Catalog · Kaon · K003

K003 $\mathrm{Re}(\varepsilon'/\varepsilon)$

Direct CP violation in K $ \to \pi \pi$

Status REVIEWED VERIFIED High Code: NO Priority Medium

PDG / equivalent values

Observable	Value	Year	Experiment / source	Provenance
$Re(\epsilon'/\epsilon$)	$Re(\epsilon'/\epsilon) = 0.00166 +/- 0.00023 = (16.6 +/- 2.3) x 10^-4$	2025	Particle Data Group pdgLive K0 listing, row S013EPS	source ↑

Why this constrains the RS scan

Unlike $\varepsilon_K$, this is a $\Delta S=1$ nonleptonic observable. It tests CP-odd short-distance contributions to the $K\to\pi\pi$ amplitudes after they are filtered through long-distance QCD. In warped or composite flavor models with anarchic Yukawas, the dangerous effects are not the repo's current neutral-meson-mixing operators but new penguin, scalar/tensor, and dipole structures. BSM master-formula work identifies strong sensitivity to electroweak left-right penguin $Q_8$, QCD penguin $Q_6$, and chromo-magnetic $O_{8g}$-type operators, making the channel a natural stress test for UV completions with non-minimal chirality structure.

What's changed since the original paper

The experimental average has not been replaced by a newer kaon experiment, but KTeV's final $K\to\pi\pi$ result was published after the CFW-era baseline. The main post-2008 changes are theoretical. RBC/UKQCD produced a physical-kinematics lattice calculation of $A_0$ and $\varepsilon'$, with $\mathrm{Re}(\varepsilon'/\varepsilon)= 21.7(2.6)(6.2)(5.0)\times10^{-4}$. Aebischer, Bobeth, and Buras then reanalysed the ratio with NNLO electroweak-penguin corrections and ChPT isospin-breaking inputs, obtaining $(17.4\pm6.1)\times10^{-4}$ in the octet treatment and $(13.9\pm5.2)\times10^{-4}$ in the nonet treatment. In parallel, 2019 BSM master-formula papers organized the $\Delta S=1$ operator dependence in WET/SMEFT language rather than treating $\varepsilon'/\varepsilon$ as a single phenomenological number.

Validity and model dependence

As a catalog constraint, $K003$ is highly informative but not plug-and-play. The experimental number is cleanly established, while the SM subtraction and BSM interpretation depend on hadronic matrix elements, isospin breaking, operator matching, and RG evolution. It should be classified as a theory-limited, model-dependent $\Delta S=1$ amplitude constraint rather than a robust tree-level exclusion like the current $\Delta F=2$ kaon lane.

Code coverage in this repo

NO. Greps over quarkConstraints/, qcd/, flavorConstraints/, neutrinos/, yukawa/, warpConfig/, solvers/, scanParams/, and tests/ found no direct implementation of $\varepsilon'/\varepsilon$, $K\to\pi\pi$, $\Delta S=1$, $Q_6$, $Q_8$, or $O_{8g}$. The nearby kaon code is explicitly a $\Delta F=2$ benchmark slice in quarkConstraints/deltaf2.py:1, with default inputs for $\varepsilon_K$ at quarkConstraints/deltaf2.py:209 and an $\varepsilon_K$ evaluator at quarkConstraints/deltaf2.py:729. The modern policy surface likewise enumerates only $\varepsilon_K$, $K$, $B_d$, $B_s$, and $D^0$ systems at quarkConstraints/modern/phenomenology.py:23.

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

Implementation difficulty

HIGH. A production constraint would require a new $\Delta S=1$ operator basis, matching from the warped/composite UV model to WET/SMEFT coefficients, RG running to hadronic scales, and lattice/ChPT inputs for $K\to\pi\pi$ matrix elements. The current $\Delta F=2$ VLL/VRR/LR machinery cannot be reused as a direct evaluator.

Reason: Requires new $\Delta S = 1$ WET/SMEFT matching, RG evolution, $K \to \pi \pi$ matrix elements, and treatment of electroweak/QCD penguin plus chromomagnetic operators; the repo's $\Delta F = 2$ machinery is not a direct evaluator.

Key references

Local source keys: pdg\_live\_S013\_20260516, pdg\_live\_S013EPS\_datablock\_20260516, ktev\_2011, na48\_2002, rbc\_ukqcd\_2020, aebischer\_buras\_2020, bsm\_master\_2019, bsm\_anatomy\_2019, and cfw\_2008.

display_value Re(epsilon'/epsilon) = 0.00166 +/- 0.00023 = (16.6 +/- 2.3) x 10^-4

RESOLVED

Match snapshot line 9

L6: Relevant excerpt, manually transcribed from row S013EPS:
L7: 
L8:   Re(epsilon'/epsilon) = (1 - |eta_00/eta_+-|)/3
L9:   Value: 0.00166 +/- 0.00023 (S = 1.6)
L10: 
L11: PDG note on the same listing:
L12: