anarchic-flavor language it is sensitive to nonuniversal lepton couplings and flavor-changing $b$-$s$ currents from KK gauge, $Z$, or other semileptonic effects. It is therefore complementary to the repo's existing neutral-meson $\Delta F=2$ constraints and to B018's pseudoscalar $R_K$ ratio.

What's changed since the original paper

The CFW 2008 baseline (CsakiFalkowskiWeiler2008:CompositeFlavor) predates the $R_{K^*}$ anomaly program. The key post-2008 milestone was the LHCb 2017 measurement (LHCb2017:RKstar): $R_{K^*}=0.66^{+0.11}_{-0.07}\pm0.03$ for $0.045LHCb2023:RKRKstarDetailed). Theory work by Bordone--Isidori--Pattori clarified that the central bin is SM-unity to about a \(0.01$ QED uncertainty, while low-$q^2$ $R_{K^*}$ needs explicit photon-pole and radiative treatment (BordoneIsidoriPattori2016:RKRKstarSM).

Validity and model dependence

This is a clean LFU null test, but it is not a drop-in bound for the current quark scan. The ratio cancels many hadronic uncertainties, yet a usable constraint still depends on bin definitions, electron bremsstrahlung, radiative corrections, correlations, and a model prediction for lepton-specific $C_9^{\ell}$, $C_{10}^{\ell}$, and primed semileptonic coefficients. In custodial RS, reduced $Z b_L b_L$ pressure can make $R_{K^*}$ relatively more discriminating as an LFU cross-check; quote RS bounds only after specifying custodial protection, fermion embeddings, and brane kinetic terms. Use $R_K/R_{K^*}$ as precision LFU null tests; do not impose the pre-2023 anomaly narrative as a prior.

Code coverage in this repo

NO. Required greps over quarkConstraints/, qcd/, flavorConstraints/, neutrinos/, yukawa/, warpConfig/, solvers/, scanParams/, and tests/ found no $R_{K^*}$, $K^{*0}e e$, $K^{*0}\mu\mu$, $C_9$, $C_{10}$, LFU, or $b\to s\ell\ell$ implementation. The modern phenomenology surface enumerates only $\epsilon_K$, $K$, $B_d$, $B_s$, and $D^0$ at quarkConstraints/modern/phenomenology.py:23, and it is policy-only at quarkConstraints/modern/phenomenology.py:166. The legacy inputs are $\Delta F=2$ at quarkConstraints/deltaf2.py:209, with $B_d$ and $B_s$ mixing evaluators at quarkConstraints/deltaf2.py:903 and quarkConstraints/deltaf2.py:922. The only live lepton-flavor routine found is $\mu\to e\gamma$ at flavorConstraints/muToEGamma.py:75.

Linked evidence (opens GitHub blob at flavor-catalog-website/2026q2):

Implementation difficulty

HIGH. Integration requires a new $\Delta B=1$ semileptonic Hamiltonian, lepton-specific $C_9/C_{10}$ and primed coefficients, bin-aware SM/QED predictions, and HFLAV/LHCb likelihood or covariance handling.

Key references

Process-local reference keys before bibliography consolidation: HFLAV2025Dec:RKstarLowQ2LHCb, HFLAV2025Dec:RKstarCentralQ2, LHCb2023:RKRKstarDetailed, LHCb2017:RKstar, BordoneIsidoriPattori2016:RKRKstarSM, and CsakiFalkowskiWeiler2008:CompositeFlavor.

fallback_value_uncertainty R_K* low-q2 = 0.927 +- +/- 0.097

AMBIGUOUS

Match 1 of 2 snapshot line 15

L12: <h1>$\frac{ {\cal{B}}(B^0 \to K^*(892)^0 \mu^+ \mu^-) }{ {\cal{B}}(B^0 \to K^*(892)^0 e^+ e^-) },~0.1 < m^2_{\ell^+\ell^-} < 1.1~\rm{GeV^2/c^4}$</h1>
L13: <p><img src="BR_B0_K*0_mu+_mu-..BR_B0_K*0_e+_e-__bin1b.png"></p>
L14: <p><table border="1"><tr><th>Experiment</th><th>Measurement [10<sup>0</sup>]</th><th>$\Delta\chi^2$</th><th>Reference</th><th>Comments</th></tr>
L15: <tr><td><b>Average</b></td><td><b>$0.927 \pm0.097$</b></td><td></td><td></td><td></td></tr>
L16: <tr><td>LHCb</td><td>$0.927\,^{+0.093}_{-0.087}\,^{+0.036}_{-0.035}$</td><td>0.00</td>
L17: <td><a href="https://inspirehep.net/literature/2684465">Phys.Rev.D <b>108</b>,032002 (2023)</a></td><td></td></tr>
L18: </table>

