B008 $B_s \to \tau^+\tau^-, B_d \to \tau^+\tau^-$
Rare tauonic leptonic neutral-B decays Status REVIEWED VERIFIED Medium Code: NO Priority Low
PDG / equivalent values
Why this constrains the RS scan
This this catalog wave entry is tagged SECONDARY; see
flavor\_catalog/PRIORITY\_TIERS.md for the tier policy. The mode is
secondary because the direct limits are still far above the Standard Model
expectation and are experimentally difficult, but it is a useful tau-specific
handle on scalar and pseudoscalar structures. In warped/anarchic-flavor
models, fermion localization and Yukawa misalignment can induce flavor-changing
\(Z\), Higgs, or heavy-electroweak/Kaluza--Klein exchange contributions to the
\(\Delta B=1\) Wilson coefficients \(C_{10}\), \(C_S\), and \(C_P\). The tau
mass weakens the helicity suppression relative to electron and muon final
states, and scalar/pseudoscalar operators can produce especially large effects.
KK-gluon exchange is more directly constrained by \(B_{s,d}\) mixing, but the
same flavor rotations and localization choices feed the rare leptonic channel.
Dipole operators are not the leading pure-leptonic contribution, yet they are
part of the same RS flavor-misalignment diagnostic suite.What's changed since the original paper
Relative to the Csaki--Falkowski--Weiler/Perez--Randall-era flavor literature,
the decisive experimental update is the LHCb search
arXiv:1703.02508, published as PRL 118, 251802. It used \(3\,{\rm fb}^{-1}\)
of 2011--2012 data and tau reconstruction through
\(\tau^-\to\pi^-\pi^+\pi^-\nu_\tau\), setting the first direct
\(B_s^0\to\tau^+\tau^-\) limit and the strongest \(B^0\to\tau^+\tau^-\)
limit at publication. The older BABAR direct \(B^0\) result,
arXiv:hep-ex/0511015, remains useful history but is superseded in PDG by LHCb.
The BABAR arXiv:1605.09637 result is a related \(B^+\to K^+\tau^+\tau^-\)
semileptonic input, not the B008 neutral-leptonic observable.
On the theory side, Bobeth et al. arXiv:1311.0903 supplied the
reduced-uncertainty SM normalization for \(B_{s,d}\to\ell^+\ell^-\) modes.
Capdevila et al. arXiv:1712.01919 showed why \(b\to s\tau^+\tau^-\) can remain
a high-leverage new-physics probe in lepton-flavor-nonuniversal scenarios.
Bordone and Fernandez Navarro arXiv:2307.07013 connected \(b\to s\tau\tau\)
new physics to \(\tau_{B_s}/\tau_{B_d}\) and \(\Delta\Gamma_s\), emphasizing
that scalar operators make \(B_s\to\tau^+\tau^-\) particularly sensitive
through chiral enhancement.
Validity and model dependence
Class: upper-limit and model-dependent for new-physics interpretation. The
experimental limits are robust as one-mode-at-a-time upper limits, but they are
not measurements of a branching fraction and should not be treated as Gaussian
averages. A simultaneous RS scan with both \(B_s^0\) and \(B^0\) tauonic
decays would ideally use a two-dimensional likelihood or reproduce the LHCb
assumptions, because each quoted limit assumes the other neutral mode is absent.
Theory translation requires a consistent normalization for time-integrated
branching fractions, tau-mass phase space, and \(C_{10}\), \(C_S\), and
\(C_P\) Wilson coefficients.
Code coverage in this repo
NO. The required coverage greps across
quarkConstraints/, qcd/, flavorConstraints/,
neutrinos/, yukawa/, warpConfig/,
solvers/, scanParams/, and tests/ found no B008
rare-leptonic implementation. Existing hits cover \(B_d\) and \(B_s\)
\(\Delta F=2\) mixing
(quarkConstraints/deltaf2.py:903 and
quarkConstraints/deltaf2.py:922), bridge wrappers for the same mixing
observables (quarkConstraints/modern/phenomenology.py:646 and
quarkConstraints/modern/phenomenology.py:657), an unrelated
\(\mu\to e\gamma\) routine (flavorConstraints/muToEGamma.py:75), and
a scan-parameter example involving \(y_\tau\) (scanParams/README.md:161).
They do not implement a \(B_{s,d}\to\tau^+\tau^-\) branching ratio, a
\(b\to s,d\,\tau^+\tau^-\) likelihood, or a tauonic \(C_{10}\), \(C_S\), or
\(C_P\) rare-decay evaluator.
Linked evidence (opens GitHub blob at flavor-catalog-website/2026q2):
- Focused B008 grep found no B_s/B_d -> tau+ tau- or b -> s,d tau+ tau- rare-leptonic observable implementation.
- quarkConstraints/deltaf2.py:903 defines evaluate_bd_mixing, a Delta F = 2 B_d-mixing observable, not B_d -> tau+ tau-.
- quarkConstraints/deltaf2.py:922 defines evaluate_bs_mixing, a Delta F = 2 B_s-mixing observable, not B_s -> tau+ tau-.
- quarkConstraints/modern/phenomenology.py:646 and quarkConstraints/modern/phenomenology.py:657 evaluate B_d/B_s mixing from the bridge; no Delta B = 1 rare leptonic branch is present.
- flavorConstraints/muToEGamma.py:75 defines check_mu_to_e_gamma, an unrelated charged-lepton dipole constraint.
- scanParams/README.md:161 mentions y_tau as a scan parameter, not a B -> tau tau observable.
Implementation difficulty
MEDIUM. A catalog-level constraint can be built from the standard
pure-leptonic \(B_q\to\ell^+\ell^-\) formula with tau-mass phase space,
time-integration conventions, and scalar/pseudoscalar Wilson coefficients.
This is more work than wiring a published average, but it avoids the exclusive
form-factor and angular-analysis machinery needed for semileptonic
\(b\to s\tau^+\tau^-\) modes. A faithful reproduction of the experimental
two-mode likelihood would raise the difficulty.
Key references
Process-local source keys before bibliography consolidation:
PDG2026\_BsTauTau, PDG2026\_BdTauTau,
AaijEtAl2017\_BqTauTau, AubertEtAl2006\_BdTauTau,
LeesEtAl2017\_BKTauTauRelated, BobethEtAl2014\_BqTauTauSM,
CapdevilaEtAl2018\_BSTauTauNP,
BordoneNavarro2023\_BSTauTauNP, and
CsakiFalkowskiWeiler2008\_RSFlavor.