Table of contents

FOREWORD KAON 2019

The 2019 edition of the International Conference on Kaon Physics – KAON 2019 – continues the KAON series started in 1988, which offers a remarkable opportunity to the community of High Energy Physicists to discuss topical issues and upcoming experiments on kaon physics.

KAON 2019 was organized in collaboration with the Perugia INFN Department and the Physics and Geology Department of the University. Hosted in the Aula Magna of the University of Perugia, it took place from September 10 to September 13. The conference was dedicated to the memory of Professor Aniello Nappi (1948-2012), a valued colleague and friend which carried out research in kaon physics in Perugia for many years.

All active physics groups and communities, both experimentalists and theorists were represented at KAON 2019. More than 90 participants attended the conference; many of them were young physicists. A remarkable presence of women scientists from institutions of different countries has to be mentioned.

All papers published in this volume of Journal of Physics: Conference Series have been peer reviewed through processes administered by the proceedings Editors. Reviews were conducted by expert referees to the professional and scientific standards expected of a proceedings journal published by IOP Publishing.

The KAON2019 is the 11th conference in the series which started in 1988. Many kaon experiments have evolved during these years. In this talk, challenges and developments of the experiments for Re(^'/) and rare $K\to \pi \nu \bar{\nu }$ decays are reviewed.

The KOTO experiment aims to study the CP-violating rare decay ${K}_{L}\to {\pi }^{0}\nu \bar{\nu }$ at J-PARC. The analysis of the data set taken in 2016, 2017 and 2018 is reported. In order to reduce backgrounds and to improve the signal acceptance, a new barrel photon detector and a new trigger system were installed and new analysis techniques were developed. The K_L yield was 7.1×10¹². The single event sensitivity was estimated to be 6.9×10⁻¹⁰, which was improved by a factor of 2 compared to the data set taken in 2015. The number of background events was estimated to be 0.05 ± 0.02. Four candidate events were observed in the signal region, and their studies are on-going extensively to nd their sources.

The NA62 experiment at the CERN SPS is designed to measure the branching ratio of the ${K}^{+}\to {\pi }^{+}\nu \bar{\nu }$ with a decay-in-flight technique and took data in 2016–2018. The statistics collected in 2017 allows NA62 to achieve the best up–to–date single event sensitivity for ${K}^{+}\to {\pi }^{+}\nu \bar{\nu }$ corresponding to more than 2 Standard Model ${K}^{+}\to {\pi }^{+}\nu \bar{\nu }$ expected events. The analysis of the 2017 data has revealed 2 candidate ${K}^{+}\to {\pi }^{+}\nu \bar{\nu }$ events, while 1.5 background were expected. Together with the candidate found on the 2016 data, this result leads to 1.85 × 10⁻¹⁰ as preliminary upper limit at 90% C.L. on the branching ratio of the ${K}^{+}\to {\pi }^{+}\nu \bar{\nu }$ decay. The 2017 data also allow NA62 to achieve the best up–to–date sensitivity on the search for the π⁰ → invisible decay.

The first observation of the rare decay K^± → π^±π⁰e⁺e⁻ is reported by the NA48/2 experiment at CERN, based on 4919 candidates with 4.9% background contamination. From the analysis of 1.7 × 10¹¹ kaon decays collected in 2003–2004, the branching ratio in the full kinematic region is measured to be BR(K^± → π^±π⁰e⁺e⁻)= (4.24 ± 0.14) × 10⁻⁶. A detailed study of the kinematic space shows evidence for a structure dependent contribution. Both measured BR and structure dependent contribution are in perfect agreement with theoretical predictions based on Chiral Perturbation Theory. Several P- and CP-violating asymmetries are also evaluated.

The NA48/2 experiment collected unprecedent statistics of charged kaon decays in 2003 and 2004. The main purpose of the experiment was to measure direct CP violation in kaon decays to three pions while an extensive physics program was carried out together with the main goal. The huge statistics collected allowed to test with a high accuracy the predictions of low energy QCD theories in several charged kaon decay processes. The precise measurement of the charged kaon semileptonic form factors are reported here, based on data collected in 2004 with a dedicated minimum bias trigger.

The entanglement in the neutral kaon pairs produced at the DAΦNE ϕ-factory is a unique tool to test discrete symmetries and quantum coherence at the utmost sensitivity, in particular strongly motivating the experimental searches of possible CPT violating effects, which would unambiguously signal New Physics. KLOE and KLOE-2 data sets with about 2.4×10¹⁰ϕ-meson produced represent the largest sample ever collected at the ϕ-meson peak. The lepton charge asymmetry measured in K_S semileptonic decays with 1.7 fb⁻¹ of KLOE data, improving the statistical uncertainty of present result by about a factor two, has been presented together with the test of CPT in transitions in ϕ → K_SK_L → π^±e^∓ν, 3π⁰ and K_SK_L → π⁺π⁻, π^±e^∓ν decays.

Precision measurements of CP violating observables in the decays of b and c hadrons are powerful probes to search for physics beyond the Standard Model. The most recent results on CP violation in the decay, mixing and interference of both b and c hadrons obtained by the LHCb Collaboration with Run I and years 2015-2016 of Run II are presented, including the first observation of CP violation in the charm system. In particular world best constraints and world first measurements are provided for CKM elements, unitarity angles and charm parameters. Prospects for future sensitivities are also discussed.

The KLOE-2 experiment at the upgraded e⁺e⁻ DAΦNE collider of the INFN Laboratori Nazionali di Frascati completed its data taking campaign at the end of March 2018, collecting 5.5 fb⁻¹ at the center of mass energy corrisponding to the mass of the ϕ-meson. Together with the data set of its predecessor KLOE, the acquired data sample of 8 fb⁻¹ corresponds to 2.4×10¹⁰ϕ-meson produced: the largest sample ever collected at the ϕ(1020) at e⁺e⁻ colliders.

KLOE-2 Collaboration activities are now focused on data reconstruction and analysis, continuing the KLOE long-standing tradition of flavour physics precision measurements in the kaon sector, to probe CKM unitarity and search for dark force mediator. Latest results on K_S rare decays will be presented and discussed in the framework of Flavour Physics and CP Violation tests, focusing on the measurement of K_S semileptonic branching ratios, using 1.7 fb⁻¹ KLOE data, and the search for the pure CP-violating K_S → 3π⁰ decay.

The CMD-3 detector started data taking at the electron-positron collider VEPP-2000 in December 2010 with a goal to collect about 1 fb⁻¹. The collected data sample corresponds to an integrated luminosity of 200 pb⁻¹ in the center-of-mass energy range from 0.32 up to 2 GeV. This paper reports recent results on the hadronic cross sections measurements with the CMD-3 detector.

We present an updated analysis of isospin-violating corrections to ε^'/ε in the framework of chiral perturbation theory, taking advantage of the currently improved knowledge on quark masses and nonperturbative parameters. The role of the different ingredients entering into the analysis is carefully assessed. Our final result is ${\Omega }_{\text{eff}}={0.110}_{-0.088}^{+0.090}$ [1].

We briefly overview the historical controversy around Standard Model predictions of ε^'/ε and clarify the underlying physics. A full update of this important observable is presented, with all known short- and long-distance contributions, including isospin-breaking corrections. The current Standard Model prediction, Re(ε^'/ε) = (14 ± 5) · 10⁻⁴ [1, 2], is in excellent agreement with the experimentally measured value.

An overview of the kaon physics program of the RBC and UKQCD collaborations will be presented with a focus on the lattice calculation of K → ππ decay and the direct CP violation parameter ε^'. We will describe substantial improvements to our earlier 2015 K → ππ calculation, including the use of three independent ππ interpolating operators and the results we obtain for I = 0 ππ scattering for energies at and below the kaon mass. While the new result for ^' is not yet complete, the enhanced statistics and improved analysis that underlies our expanded calculation will be presented.

Despite not being designed for it, the LHCb experiment has given world-leading contributions in kaon and hyperon physics. In this contribution I review the prospects for kaon physics at LHCb exploiting the already acquired data and the current and future Upgrade scenarios.

The NA62 experiment at the CERN SPS provides unique opportunity to study rare and forbidden decays of K⁺ mesons. Using the data collected in 2017 a search for the lepton number violating decays K⁺ → π⁻µ⁺µ⁺ and K⁺ → π⁻e⁺e⁺ has been performed. New upper limits on the branching ratio have been obtained: 4.2×10⁻¹¹ for the muon and 2.2×10⁻¹⁰ for the electron mode (90% confidence level). These results improve the existing limits by factors of 2 and 3 respectively.

The K → πℓ⁺ℓ⁻ decay is a flavor changing neutral current process which is forbidden at tree level in the Standard Model. This suppression causes the decay to be sensitive to potential New Physics. The decay channels are dominated by long-distance contributions, which require non-perturbative methods of investigation. Previous lattice calculations by the RBC and UKQCD collaborations, at unphysical kaon/pion masses, have successfully extracted the matrix elements needed to describe the form factor of the decays. A new lattice calculation, on a gauge configuration with m_π ≈ 140 MeV and m_K ≈ 500 MeV, is underway and will be discussed here.

We discuss generic effects of new physics on the rare decay modes ${K}_{L}\to {\pi }^{0}\nu \bar{\nu }$ and ${K}^{+}\to {\pi }^{+}\nu \bar{\nu }$ from the point of view of the neutrino sector. We pay particular attention to the cases of right handed neutrino couplings and neutrino lepton flavour violating interactions. The first of these examples requires the existence of a new light (sterile) right-handed neutrino and its contribution to both rates is always additive to the standard model. It is motivated as a possible solution to the so called charged B anomalies. The case of neutrino lepton flavour violating couplings produces interesting constraints on new physics which are competitive with those from standard searches for charged lepton flavour violating in kaons and in some cases better than those from tau decay.

Several radiative decays are under study by OKA setup at U-70 synchrotron. First, the radiative decay K⁺ → µ⁺νγ(K_µ2γ) is studied on statistics of about 95K events for 25 MeV < ${E}_{\gamma }^{* }$ < 150 MeV. A clear destructive interference between bremsstrahlung and structure dependent SD⁻ term is observed. As a result, the vector and axial-vector form factors difference is measured: F_V−F_A = 0.134 ± 0.021(stat.) ± 0.027(syst.) which is 2.3 σ away from_χP T O(p⁴). Moreover, the decay K⁺ → π⁺π⁻π⁺γ is studied on statistics of about 450 events for 30 Mev < ${E}_{\gamma }^{* }$ < 70 Mev. The total and differential branching fractions of the decay are measured. Br(K⁺ → π⁺π⁻π⁺γ) = (7.1±0.4(stat.)±0.3(syst.))·10⁻⁶ to be compared with_χP T O(p⁴) (6.65 ± 0.05) · 10⁻⁶. In addition, a search for an up-down photon asymmetry with respect to the hadronic system decay plane is performed.

We report a preliminary result of a new search for the K_L → π⁰γ decay, which is forbidden by the Lorentz invariance and gauge principle. The search was carried out using the data obtained from 2016 to 2018 at the J-PARC proton beam facility using the KOTO detector. The achieved single event sensitivity was (6.9 ± 0.3_stat. ± 1.5_syst.) × 10⁻⁸. No signal candidate was found in the signal region and the upper limit was set to B(K_L → π⁰γ) < 1.7 × 10⁻⁷ at the 90% con dence level.

Following the recent analysis done in collaboration with Jason Aebischer and Christoph Bobeth, I summarize the optimal, in our view, strategy for the present evaluation of the ratio ε^'/ε in the Standard Model. In particular, I emphasize the importance of the correct matching of the long-distance and short-distance contributions to ε^'/ε, which presently is only achieved by RBC-UKQCD lattice QCD collaboration and by the analytical Dual QCD approach. An important role play also the isospin-breaking and QED effects, which presently are best known from chiral perturbation theory, albeit still with a significant error. Finally, it is essential to include NNLO QCD corrections in order to reduce unphysical renormalization scheme and scale dependences present at the NLO level. Here µ_c in m_c(µ_c) in the case of QCD penguin contributions and µ_t in m_t(µ_t) in the case of electroweak penguin contributions play the most important roles. Presently the error on ε^'/ε is dominated by the uncertainties in the QCDP parameter $B_6^{(1/2)}$ and the isospin-breaking parameter $\hat \Omega _{{\rm{eff}}}$. We present a table illustrating this.

Lepton Flavour Violation effects are predicted in several extensions of the Standard Model at a measurable level. Since the Standard Model background, even including ν oscillations and mixing, is completely negligible, the observation of such effects would be a strong evidence for New Physics beyond the Standard Model, while a non observation with high precision experiments would put severe constraints on possible Standard Model extensions. In this talk I review the present status and the future perspectives of the Lepton Flavour Violation experiments involving µ's and discuss the sensitivity improvements which could be obtained from new high intensity machines coupled with high resolution detectors.

A search for Σ⁺ → pµ⁺µ⁻ decays with LHCb Run 1 data is presented, yielding an evidence for this decay and a measurement of a branching fraction compatible with the Standard Model. The HyperCP anomaly in the dimuon invariant mass distribution is not confirmed, and its branching fraction central value is excluded at 95% CL. Prospects for the future of this measurement in LHCb are also presented.

Semileptonic Hyperon Decays (SHD) allow to test Beyond the Standard Model physics with operators not accessible to kaon decays. In this document we will discuss the prospects of the LHCb experiment to improve the existing measurement of muonic SHD. A background rejection study has been made using the LHCb simulation in order to investigate the power to distinguish between the ${\Lambda }^{0}\to p{\mu }^{-}\bar{\nu }$ decay and its main background, the Λ⁰ → pπ⁻ decay. Two variables were explored, and their rejection power was estimated by applying a selection criteria. In addition, the estimated ${\Lambda }^{0}\to p{\mu }^{-}\bar{\nu }$ yield at LHCb was calculated.

The DAΦNE electron-positron collider of the Laboratori Nazionali di Frascati of INFN is a worldwide unique low-energy kaon source and for this reason is suitable for low-energy kaon physics like kaonic atoms and kaon-nucleons/nuclei interaction studies. Kaonic atoms are atomic systems where an electron is replaced by a negatively charged kaon, containing the strange quark, which interacts in the lowest orbits with the nucleus also by the strong interaction. As a result, their study offers the unique opportunity to perform experiments equivalent to scattering at vanishing relative energy. This allows to study the strong interaction between the antikaon and the nucleon or the nucleus "at threshold", without the need of ad hoc extrapolation to zero energy, as in scattering experiments. The most precise kaonic hydrogen measurement to date, together with an exploratory measurement of kaonic deuterium, were carried out by the SIDDHARTA collaboration at the DAΦNE electron-positron collider of LNF-INFN, by combining the excellent quality kaon beam delivered by the collider with new experimental techniques, as fast and precise Silicon-Drift X-ray Detectors. The measurement of kaonic deuterium will be realized in the near future by SIDDHARTA-2, a major upgrade of SIDDHARTA.

The AMADEUS collaboration aims to provide precise experimental information on the K⁻ strong interaction with nucleons in the low-energy regime. The step 0 of AMADEUS consists in the re-analysis of the data collected with the KLOE detector at the DAΦNE collider during the 2004/2005 data taking campaign. The absorptions of low-momentum K⁻s in the nuclei contained in the detector and the beam pipe setup (H, ⁴He, ⁹Be and ¹²C) are investigated. Information on the K⁻ single and multi-nucleon interactions are extracted from the study of the Λπ⁻ and p correlated production in the final state.

We are searching for the decay ${K}_{L}\to {\pi }^{0}\nu \bar{\nu }$ in the KOTO experiment at J-PARC. The signal is identified by detecting two photons from the π⁰ decay with a calorimeter composed of undoped CsI crystals. The main background "hadron cluster background" is caused by a neutron hitting the calorimeter to form two clusters: a neutron in the beam halo hits the calorimeter to generate the first cluster, and a secondary neutron generated in the interaction creates the second separated cluster. In order to reduce this background, we upgraded the calorimeter to have both-end readout by attaching MPPCs on the upstream face of each CsI crystal in addition to the original PMT attached on the downstream face. The background can be rejected exploiting the timing difference between the MPPC and PMT, since neutrons tend to interact deeper inside the crystals. We installed the MPPCs in 2018, and evaluated the performance with data taken in 2019. The principle in the calorimeter upgrade and the performance of the background reduction are reported.

KOTO is the first experiment with the designed sensitivity of O(10⁻¹¹) to probe for new physics through the rare ${K}_{L}^{0}\to {\pi }^{0}\nu \bar{\nu }$ decay. From 2017 to 2019, there were critical changes in the data acquisition system that further improved the research potential of KOTO for diverse research topics. In this article, we present the new trigger system of KOTO and several byproduct analysis.

A next-generation experiment at J-PARC to measure the branching ratio of ${K}_{L}^{0}\to {\pi }^{0}\nu \bar{\nu }$ is being considered. The currently-running experiment in the Hadron Experimental Facility of J-PARC, the KOTO experiment, will reach a sensitivity below 10⁻¹⁰ in 3–4 years but would take longer time toward the sensitivity predicted by the Standard Model. It is desirable to have a new experiment that can observe O(100) events and measure the branching ratio of ${K}_{L}^{0}\to {\pi }^{0}\nu \bar{\nu }$. Such an experiment, so-called KOTO step-2, has been discussed as a part of the project of the facility extension. A new beam line with a smaller production angle and a larger detector, accommodated in the extended facility, will provide a higher kaon ux and a larger detection acceptance, and thus brings a better sensitivity. In this paper, a baseline design of the KOTO step-2 and its potential sensitivity are discussed.

Precise measurements of the branching ratios for the flavor-changing neutral current decays $K\to \pi \nu \bar{\nu }$ can provide unique constraints on CKM unitarity and, potentially, evidence for new physics. It is important to measure both decay modes, ${K}^{+}\to {\pi }^{+}\nu \bar{\nu }$ and ${K}_{L}\to {\pi }^{0}\nu \bar{\nu }$, since different new physics models affect the rates for each channel differently. The NA62 experiment at the CERN SPS will measure the BR for the charged channel to better than 20%. The BR for the neutral channel has never been measured. We are designing the KLEVER experiment to measure BR(${K}_{L}\to {\pi }^{0}\nu \bar{\nu }$) to ∼20% using a high-energy neutral beam at the CERN SPS. The boost from the high-energy beam facilitates the rejection of background channels such as K_L → π⁰π⁰ by detection of the additional photons in the final state. On the other hand, the layout poses particular challenges for the design of the small-angle vetoes, which must reject photons from K_L decays escaping through the beam exit amid an intense background from soft photons and neutrons in the beam. We present findings from our design studies, with an emphasis on the challenges faced and the potential sensitivity for the measurement of BR(${K}_{L}\to {\pi }^{0}\nu \bar{\nu }$).

Feebly-interacting particles represent an alternative paradigm with respect to the traditional strongly-coupled Beyond the Standard Model physics explored at the LHC and can provide an answer to many fundamental open questions in particle physics. This document presents the state of the art of searches for feebly-interacting particles at accelerator-based experiments including projects proposed at CERN and currently discussed in the European Strategy for Particle Physics update.

Very weakly coupled new-physics particles in the MeV-GeV range appear as mediators in various "portals" to a hidden sector. Their interaction with Standard Model particles is feeble and these states are usually long-lived, so that the experimental search fully profits of a high-intensity setup, such as that of fixed-target experiments. Within the vector portal hidden-sector model a dark photon might exist which predominantly decays to dark matter particles. A search for such an invisible particle has been performed, exploiting the efficient photon-veto capability and high resolution tracking of the NA62 detector at CERN. The signal stems from the chain K⁺ → π⁺π⁰ followed by the π⁰ decay to a photon-dark-photon pair. No significant statistical excess has been identified. Upper limits on the dark photon coupling to the ordinary photon as a function of the dark photon mass have been set.

The Belle II experiment at the SuperKEKB energy-asymmetric e⁺e⁻ collider is a substantial upgrade of the KEKB facility at the Japanese KEK laboratory. The design luminosity of the machine is 8 · 10³⁵ cm⁻²s⁻¹ and the Belle II experiment aims to record 50 ab⁻¹ of data, a factor of 50 more than its predecessor. From February to July 2018, the machine has completed a commissioning run, where about 0.5 fb⁻¹ of data have been collected. Regular operation of SuperKEKB has started in March 2019: the machine has achieved a peak luminosity of 10³⁴ cm⁻²s⁻¹, and Belle II has recorded a data sample of about 6.5 fb⁻¹. Already this early data set with specifically designed triggers offers the possibility to search for a large variety of dark sector particles in the GeV mass range complementary to searches at LHC and dedicated low energy experiments. The Belle II dark matter analyses will benefit from more data in the process of being accumulated. This talk will review the state of the dark sector searches at Belle II with a focus on the discovery potential of the early data, and show the first results.

We report the performance of a new scintillator array Downstream Charged Veto (DCV) for the J-PARC KOTO experiment to suppress the K_L → π⁺π⁻π⁰ decay background. Since the background originates from undetected charged pions passing through the beam hole of the electromagnetic calorimeter, the DCV detector was installed in vacuum downstream of the calorimeter. The DCV is composed of two plastic scintillator pipes read out by Multi Pixel Photon Counters through wavelength shifting fibers. The light yield was found to be 60 photoelectrons/0.8 MeV in a test bench when cosmic-rays pass through the center of the DCV. Energy calibration was performed using cosmic-rays after installation.

The RICH detector of the NA62 experiment is one of the key detectors to achieve the muon rejection needed in the search for the ${K}^{+}\to {\pi }^{+}\nu \bar{\nu }$ decay, performed by NA62. Since BR(K⁺ → µ⁺ν) is higher than BR(${K}^{+}\to {\pi }^{+}\nu \bar{\nu }$) by more than 9 orders of magnitude, it represents one of the most relevant background contributions. Its rejection is performed with kinematic reconstruction of the event and identification of the charged particles in the final state (π⁺ against µ⁺). The pion identification efficiency using the RICH detector is measured to be 83% in the momentum range between 15 and 35 GeV/c, with a misidentification probability for muons of 0.2%, while the track crossing time is measured with a resolution of 70 ps. The RICH detector is also exploited to provide trigger for charged particles with an efficiency greater than 99%.

In order to collect the events efficiently with a high intensity beam, we built a new trigger electronics system based on the calibrated energy information and the number of electromagnetic shower clusters in the calorimeter for the J-PARC KOTO experiment. The dead time of this system is 0.16 µs and the loss was measured to be less than 1%. By performing the online clustering algorithm on the simulated data, the trigger efficiency for the primary mode ${K}_{L}\to {\pi }^{0}\nu \bar{\nu }$ is estimated to be 99.6%.

The KOTO experiment is searching for the rare decay of the neutral kaon, ${K}_{L}^{0}\to {\pi }^{0}\nu \bar{\nu }$. KOTO collected data from 2016 to 2018 and accumulated 3.1 × 10¹⁹ Protons on Target (POT). Results on the normalization analysis of this dataset are described. Three normalization modes, ${K}_{L}^{0}\to 3{\pi }^{0}$, ${K}_{L}^{0}\to 2{\pi }^{0}$, and ${K}_{L}^{0}\to 2{\gamma}$, are used to calculate the ${K}_{L}^{0}$ flux and the number of kaons at the beam exit. The data is well reproduced by the Monte Carlo and the total number of kaons is (7.14 ± 0.05) × 10¹². This gives a Single Event Sensitivity (SES) of 6.9 × 10⁻¹⁰.

We study the rare decay ${K}_{L}\to {\pi }^{0}\nu \bar{\nu }$ at the KOTO experiment at J-PARC. To detect two photons from the π⁰, the KOTO detector consists of a cesium iodide (CsI) calorimeter and hermetical veto counters. The calorimeter is made of 50 cm-long CsI crystals stacked in a cylinder of 1.9 m diameter. Each crystal is read out with a PMT on its rear side. One of the major backgrounds is caused by a neutron generating two clusters in the calorimeter. To reject such events, we have upgraded the calorimeter to distinguish photon clusters from neutron clusters by measuring the time difference of the scintillation light at the front and rear ends of the crystals. We established the methods to install 4080 silicone photomultipliers on the front surface of crystals for this purpose.

We are searching for the ${K}_{L}\to {\pi }^{0}\nu \bar{\nu }$ decay at the J-PARC KOTO experiment. The signature of the signal events is two photons from a π⁰ decay and no other detectable particles. One of the main backgrounds is caused by neutrons in the beam halo. If a beam halo neutron produces a hadronic shower in the calorimeter and a secondary neutron interacts at a different position in the calorimeter, it can mimic the ${K}_{L}\to {\pi }^{0}\nu \bar{\nu }$ decay. To suppress this hadron-cluster background, we installed MPPCs (silicon photo sensor) on the upstream surface of the CsI calorimeter in 2018. Neutrons and photons can be distinguished by using the timing difference between the MPPC signal from upstream and the PMT signal from downstream. The hadron-cluster background is suppressed to a 2.2% level retaining the 90% signal efficiency.

The recent precise measurements of the e⁺e⁻ → K⁺K⁻ and e⁺e⁻ → K_SK_L cross sections and the hadronic spectral function of the τ⁻ → K⁻K_Sν_τ decay are used to extract the isoscalar and isovector electromagnetic kaon form factors and their relative phase in a model independent way. The experimental results are compared with a fit based on the vector-meson-dominance model.