Match 2 of 2 snapshot line 16

L13: <p><img src="BR_B0_K*0_mu+_mu-..BR_B0_K*0_e+_e-__bin1b.png"></p>
L14: <p><table border="1"><tr><th>Experiment</th><th>Measurement [10<sup>0</sup>]</th><th>$\Delta\chi^2$</th><th>Reference</th><th>Comments</th></tr>
L15: <tr><td><b>Average</b></td><td><b>$0.927 \pm0.097$</b></td><td></td><td></td><td></td></tr>
L16: <tr><td>LHCb</td><td>$0.927\,^{+0.093}_{-0.087}\,^{+0.036}_{-0.035}$</td><td>0.00</td>
L17: <td><a href="https://inspirehep.net/literature/2684465">Phys.Rev.D <b>108</b>,032002 (2023)</a></td><td></td></tr>
L18: </table>
L19: </p>

fallback_value_uncertainty R_K* central-q2 = 1.028 +- +/- 0.074

RESOLVED

Match snapshot line 15

L12: <h1>$\frac{ {\cal{B}}(B^0 \to K^*(892)^0 \mu^+ \mu^-) }{ {\cal{B}}(B^0 \to K^*(892)^0 e^+ e^-) },~1.1 < m^2_{\ell^+\ell^-} < 6.0~\rm{GeV^2/c^4}$</h1>
L13: <p><img src="BR_B0_K*0_mu+_mu-..BR_B0_K*0_e+_e-__bin2.png"></p>
L14: <p><table border="1"><tr><th>Experiment</th><th>Measurement [10<sup>0</sup>]</th><th>$\Delta\chi^2$</th><th>Reference</th><th>Comments</th></tr>
L15: <tr><td><b>Average</b></td><td><b>$1.028 \pm0.074$</b></td><td>0.00</td><td>$p=0.95$ (ndf=1)</td><td></td></tr>
L16: <tr><td>LHCb</td><td>$1.027\,^{+0.072}_{-0.068}\,^{+0.027}_{-0.026}$</td><td>0.00</td>
L17: <td><a href="https://inspirehep.net/literature/2684465">Phys.Rev.D <b>108</b>,032002 (2023)</a></td><td></td></tr>
L18: <tr><td>Belle</td><td>$1.06\,^{+0.63}_{-0.38} \pm0.14$</td><td>0.00</td>

fallback_value_uncertainty LHCb 2017 low-q2 R_K* = 0.66 +- +0.11/-0.07 stat, +/-0.03 syst

RESOLVED

Match snapshot line 13

L10: 
L11: Relevant arXiv-source excerpt from title/results/conclusion:
L12: The measured ratios were
L13:   R_K* = 0.66^{+0.11}_{-0.07} (stat) +/- 0.03 (syst)
L14:     for 0.045 < q^2 < 1.1 GeV^2/c^4,
L15:   R_K* = 0.69^{+0.11}_{-0.07} (stat) +/- 0.05 (syst)
L16:     for 1.1 < q^2 < 6.0 GeV^2/c^4.

fallback_value_uncertainty LHCb 2017 central-q2 R_K* = 0.69 +- +0.11/-0.07 stat, +/-0.05 syst

RESOLVED

Match snapshot line 15

L12: The measured ratios were
L13:   R_K* = 0.66^{+0.11}_{-0.07} (stat) +/- 0.03 (syst)
L14:     for 0.045 < q^2 < 1.1 GeV^2/c^4,
L15:   R_K* = 0.69^{+0.11}_{-0.07} (stat) +/- 0.05 (syst)
L16:     for 1.1 < q^2 < 6.0 GeV^2/c^4.
L17: 
L18: The publication reported compatibility with SM expectations at approximately

fallback_value_uncertainty LHCb 2023 SM compatibility = 0.2 standard deviations

RESOLVED

Match snapshot line 30

L27: 
L28: Conclusion excerpt:
L29: The four measured relative decay rates are compatible with the SM, with the
L30: combined result agreeing with the SM prediction at 0.2 standard deviations.
L31: The results supersede previous LHCb measurements of R_K and R_K*; both R_K*
L32: central values move upward relative to the previous R_K* publication.

fallback_value_uncertainty BIP 2016 central-q2 SM R_K* = 1.00 +- +/- 0.01_QED

AMBIGUOUS

Match 1 of 3 snapshot line 17

L14: physics beyond the SM with small theoretical uncertainties.
L15: 
L16: For central q^2, the authors quote
L17:   R_{K*}[1.1, 6.0]^{SM} = 1.00 +/- 0.01_QED.
L18: 
L19: For low q^2, their added note gives
L20:   R_{K*}[0.045, 1.1]^{SM} = 0.906 +/- 0.028_th,

Match 2 of 3 snapshot line 20

L17:   R_{K*}[1.1, 6.0]^{SM} = 1.00 +/- 0.01_QED.
L18: 
L19: For low q^2, their added note gives
L20:   R_{K*}[0.045, 1.1]^{SM} = 0.906 +/- 0.028_th,
L21:   R_{K*}[0.1, 1.1]^{SM} = 0.983 +/- 0.014_th.
L22: 
L23: They state that a deviation of R_K or R_K* from unity exceeding the percent

Match 3 of 3 snapshot line 21

L18: 
L19: For low q^2, their added note gives
L20:   R_{K*}[0.045, 1.1]^{SM} = 0.906 +/- 0.028_th,
L21:   R_{K*}[0.1, 1.1]^{SM} = 0.983 +/- 0.014_th.
L22: 
L23: They state that a deviation of R_K or R_K* from unity exceeding the percent
L24: level, with consistent experimental cuts and radiative treatment, is a clean

fallback_value_uncertainty BIP 2016 low-q2 SM R_K* for LHCb 2023 bin = 0.983 +- +/- 0.014_th

RESOLVED

Match snapshot line 21

L18: 
L19: For low q^2, their added note gives
L20:   R_{K*}[0.045, 1.1]^{SM} = 0.906 +/- 0.028_th,
L21:   R_{K*}[0.1, 1.1]^{SM} = 0.983 +/- 0.014_th.
L22: 
L23: They state that a deviation of R_K or R_K* from unity exceeding the percent
L24: level, with consistent experimental cuts and radiative treatment, is a clean