Catalog · Beauty · B015

B015 $B \to X_s \ell^+ \ell^-$

Inclusive b $ \to $ s $\ell^+ \ell^-$ rare B decay

Status SUBTLETY-ADDED VERIFIED High Code: NO Priority Medium

Why this constrains the RS scan

This is a $\Delta B=1$ semileptonic FCNC channel. It probes flavor-changing $Z$ couplings, electroweak-penguin matching, and dipole correlations with $b\to s\gamma$, rather than the $\Delta F=2$ four-quark operators already used by the repo's neutral-meson constraints. In RS/anarchic flavor it is most useful as a diagnostic of semileptonic Wilson coefficients such as $C_7$, $C_9$, $C_{10}$ and their chirality-flipped partners.

What's changed since the original paper

Since the CFW 2008 RS-flavor baseline, the inclusive channel has gained a BaBar measurement and a modern HFLAV average, but it remains statistics-limited and experimentally based on sum-of-exclusive reconstruction. Theory has also matured: the 2015 Huber--Hurth--Lunghi analysis includes NNLO QCD, NLO QED, power corrections, collinear-photon effects, and Belle II projections with $50\,\mathrm{ab}^{-1}$. Current inclusive branching fractions are compatible with the SM within uncertainties; the sharper exclusive and LFU anomaly discussions belong in B016--B019.

Validity and model dependence

The inclusive perturbative windows are cleaner than exclusive form-factor observables, but a catalog single number is not a plug-in hard bound. The interpretation depends on $q^2$ binning, charm-resonance vetoes, photon treatment, and the mapping from RS flavor parameters to the $\Delta B=1$ weak Hamiltonian. It is best classified as a theory-controlled but mode-calculation-limited rare-decay constraint. In custodial RS, reduced $Z b_L b_L$ pressure can make this observable relatively more discriminating; quote RS bounds only after specifying custodial protection, fermion embeddings, and brane kinetic terms.

Code coverage in this repo

NO. The modern phenomenology policy enumerates only $\epsilon_K$, $K$, $B_d$, $B_s$, and $D^0$ at quarkConstraints/modern/phenomenology.py:23, and states that this is policy-only rather than a numeric backend at quarkConstraints/modern/phenomenology.py:166. The only live lepton flavor routine found is $\mu\to e\gamma$ at flavorConstraints/muToEGamma.py:75. Required greps over quarkConstraints/, qcd/, flavorConstraints/, neutrinos/, yukawa/, warpConfig/, solvers/, scanParams/, and tests/ found no $b\to s\ell\ell$, $X_s\ell\ell$, $C_9$, or $C_{10}$ implementation.

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

Implementation difficulty

HIGH. Production use would require a new $\Delta B=1$ semileptonic operator basis, matching and running for $C_7,C_9,C_{10}$ plus primed operators, bin-aware SM predictions, charm/QED treatment, and an experimental likelihood or covariance model.

Key references

Process-local snapshots: HFLAV2024Dec:BtoXsll, BaBar2014:BtoXsll, Belle2005:BtoXsll, HuberHurthLunghi2015:BtoXsll, and CsakiFalkowskiWeiler2008:CompositeFlavor.

fallback_value_uncertainty BR(B -> X_s ell+ ell-) = 5.84 +- +/- 0.69 10^-6

AMBIGUOUS

Match 1 of 2 snapshot line 12

L9: Relevant HFLAV Dec. 2024 table excerpt, units 10^-6:
L10: 
L11: Experiment | Measurement | Delta chi^2 | Reference | Comments
L12: Average | 5.84 +/- 0.69 | 3.22 | p=0.073 (ndf=1) |
L13:   Belle uses m_ll > 0.2 GeV/c^2, BABAR uses m_ll > 0.1 GeV/c^2.
L14:   The PDG uncertainty includes a scale factor. Treatment of charmonium
L15:   intermediate components differs between the results.

Match 2 of 2 snapshot line 16

L13:   Belle uses m_ll > 0.2 GeV/c^2, BABAR uses m_ll > 0.1 GeV/c^2.
L14:   The PDG uncertainty includes a scale factor. Treatment of charmonium
L15:   intermediate components differs between the results.
L16: PDG | 5.84 +1.31 -1.23 | | pdgLive |
L17: BaBar | 6.73 +0.70 -0.64 +0.60 -0.56 | 1.09 |
L18:   Phys. Rev. Lett. 112, 211802 (2014). Multiple systematic uncertainties
L19:   are added in quadrature.

fallback_value_uncertainty PDG-listed BR(B -> X_s ell+ ell-) = 5.84 +- +1.31/-1.23 10^-6

AMBIGUOUS

Match 1 of 2 snapshot line 12

L9: Relevant HFLAV Dec. 2024 table excerpt, units 10^-6:
L10: 
L11: Experiment | Measurement | Delta chi^2 | Reference | Comments
L12: Average | 5.84 +/- 0.69 | 3.22 | p=0.073 (ndf=1) |
L13:   Belle uses m_ll > 0.2 GeV/c^2, BABAR uses m_ll > 0.1 GeV/c^2.
L14:   The PDG uncertainty includes a scale factor. Treatment of charmonium
L15:   intermediate components differs between the results.

