CP Violation In Kaon Decays Research Articles

Direct CP violation and the ΔI= 1/2 rule inK→ππdecay in the Standard Model

We discuss the RBC & UKQCD collaborations’ recent [1] lattice calculation of ϵ′, the measure of direct CP-violation in kaon decays. This result significantly improves on our previous 2015 calculation, with nearly 4× the statistics and more reliable systematic error estimates. We discuss how our results demonstrate the Standard Model origin of the ΔI= 1/2 rule, and present our plans for future calculations.

Z′ models with less-minimal flavor violation

We study the phenomenology of simplified $Z^\prime$ models with a global $U(2)^3$ flavour symmetry in the quark sector, broken solely by the Standard Model Yukawa couplings. This flavour symmetry, known as less-minimal flavour violation, protects $\Delta F=2$ processes from dangerously large new physics (NP) effects, and at the same time provides a free complex phase in $b\to s$ transitions, allowing for an explanation of the hints for additional direct CP violation in kaon decays ($\epsilon^\prime/\epsilon$) and in hadronic $B$-decays ($B\to K\pi$ puzzle). Furthermore, once the couplings of the $Z^\prime$ boson to the leptons are included, it is possible to address the intriguing hints for NP (above the 5$\,\sigma$ level) in $b\to s \ell^+\ell^-$ transitions. Taking into account all flavour observables in a global fit, we find that $\epsilon^\prime/\epsilon$, the $B\to K\pi$ puzzle and $b\to s \ell^+\ell^-$ data can be explained simultaneously. Sizeable CP violation in $b\to s \ell^+\ell^-$ observables, in particular $A_8$, is predicted, which can be tested in the near future, and an explanation of the $B\to K\pi$ and $\epsilon^\prime/\epsilon$ puzzles leads to effects in di-jet tails at the LHC, that are not far below the current limits. Once $b\to s \ell^+\ell^-$ is included, cancellations in di-muon tails, possibly by a second $Z^\prime$, are required by LHC data.

Towards NNLO accuracy for ε′/ε

The quantity ε′/ε measures direct CP violation in Kaon decays. Recent SM predictions show a 2.9σ tension with data, with the theoretical uncertainty dominating. As rapid progress on the lattice is bringing nonperturbative long-distance effects under control, a more precise knowledge of short-distance contributions is needed. We describe the first NNLO results for ε′/ε and discuss future prospects, as well as issues of scheme dependence and the separation of perturbative and nonperturbative effects. Finally we also comment on the solution of the renormalisation-group evolution in one of the talks at this conference and present the correct solution.

Higher order effects in ϵ'/ϵ

The quantity ϵ'/ϵ measures direct CP violation in Kaon decays. Recent analysis of this ratio resulted in a 2.9 sigma discrepancy between the Standard Model predictions and the experimental data. Our ability to observe or constrain New Physics depends on the accuracy of determining the SM “background”, hence a precise evaluation of ϵ'/ϵ is particularly important. We discuss the Standard Model prediction and the relevant matching calculations at NNLO for this observable.

CP Violation in Kaon Decay in the Scalar Strong Interaction Hadron Theory

CP conservation and violation in neutral kaon decay are considered from a first principles’ theory, recently published as “Scalar Strong Interaction Hadron Theory”. The arbitrary phase angle relating K0 and 0 in current phenomenology is identified to be related to the product of the relative energy to the relative time between the s and d quarks in these kaons. The argument of the CP violating parameter ? is predicted to be 45? without employing measured data. The K0S decay rate is twice the K0L -K0S masss difference, in near agreement with data, and both are proportional to the square of the relative energy 29.44 eV. Any pion from K0L decay will also have a mass shift of ≈1.28 × 10-5 eV. The present first principles’ theory is consistent with CP conservation. To achieve CP violation, the relative time cannot extend to both +∞ and -∞ but is bounded in at least one direction. The values of these bounds lie outside the present theory and it is unknown how they can be brought forth. -B0 mixing is also considered and the relative energy is 663.66 eV.

Kaon physics and CP violation calculations on QCDOC

The violation of charge conjugation (C) and parity (P) in kaon decays, first observed in Nobel-prize winning experiments at Brookhaven National Lab in 1964, is allowed by the Standard Model of particle physics. Predicting indirect CP violation in kaon decays requires the values for standard model parameters and the evaluation of a four-quark matrix element inside a kaon. Using lattice QCD with domain wall fermions and the current QCDOC computers, calculations are underway that will yield, among other results, the value for this matrix element, allowing more precise comparisons between theory and experiment for CP violation in kaon decays.

The KLOE drift chamber VCI 2001

The main goal of the KLOE experiment at the Frascati DAΦNE φ− factory is the study CP violation in kaon decays. The tracking device of the experiment is a drift chamber whose dimensions, 4 m of diameter and 3.3 m length, provide a large acceptance volume for the decay products of low momentum K L ( λ L =3.4 m ). A complete stereo geometry with 12.582 cells arranged in 58 layers guarantees a high and uniform efficiency in the reconstruction of the charged K L decays. Very light materials have been chosen both for the drift medium, a helium-based gas mixture, and for the mechanical structure, made of carbon fiber, to minimize multiple scattering and conversion of low-energy photons. The design requirements, the adopted solutions together with the calibration procedure and the tracking performances of the drift chamber are discussed.

Classical illustrations of CP violation in kaon decays

It is easy to construct classical two-state systems illustrating the behavior of the short-lived and long-lived neutral K mesons in the limit of CP conservation. The emulation of CP violation is more tricky, but is provided by the two-dimensional motion of a Foucault pendulum. Analogies are drawn between the pendulum and observables in neutral kaon decays. An emulation of CP and CPT violation using electric circuits is also discussed.

The KLOE eetector at DAΦNE

The e + e − φ -factory DAΦNE, under construction at the Laboratori Nazionali di Frascati was primarily designed to study CP violation in kaon decays. The KLOE detector, being built for performing this and other physics, is described.

CP VIOLATION IN KAON DECAYS

We review the Standard Model predictions of CP violation in kaon decays. We present an elementary introduction to Chiral Perturbation Theory, four-quark effective Hamiltonians and the relation among them. Particular attention is devoted to K→3π, K→ 2πγ and [Formula: see text] decays.

Quantum chromodynamic effects and CP violation in the Kobayashi-Maskawa model

We study, in the context of the Kobayashi-Maskawa model, the effects that quantum chromodynamics has on the predictions for CP violation in kaon decays. We derive an effective hamiltonian for ΔS = 1 transitions in which all-order corrections in the strong coupling constant α s are incorporated, including those arising from penguin diagrams. We examine, in particular, the predictions of this hamiltonian for the ratio of the CP-violating parameters | ϵ′/ ϵ|. Our results for this ratio are well within the present experimental bound, but are considerably smaller than the recent calculation of Gilman and Wise. The discrepancy between our results and those of Gilman and Wise arises because of the different way we have estimated the amplitude for K 0 decay. A discussion of the reliability of both our estimate and that of Gilman and Wise is included.