Flavor Catalog v0.4
102 entries
Catalog · Kaon · K012

K012 $K_S^0 \to \mu^+ \mu^-$

Short-lived neutral-kaon dimuon decay
Status REVIEWED VERIFIED High Code: NO Priority Low

Why this constrains the RS scan

In warped or anarchic-flavor scenarios this mode probes \(s\to d\mu^+\mu^-\) neutral currents rather than the \(\Delta F=2\) kaon-mixing surface already implemented in the repo. Modified \(Z\) couplings, heavy neutral-gauge exchange, electroweak penguins, and scalar or pseudoscalar lepton operators can feed the dimuon final state. The sidecar pdg\_or\_equivalent entry from chobanova\_2018\_ksmumu\_susy\_arxiv.txt gives the Standard Model scale as approximately \(5\times10^{-12}\), so the present limit mainly bounds large new-physics enhancements rather than precision SM-sized effects.

What's changed since the original paper

The post-2008 change is mostly experimental: LHCb moved the bound from the Run-1 \(0.8\times10^{-9}\) result to the combined \(2.1\times10^{-10}\) limit, with both values recorded in the sidecar. On the theory side, Chobanova et al. supplied the SM-scale and Higgs-penguin context, while Dery, Ghosh, Grossman, and Schacht showed that time-dependent \(K\to\mu^+\mu^-\) interference can isolate the \(\ell=0\) \(K_S\) component with hadronic uncertainty below \(1\%\); the latter number is stored in the sidecar entry for dery\_ghosh\_grossman\_schacht\_2021\_kmumu\_arxiv.txt.

Validity and model dependence

The experimental upper limit is robust, but a model interpretation is operator-dependent. The total \(K_S\to\mu^+\mu^-\) branching fraction includes long-distance physics and is not the same object as a clean short-distance \(\ell=0\) extraction. A catalog-to-code constraint should therefore distinguish vector/axial \(s\to d\mu\mu\) contributions from scalar or pseudoscalar operators and should not treat the PDG limit as a pure \(\Delta F=2\) bound.

Code coverage in this repo

NO. Targeted greps across quarkConstraints/, qcd/, flavorConstraints/, neutrinos/, yukawa/, warpConfig/, solvers/, scanParams/, and tests/ found no \(K_S\to\mu^+\mu^-\), dimuon rare-kaon, or \(s\to d\ell^+\ell^-\) implementation. The nearest kaon hit is quarkConstraints/deltaf2.py:615, the \(K_L-K_S\) mass difference used for \(\Delta F=2\) mixing, not this decay.

Implementation difficulty

HIGH. K012 needs a new rare-kaon \(\Delta S=1\) semileptonic calculation, Wilson/operator mapping for \(s\to d\mu^+\mu^-\), and a documented treatment of long-distance and \(K_S/K_L\) interference effects. The existing SLL/SLR/VLL/VRR/LR \(\Delta F=2\) basis is not sufficient for this observable.

Reason: Requires a new $\Delta S = 1$ rare-kaon semileptonic/dilepton observable, Wilson/operator mapping for $s \to d$ mu+ mu-, and a treatment of long-distance and K_S/K_L interference effects; the existing $\Delta F = 2$ SLL/SLR/VLL/VRR/LR basis does not cover this decay.

Key references

  • PDG2025:K012: PDG \(K_S^0\) particle listing, \(\Gamma_{12}\), and headline limit.
  • LHCb2020:KSmumu: standalone and combined LHCb upper limits.
  • LHCb2017:KSmumu: Run-1 predecessor limit.
  • Chobanova2018:KSmumuSUSY: SM scale and BSM Higgs-penguin context.
  • DeryGhoshGrossmanSchacht2021:KMuMuClean: time-dependent clean-probe proposal.
Source SHAs
5 snapshot(s) tracked in flavor_catalog/processes/kaon/K012.yaml
Access dates
2026-05-16
Worklog
flavor_catalog/worklogs/K012/
LaTeX source
flavor_catalog/processes/kaon/K012.tex
Anchors generated
2026-05-18T01:54:04Z

PDG2025:K012:headline_limit

https://pdg.lbl.gov/2025/listings/rpp2025-list-K-zero-S.pdf
accessed 2026-05-16 sha 5bed3ef38dfd... snapshot K012/pdg2025_ks_decay_modes.txt AMBIGUOUS
value <2.1e-10
AMBIGUOUS
Match 1 of 3 snapshot line 12 
L9: and 2025 update.
L10: 
L11: K0S decay modes, CP violating and Delta S = 1 weak neutral current modes:
L12: Gamma_12: mu+ mu-    S1    < 2.1 x 10^-10    CL=90%
L13: 
L14: Detailed listing:
L15: Gamma(mu+ mu-) / Gamma(total), Gamma_12 / Gamma.
Match 2 of 3 snapshot line 20 
L17: combined with electromagnetic interaction.
L18: 
L19: VALUE                 CL%      DOCUMENT ID       TECN
L20: <2.1 x 10^-10          90      1 AAIJ 20AE       LHCB
L21: 
L22: Data not used for current averages, fits, limits:
L23: <8 x 10^-10            90      2 AAIJ 17BQ       LHCB
Match 3 of 3 snapshot line 23 
L20: <2.1 x 10^-10          90      1 AAIJ 20AE       LHCB
L21: 
L22: Data not used for current averages, fits, limits:
L23: <8 x 10^-10            90      2 AAIJ 17BQ       LHCB
L24: <9 x 10^-9             90      3 AAIJ 13G        LHCB
L25: 
L26: PDG note 1:
Snapshots live under flavor_catalog/references/<process_id>/. Source-line anchoring is automated; the status pill reflects match confidence, not editorial review.

LHCb2020:K012:standalone_2016_2018_limit

https://arxiv.org/abs/2001.10354
accessed 2026-05-16 sha d5a95b6ce20e... snapshot K012/lhcb_2020_ksmumu_arxiv.txt AMBIGUOUS
value <2.2e-10
AMBIGUOUS
Match 1 of 2 snapshot line 18 
L15: corresponding to an integrated luminosity of 5.6 fb^-1, collected with the LHCb
L16: experiment during 2016, 2017 and 2018 at a center-of-mass energy of 13 TeV.
L17: The observed signal yield is consistent with zero, yielding
L18: B(K0_S -> mu+ mu-) < 2.2 x 10^-10 at 90% CL.
L19: The limit reduces to B(K0_S -> mu+ mu-) < 2.1 x 10^-10 at 90% CL once combined
L20: with the result from data taken in 2011 and 2012.
Match 2 of 2 snapshot line 19 
L16: experiment during 2016, 2017 and 2018 at a center-of-mass energy of 13 TeV.
L17: The observed signal yield is consistent with zero, yielding
L18: B(K0_S -> mu+ mu-) < 2.2 x 10^-10 at 90% CL.
L19: The limit reduces to B(K0_S -> mu+ mu-) < 2.1 x 10^-10 at 90% CL once combined
L20: with the result from data taken in 2011 and 2012.
Snapshots live under flavor_catalog/references/<process_id>/. Source-line anchoring is automated; the status pill reflects match confidence, not editorial review.

LHCb2020:K012:combined_limit

https://arxiv.org/abs/2001.10354
accessed 2026-05-16 sha d5a95b6ce20e... snapshot K012/lhcb_2020_ksmumu_arxiv.txt AMBIGUOUS
value <2.1e-10
AMBIGUOUS
Match 1 of 2 snapshot line 18 
L15: corresponding to an integrated luminosity of 5.6 fb^-1, collected with the LHCb
L16: experiment during 2016, 2017 and 2018 at a center-of-mass energy of 13 TeV.
L17: The observed signal yield is consistent with zero, yielding
L18: B(K0_S -> mu+ mu-) < 2.2 x 10^-10 at 90% CL.
L19: The limit reduces to B(K0_S -> mu+ mu-) < 2.1 x 10^-10 at 90% CL once combined
L20: with the result from data taken in 2011 and 2012.
Match 2 of 2 snapshot line 19 
L16: experiment during 2016, 2017 and 2018 at a center-of-mass energy of 13 TeV.
L17: The observed signal yield is consistent with zero, yielding
L18: B(K0_S -> mu+ mu-) < 2.2 x 10^-10 at 90% CL.
L19: The limit reduces to B(K0_S -> mu+ mu-) < 2.1 x 10^-10 at 90% CL once combined
L20: with the result from data taken in 2011 and 2012.
Snapshots live under flavor_catalog/references/<process_id>/. Source-line anchoring is automated; the status pill reflects match confidence, not editorial review.

LHCb2017:K012:run1_limit

https://arxiv.org/abs/1706.00758
accessed 2026-05-16 sha a35a20eef31d... snapshot K012/lhcb_2017_ksmumu_arxiv.txt RESOLVED
value <0.8e-9 at 90%; <1.0e-9 at 95%
RESOLVED
Match snapshot line 18 
L15: collisions corresponding to an integrated luminosity of 3 fb^-1, collected by
L16: LHCb at center-of-mass energies of 7 and 8 TeV. The observed yield is consistent
L17: with the background-only hypothesis, yielding
L18: B(K0_S -> mu+ mu-) < 0.8 (1.0) x 10^-9 at 90% (95%) confidence level.
L19: This result improves the previous upper limit on the branching fraction by an
L20: order of magnitude.
Snapshots live under flavor_catalog/references/<process_id>/. Source-line anchoring is automated; the status pill reflects match confidence, not editorial review.

Chobanova2018:K012:sm_estimate

https://arxiv.org/abs/1711.11030
accessed 2026-05-16 sha 7b25e1bf225f... snapshot K012/chobanova_2018_ksmumu_susy_arxiv.txt AMBIGUOUS
value approximately 5e-12
AMBIGUOUS
Match 1 of 7 snapshot line 3 
L1: Source: arXiv abstract page
L2: URL: https://arxiv.org/abs/1711.11030
L3: Accessed: 2026-05-16
L4: 
L5: arXiv:1711.11030 [hep-ph]
L6: Title: Probing SUSY effects in K_S^0 -> mu+ mu-
Match 2 of 7 snapshot line 10 
L7: Authors: Veronika Chobanova, Giancarlo D'Ambrosio, Teppei Kitahara,
L8: Miriam Lucio Martinez, Diego Martinez Santos, Isabel Suarez Fernandez,
L9: Kei Yamamoto
L10: Submitted: 2017-11-29; revised version v2: 2018-05-28
L11: Journal reference: JHEP 05 (2018) 024
L12: DOI: 10.1007/JHEP05(2018)024
L13:
Match 3 of 7 snapshot line 11 
L8: Miriam Lucio Martinez, Diego Martinez Santos, Isabel Suarez Fernandez,
L9: Kei Yamamoto
L10: Submitted: 2017-11-29; revised version v2: 2018-05-28
L11: Journal reference: JHEP 05 (2018) 024
L12: DOI: 10.1007/JHEP05(2018)024
L13: 
L14: Minimal abstract excerpt:
Match 4 of 7 snapshot line 12 
L9: Kei Yamamoto
L10: Submitted: 2017-11-29; revised version v2: 2018-05-28
L11: Journal reference: JHEP 05 (2018) 024
L12: DOI: 10.1007/JHEP05(2018)024
L13: 
L14: Minimal abstract excerpt:
L15: The Standard Model predicts B(K_S^0 -> mu+ mu-) approximately 5 x 10^-12.
Match 5 of 7 snapshot line 15 
L12: DOI: 10.1007/JHEP05(2018)024
L13: 
L14: Minimal abstract excerpt:
L15: The Standard Model predicts B(K_S^0 -> mu+ mu-) approximately 5 x 10^-12.
L16: Flavour-violating Higgs-penguin contributions in MSSM scenarios can enhance the
L17: branching fraction up to approximately 35 x 10^-12 or suppress it to
L18: approximately 0.78 x 10^-12. Fine-tuned regions can bring the branching
Match 6 of 7 snapshot line 17 
L14: Minimal abstract excerpt:
L15: The Standard Model predicts B(K_S^0 -> mu+ mu-) approximately 5 x 10^-12.
L16: Flavour-violating Higgs-penguin contributions in MSSM scenarios can enhance the
L17: branching fraction up to approximately 35 x 10^-12 or suppress it to
L18: approximately 0.78 x 10^-12. Fine-tuned regions can bring the branching
L19: fraction up to the then-current experimental upper bound, 8 x 10^-10.
L20: The paper also discusses correlations with B(K_L^0 -> mu+ mu-) and CP-asymmetry
Match 7 of 7 snapshot line 18 
L15: The Standard Model predicts B(K_S^0 -> mu+ mu-) approximately 5 x 10^-12.
L16: Flavour-violating Higgs-penguin contributions in MSSM scenarios can enhance the
L17: branching fraction up to approximately 35 x 10^-12 or suppress it to
L18: approximately 0.78 x 10^-12. Fine-tuned regions can bring the branching
L19: fraction up to the then-current experimental upper bound, 8 x 10^-10.
L20: The paper also discusses correlations with B(K_L^0 -> mu+ mu-) and CP-asymmetry
L21: predictions in K0 -> mu+ mu- decays.
Snapshots live under flavor_catalog/references/<process_id>/. Source-line anchoring is automated; the status pill reflects match confidence, not editorial review.

DeryGhoshGrossmanSchacht2021:K012:ell0_hadronic_uncertainty

https://arxiv.org/abs/2104.06427
accessed 2026-05-16 sha ecf9094e5782... snapshot K012/dery_ghosh_grossman_schacht_2021_kmumu_arxiv.txt RESOLVED
value <1%
RESOLVED
Match snapshot line 20 
L17: states. This quantity is theoretically clean and can be used to test the
L18: Standard Model. It can extract the CKM combination
L19: |V_ts V_td sin(beta + beta_s)| approximately |A^2 lambda^5 eta_bar| with
L20: hadronic uncertainties below 1%.
Snapshots live under flavor_catalog/references/<process_id>/. Source-line anchoring is automated; the status pill reflects match confidence, not editorial review.