Match 2 of 2 snapshot line 16

L13:   Belle uses m_ll > 0.2 GeV/c^2, BABAR uses m_ll > 0.1 GeV/c^2.
L14:   The PDG uncertainty includes a scale factor. Treatment of charmonium
L15:   intermediate components differs between the results.
L16: PDG | 5.84 +1.31 -1.23 | | pdgLive |
L17: BaBar | 6.73 +0.70 -0.64 +0.60 -0.56 | 1.09 |
L18:   Phys. Rev. Lett. 112, 211802 (2014). Multiple systematic uncertainties
L19:   are added in quadrature.

fallback_value_uncertainty BaBar input BR(B -> X_s ell+ ell-) = 6.73 +- +0.70/-0.64 stat, +0.60/-0.56 total systematic per HFLAV quadrature 10^-6

AMBIGUOUS

Match 1 of 2 snapshot line 17

L14: two or fewer charged pions, and at most one pi0.
L15: Lepton-flavor-averaged inclusive branching fraction:
L16:   BF(B -> X_s l+ l-) =
L17:   (6.73 +0.70 -0.64 [stat] +0.34 -0.25 [exp syst] +/- 0.50 [model syst])
L18:   x 10^-6 for m(l+l-)^2 > 0.1 GeV^2/c^4.
L19: Direct CP asymmetry over the full dilepton mass range:
L20:   A_CP = 0.04 +/- 0.11 +/- 0.01.

Match 2 of 2 snapshot line 23

L20:   A_CP = 0.04 +/- 0.11 +/- 0.01.
L21: 
L22: Note: HFLAV combines the systematic uncertainties in quadrature and lists
L23: the BABAR input as 6.73 +0.70 -0.64 +0.60 -0.56 in units of 10^-6.

fallback_value_uncertainty Belle input BR(B -> X_s ell+ ell-) = 4.11 +- +/-0.83 stat, +0.85/-0.81 syst 10^-6

RESOLVED

Match snapshot line 16

L13: Reconstruction: X_s hadronic system from one charged kaon or K_S^0 and up
L14: to four pions, with at most one neutral pion.
L15: Lepton-flavor averaged inclusive branching fraction:
L16:   Br(B -> X_s l+ l-) = (4.11 +/- 0.83 [stat] +0.85 -0.81 [syst]) x 10^-6
L17:   for M_ll > 0.2 GeV/c^2.

fallback_value_uncertainty Experimental low-q2 weighted average = 1.58 +- +/-0.37 10^-6

RESOLVED

Match snapshot line 21

L18:   expected theory precision in these windows: order 10 percent
L19: 
L20: Experimental weighted averages quoted in the paper:
L21:   B(Bbar -> X_s l+ l-)_low^exp = (1.58 +/- 0.37) x 10^-6
L22:   B(Bbar -> X_s l+ l-)_high^exp = (0.48 +/- 0.10) x 10^-6
L23: 
L24: SM branching-ratio predictions quoted in the paper:

fallback_value_uncertainty Experimental high-q2 weighted average = 0.48 +- +/-0.10 10^-6

RESOLVED

Match snapshot line 22

L19: 
L20: Experimental weighted averages quoted in the paper:
L21:   B(Bbar -> X_s l+ l-)_low^exp = (1.58 +/- 0.37) x 10^-6
L22:   B(Bbar -> X_s l+ l-)_high^exp = (0.48 +/- 0.10) x 10^-6
L23: 
L24: SM branching-ratio predictions quoted in the paper:
L25:   B[1,6]_ee = (1.67 +/- 0.10) x 10^-6

fallback_value_uncertainty Belle II projection luminosity = 50 ab^-1

RESOLVED

Match snapshot line 31

L28:   B[>14.4]_mumu = (2.53 +/- 0.70) x 10^-7
L29: 
L30: Belle II assumptions/prospects:
L31:   Expected final integrated luminosity: 50 ab^-1.
L32:   The paper rescales from BABAR's 0.4242 ab^-1 and studies 95 percent CL
L33:   constraints in the R9-R10 plane from future Belle II measurements.

fallback_value_uncertainty SM BR[1,6]_ee = 1.67 +- +/-0.10 10^-6

RESOLVED

Match snapshot line 25

L22:   B(Bbar -> X_s l+ l-)_high^exp = (0.48 +/- 0.10) x 10^-6
L23: 
L24: SM branching-ratio predictions quoted in the paper:
L25:   B[1,6]_ee = (1.67 +/- 0.10) x 10^-6
L26:   B[1,6]_mumu = (1.62 +/- 0.09) x 10^-6
L27:   B[>14.4]_ee = (2.20 +/- 0.70) x 10^-7
L28:   B[>14.4]_mumu = (2.53 +/- 0.70) x 10^-7

fallback_value_uncertainty SM BR[1,6]_mumu = 1.62 +- +/-0.09 10^-6

RESOLVED

Match snapshot line 26

L23: 
L24: SM branching-ratio predictions quoted in the paper:
L25:   B[1,6]_ee = (1.67 +/- 0.10) x 10^-6
L26:   B[1,6]_mumu = (1.62 +/- 0.09) x 10^-6
L27:   B[>14.4]_ee = (2.20 +/- 0.70) x 10^-7
L28:   B[>14.4]_mumu = (2.53 +/- 0.70) x 10^-7
L29: