B007 $B_s^0 \to e^+ e^-, B^0 \to e^+ e^-$
Rare electronic leptonic neutral-B decays Status REVIEWED VERIFIED Medium Code: NO Priority Low
PDG / equivalent values
| Observable | Value | Year | Experiment / source | Provenance |
|---|---|---|---|---|
| $BR(B_s0 \to $ e+e-) | 9.4e-9 branching fraction 90% CL (upper) | 2026 | PDG2026_BsBdEe | source ↑ |
| BR(B0 $ \to $ e+e-) | 2.5e-9 branching fraction 90% CL (upper) | 2026 | PDG2026_BsBdEe | source ↑ |
| $BR(B_s0 \to $ e+e-) | 1.12e-8 branching fraction 95% CL (upper) | 2020 | LHCb2020_BsBdEe | source ↑ |
| BR(B0 $ \to $ e+e-) | 3e-9 branching fraction 95% CL (upper) | 2020 | LHCb2020_BsBdEe | source ↑ |
| $BR(B_s0 \to $ e+e-) | 2.8e-7 branching fraction 90% CL (upper) | 2009 | CDF2009_BsBdEe | source ↑ |
| BR(B0 $ \to $ e+e-) | 8.3e-8 branching fraction 90% CL (upper) | 2009 | CDF2009_BsBdEe | source ↑ |
| BR(B0 $ \to $ e+e-) | 1.13e-7 branching fraction 90% CL (upper) | 2008 | BaBar2008_BdEe | source ↑ |
| BR(B0 $ \to $ e+e-) | 1.9e-7 branching fraction 90% CL (upper) | 2003 | PDG2026_BsBdEe | source ↑ |
Why this constrains the RS scan
SECONDARY tier. Per
flavor\_catalog/PRIORITY\_TIERS.md,
this process is a deferred this catalog wave promotion: it is less urgent than the
this catalog wave--7 PRIMARY set, but it probes an electron-specific direction absent
from \(B005/B006\). In anarchic RS models, non-universal fermion localization
generates flavor-changing \(Z\), KK electroweak-gauge, Higgs, radion, or other
scalar exchanges after rotating to the mass basis. Axial-vector contributions
remain helicity suppressed in the Standard Model pattern, while scalar and
pseudoscalar operators can be chirality enhanced relative to the electronic SM
amplitude. The mode is therefore a useful handle on electron-sector
misalignment and on any 5D-Yukawa or brane-Higgs structure that feeds
\(C_S^{(\prime)}\) or \(C_P^{(\prime)}\) differently from \(C_{10}^{(\prime)}\).What's changed since the original paper
The CFW RS-flavor baseline is arXiv:0804.1954
(
CsakiFalkowskiWeiler2008\_RSFlavor); its quoted KK reference scales
are theory anchors and are kept out of pdg\_or\_equivalent. The
experimental landscape then moved through CDF's arXiv:0901.3803 search, which
set the previous \(B_s^0\) and \(B^0\) electronic limits later superseded by
LHCb. BaBar's arXiv:0712.1516 and Belle's older \(B^0\to e^+e^-\) bound remain
historical \(B_d\)-mode context in the PDG table. Bobeth et al.,
arXiv:1311.0903, supplied the reduced-uncertainty SM \(B_{s,d}\to\ell^+\ell^-\)
predictions and made explicit that the electron modes are suppressed by the
lepton mass in the SM. Fleischer, Jaarsma, and Tetlalmatzi-Xolocotzi,
arXiv:1703.10160, emphasized that new physics in the \(B_{s,d}\to e^+e^-\)
channels can be much less suppressed than the SM electron amplitude in
scalar/pseudoscalar scenarios. LHCb's arXiv:2003.03999 search is the decisive
post-2008 experimental update and supersedes the previous CDF limits.Validity and model dependence
The canonical observables are robust experimental upper limits, but their model
interpretation is not a direct neutral-meson-mixing constraint. The LHCb limits
are quoted one channel at a time, assuming no contribution from the other
neutral-\(B\) electronic mode, and the \(B_s^0\) result assumes the mean
\(B_s^0\) lifetime; the paper reports a \(2.4\%\) shift for SM-like CP-odd or
CP-even alternatives. A production RS implementation needs a consistent
\(\Delta B=1\) Hamiltonian, the \(B_q\) decay constants and CKM inputs as
theory inputs, a convention for electron bremsstrahlung/QED effects, and
separate scalar and pseudoscalar Wilson coefficients. The limits are strongest
as exclusions on large electron-specific scalar/pseudoscalar amplitudes rather
than as precision tests of the tiny SM prediction.
Code coverage in this repo
NO. The required greps over
quarkConstraints/,
qcd/, flavorConstraints/, neutrinos/,
yukawa/, warpConfig/, solvers/,
scanParams/, and tests/ found no \(B_s^0\to e^+e^-\),
\(B^0\to e^+e^-\), \(b\to s e e\), or \(b\to d e e\) rare-decay
implementation. The exact nearby hits are neutral \(B_d/B_s\) mixing inputs at
quarkConstraints/deltaf2.py:225 and
quarkConstraints/deltaf2.py:239, and the corresponding mixing
evaluators at quarkConstraints/deltaf2.py:903 and
quarkConstraints/deltaf2.py:922; they are \(\Delta F=2\), not this
\(\Delta B=1\) electronic leptonic observable.
Linked evidence (opens GitHub blob at flavor-catalog-website/2026q2):
- No B_s0 -> e+e-, B0 -> e+e-, b -> s e e, or b -> d e e rare-leptonic observable implementation was found in the required implementation/test directories.
- quarkConstraints/deltaf2.py:239 defines the existing b_s input as B_s mixing, not B_s0 -> e+e-.
- quarkConstraints/deltaf2.py:922 defines evaluate_bs_mixing for Delta F = 2 B_s mixing.
- quarkConstraints/deltaf2.py:225 defines the existing b_d input as B_d mixing, not B0 -> e+e-.
- quarkConstraints/deltaf2.py:903 defines evaluate_bd_mixing for Delta F = 2 B_d mixing.
Implementation difficulty
MEDIUM. The first useful implementation can share the pure-leptonic
\(\Delta B=1\) machinery needed for \(B005/B006\): \(C_{10}^{(\prime)}\),
\(C_S^{(\prime)}\), \(C_P^{(\prime)}\), \(f_{B_q}\), lifetimes, CKM inputs, and
a branching-ratio formula. The electron channel adds care around QED tails and
the LHCb assumptions, but it does not require angular observables or exclusive
form-factor likelihoods.
Key references
Process-local source keys before bibliography consolidation:
PDG2026\_BsBdEe, LHCb2020\_BsBdEe,
BobethEtAl2013\_BqllSM,
CDF2009\_BsBdEe,
FleischerJaarsmaTetlalmatziXolocotzi2017\_BqllNP,
BaBar2008\_BdEe, and
CsakiFalkowskiWeiler2008\_RSFlavor.