Meson decays offer a good opportunity to probe new physics. The rare kaon decay $K^+ \rightarrow π^+ ν\barν$ is one of the cleanest of them and, for this reason, is rather sensitive to new physics, in particular, vector mediators. NA62 collaboration, running a fixed-target experiment at CERN, recently reported an unprecedented sensitivity to this decay, namely a branching fraction of $BR(K^+ \rightarrow π^+ ν\barν) = (11^{+4.0}_{-3.5})\times 10^{-11}$ at 68\% C.L. Vector mediators that couple to neutrinos may yield a sizeable contribution to this decay. Motivated by the new measurement, we interpret this result in the context of a concrete $Z^\prime$ model, and put our findings into perspective with the correlated $K_L \rightarrow π^0 ν\barν$ decay measured by KOTO collaboration, current, and future colliders, namely the High-Luminosity and High-Energy LHC.
The following proceedings contain a theory perspective on rare Kaon decays. I review rare kaon decays in the LHC era: we discuss interplay with B-anomalies and possible New Physics in direct CP violation in $K\to 2π$: very rare kaon decays like $K \to πν\barν$ are very important to this purpose. We discuss also the decays $K^0 \to μ^+ μ^-$ due to the LHCB measurement
I review recent developments in rare and radiative kaon decays from the theory side, with emphasis on those modes that are actively analyzed by the experimental collaborations.
We summarize both the study of CP violation with $K$ and $B$ mesons, as well as rare decays of kaons, emphasizing recent developments. The topics discussed include the unitarity triangle, $ε'/ε$, $K\toπν\barν$ and other rare $K$ decays, T-odd asymmetries in kaon physics, theoretical aspects of CP violation in B decays, $B\to J/ΨK_S$, $B\toππ$, $B\toπK$ and inclusive CP asymmetries.
We present a brief overview of rare K decays, emphasizing the different role of Standard Model and possible New Physics contributions in various channels.
We discuss theoretical issues in radiative rare kaon decays. The interest is twofold: to extract useful short-distance information and understand the underlying dynamics. We emphasize channels where either we can understand non-perturbative aspects of QCD or there is a chance to test the Standard Model.
Rare Kaon decays and CP violation are important tools to test the Standard Model and its extensions. We describe kaon physics observables testing CP violation and more generally short distance physics. Channels under consideration will be K -> pi nu nubar, K -> pi l+ l-, K+- > pi 3 pi, K+- -> pi+- pi gamma, KS -> mu mu and K+- -> pi+- pi0 e+ e-
We review some recent theoretical results on rare kaon decays. Particular attention is devoted to establish the short distance (direct CP violating) contribution to K_L => π^0 e \bar{e}. This is achieved by a careful study of the long distance part. As byproduct, we discuss interesting chiral tests.
We discuss issues in rare and radiative kaon decays. The interest is to extract useful short-distance information and uncover underlying dynamics. We emphasize channels where either we can understand non-perturbative aspects of QCD or there is a chance to test the Standard Model.
The theory of rare $K$ decays is reviewed, emphasizing short-distance processes and the prospects to probe the physics of flavour. A brief overview of the subject is presented, along with a more detailed discussion of the theory of $K\toπν\barν$ decays.
Most of the analytic approaches which are used at present to understand Kaon decays, get their inspiration from QCD in the limit of a large number of colours $N_c$. After a general overview, we illustrate this with a recent application to the evaluation of the process $K_L\raμ^+ μ^-$ in the Standard Model.
We explore the possibility of lepton number violation (LNV) manifesting in the rare kaon decay $K\toπνν$, and its consequences for radiative neutrino mass generation and the washout of Lepton asymmetry in high-scale leptogenesis scenarios. We perform the analysis in a model-independent framework, the Standard Model effective field theory (SMEFT), and discuss the possible LNV nature of the rare kaon decay in the context of the currently operating NA62 experiment at CERN. We find that, in case of a LNV interaction, its detection would put high-scale leptogenesis under tension and would hint to s…
We review some recent theoretical results on rare kaon decays. Particular attention is devoted to find Standard Model tests. This is theoretically easy in $K\to πν\barν$, while a careful study of the long distance contributions is needed for $K_{L}\to π^{0}e% \bar{e}$, $K_{L}\to μ\barμ$ and $K\to ππγ$
Rare K decays are an important testing ground of the electroweak flavour theory. They can provide new signals of CP-violation phenomena and, perhaps, a window into physics beyond the Standard Model. The interplay of long-distance QCD effects in strangeness-changing transitions can be analyzed with Chiral Perturbation Theory techniques. Some theoretical predictions obtained within this framework for radiative kaon decays are reviewed, together with the present experimental status.
We discuss the theory prediction of epsilon_K and the rare K -> pi nu nu-bar decays and review the structure and current status of higher-order contributions to these flavour changing processes in the standard model in some detail. This includes the next-to-next-to-leading order QCD calculation to the charm quark contribution to K+ -> pi+ nu nu-bar and to the charm-top quark contribution to epsilon_K. Electroweak corrections to the rare kaon decays are also discussed.
We review some recent theoretical results on radiative rare kaon decays. Particular attention is devoted to the channels $K\to πl\bar{% l}$ and $K\to ππγ$, where we are (or might be) able to extract the short distance contributions. This is achieved by a careful study of the long distance part. We study also CP violating observables, which are sensitive also to extensions of the SM. As byproduct, we discuss interesting chiral tests.
We review the status of theory and experiment of very rare and forbidden kaon decays. We then review the radiative non-leptonic decays, and the associated Dalitz pair modes. We pay particular attention to the study of long distance physics in radiative decays within the framework of chiral perturbation theory ($χ$PT). We discuss the experiments that will run in the near future and the modes that they will be able to study.
In framework of the chiral perturbation theory we obtain the phenomenological relations between decay branches of rare radiative kaon to pion and leptons $K^+ \to π^+ l^+ l^-$ and $K^0_S \to π^0 l^+ l^-$ and meson form factors. The comparison of these results with the present day experimental data shows us that the ChPT relations for a charge kaon can determine meson form factors from already measured decay rates at high precision level. However, in the case of the neutral kaon decays $K^0 \to π^0 e^+ e^- (μ^+ μ^-)$ the formfactor data are known to a high precision than data on the differentia…
We review some new developments in the theoretical description of the processes K ->pi gamma gamma, K_L ->gamma l^+ l^-, K_L ->pi^0 e^+ e^- and K_L ->mu^+ mu^-.
We discuss on the search for the right-handed weak interaction effects in the SU(2)$_L \times$SU(2)$_R$ model with lepton doublets $(ν_\ell, \ell^-)_L$ and $(N_\ell, \ell^-)_R$ ($\ell = e, μ, τ)$. We will point out that only the chance of the observation of the right-handed weak interaction effect will be in the rare decay $K^+ \rightarrow π^- μ^+ μ^+$.
Owing to the strong suppression of flavour-changing neutral-current transitions in the Standard Model, rare kaon decays constitute a superb tool to constrain hypothetical new-physics interactions. At the same time, they provide many interesting tests of the Standard Model itself, being sensitive both to short-distance electroweak scales and to the long-distance QCD dynamics. A brief overview of the current status is presented. The Standard Model prediction for the direct CP-violating ratio $\varepsilon'/\varepsilon$ is also discussed.
Rare Kaon decays provide sensitive probes of short distance physics. Among the most promising modes are the K+ --> pi+ nu anti-nu and K(L) --> pi0 nu anti-nu modes due to their theoretical cleanness and the dedicated experiments, NA62 and KOTO. The key to the success of New Physics searches in these modes is the precision in the standard model prediction. We review the status and the recent progress of their standard model prediction, and also discuss the predictions and New Physics sensitivities of the K(L) --> pi0 l+ l- and K(L) --> mu+ mu- decays.
The rare kaon decay K^+ --> π^+ ν\barν is considered in the framework of the models based on the SU(3)_C X SU(3)_L X U(1)_N (3 - 3 - 1) gauge group. It is shown that a lower bound of the Z' mass in the 3 - 3 - 1 model with right-handed neutrinos at a value of 3 TeV is derived, while that in the minimal version -- 1.7 TeV.
We study the rare kaon decays in the framework of general SUSY models. Unlike the results in the literature, we find the contributions from the gluino exchange to the branching ratio of $K^+\to π^+ ν\barν$ can reach the central value ($\sim 1.5 \times 10^{-10}$) of the new E787 data while the predicted value of standard model is less than $10^{-10}$. We also find that the same effects also enhance the decays of $K_{L}\to π^0 ν\barν$, $K_L\toπ^0e^{+} e^{-}$ and $K_L\toμ^+ μ^-$.
The rare kaon decay $K^+ \ra π^- μ^+ μ^+$ is violating lepton number by two units and is investigated within the context of Majorana neutrino masses. Using a new upper bound for this decay from E865 an upper limit on the effective Majorana mass term $\m_{μμ} < 500$ GeV could be obtained. This is improving existing bounds by about one order of magnitude. Implications on heavy neutrinos are discusse d as well as future possibilities to improve limits on this as well as other elements of the Majorana m ass matrix are investigated.
We analyze the contributions to rare kaon decays mediated by flavor-changing Z-penguin diagrams in a generic low-energy supersymmetric extension of the Standard Model. In order to perform a model-independent analysis we expand the squark mass matrices around the diagonal, following the so called mass-insertion approximation. We argue that in the present case it is necessary to go up to the second order in this expansion to take into account all possible large effects. The current bounds on such second-order term, which was neglected in previous analyses, are discussed in detail and the corresp…
We study the unknown coupling constants that appear at order $p^4$ in the Chiral Perturbation Theory analysis of $K \to πγ^* \to πl^+ l^-$, $K^{+-} \to π^{+-} γγ$ and $K \to ππγ$ decays. To that end, we compute the chiral realization of the $ΔS \, = \, 1$ Hamiltonian in the framework of the $1/N_c$-expansion of the low-energy action. The phenomenological implications are also discussed.
We describe possible kaon physics goals to achieve with a high luminosity phi-factory. We motivate the relevance to improve the present bounds on CPT kaon physics quantities. Also, the interferometer machine phi-factory is useful to study CP violating/conserving effects in kaon decays. Thus we investigate K --> 3 pi amplitudes: charge asymmetries are interesting in charged kaon decays. In the case of neutral kaon decays one can study directely K_S --> 3 pi or interferences effects. Interference may also be used to study the CP even K_S -->pi+ pi- pi0 and final state interactions.
We investigate the possibility to probe lepton number violating (LNV) operators in the rare kaon decay $K\toπνν$. Performing the analysis in the Standard Model effective field theory with only light active Majorana neutrinos, we determine the current limits on the corresponding LNV physics scale from the past E949 experiment at BNL as well as the currently operating experiments NA62 at CERN and KOTO at J-PARC. We focus on the specific signature of scalar currents in $K\toπνν$ arising from the LNV nature of the operators and study the effect on the experimental sensitivity, stressing the need f…
A model with $L_μ -L_τ$ gauge symmetry is the least constrained model as a resolution to the disagreement of the muon anomalous magnetic moment between the theoretical predictions and the experimental results. In this paper, we discuss how well the $L_μ - L_τ$ model can be constrained by looking for decays of the charged kaon associated with a $L_μ-L_τ$ gauge boson. More concretely, we consider searches for single muon tracks from the decays of stopped charged kaon as in the E949 experiment. In our conservative estimation, we find that the favored parameter region for the muon anomalous magnet…
Rare leptonic kaon and pion decays $K^+(π^+) \to μ^+\, ν_μ\, e^+ e^-$ can be used to probe a dark photon of mass ${\cal O}(10)$~MeV, with the background coming from the mediation of a virtual photon. This is most relevant for the 16.7-MeV dark photon proposed to explain a 6.8$σ$ anomaly recently observed in $^8$Be transitions by the Atomki Collaboration. We evaluate the reach of future experiments for different scenarios of how the dark photon couples with the standard model particles, and show that a great portion of the preferred 16.7-MeV dark photon parameter space can be decisively probed.…
Prospective searches for lepton flavor violation (LFV) in rare kaon decays at the existing and future intermediate-energy accelerators are considered. The proposed studies are complementary to LFV searches in muon-decay experiments and offer a unique opportunity to probe models with approximately conserved fermion-generation quantum number with sensitivity superior to that in other processes. Consequently, new searches for LFV in kaon decays are an important and independent part of the general program of searches for lepton flavor violation in the final states with charged leptons.
Rare kaon processes appear to be particularly suitable to study the extensions of the standard model, especially if the possibility for eventual direct evidence becomes unlikely. In this review, we discuss processes that are important as a test of either the standard model or supergravity. Moreover, some of these are important even for both the standard model and for supergravity. Particular attention is paid to the reduction of uncertainties in the calculation, especially the ones coming from the confinement effects. Recent approaches, such as chiral perturbation theory, the large $N_c$-expan…
Two photon processes are a wonderful by-product of an $e^+e^-$ collider at any energy. Two photon reactions probe the very structure of matter. A machine operating below 2 GeV has the potential to reveal the Higgs sector of the strong interaction -- the scalars with vacuum quantum numbers that reflect dynamical mass generation from the breakdown of chiral symmetry. One of the many $e^+e^-$ machines around the globe must have a dedicated $γγ$ facility.
Probing scalar and pseudoscalar new physics using rare kaon decays
INFN-Sezione di Napoli（意大利国家核物理研究所那不勒斯分部）；Indian Institute of Technology Delhi（德里印度理工学院）；Université Claude Bernard Lyon 1, CNRS/IN2P3, Institut de Physique des 2 Infinis de Lyon（里昂第一大学，法国国家科学研究中心/法国国家粒子物理研究所，里昂双无穷物理研究所）；CERN（欧洲核子研究组织）；Institut Universitaire de France (IUF)（法国高等研究院）
Recent results and future prospects in the rare kaon-decay experiments at KEK, BNL, CERN and FNAL are reviewed. Emphasis is placed on the quark flavor dynamics in the flavor-changing neutral current processes. Experimental and data-analysis techniques developed in the rare decay experiments are discussed.
New kaon photoproduction data on a proton, gamma + p --> K+ + Lambda, are analyzed using a multipole approach. The background terms are given in terms of gauge invariant, crossing symmetric, Born diagrams with hadronic form factors, while the resonances are parameterized using Breit-Wigner forms. Preliminary results suggest a number of new resonances, as predicted by many quark model studies. A comparison between the extracted multipoles and those obtained from KAON-MAID is presented.
Over the next years, the Flavour Physics community will be looking for inconsistencies of the Standard Model (SM) by exploiting new and precise measurements. In these ``indirect new physics'' searches, the key strategy is to concentrate on observables, which are theoretically clean and preferably suppressed in the SM. In this respect, the four golden modes K+->pi+ n n, KL->pi n n and KL->pi0 l+l- are very promising. The pollution from hadronic uncertainties in these decays is at present under control with good accuracy, thanks to the interplay between theory information (Chiral Perturbation Th…
We present an updated discussion of $K\raπ\bar{l} l$ decays in a combined framework of chiral perturbation theory and Large--$N_c$ QCD, which assumes the dominance of a minimal narrow resonance structure in the invariant mass dependence of the $ \bar{l} l$ pair. The proposed picture reproduces very well, both the experimental $K^+\raπ^+ e^+ e^-$ decay rate and the invariant $e^+ e^-$ mass spectrum. The predicted Br$(K_S\raπ^0 e^+ e^-)$ is, within errors, consistent with the recently reported result from the NA48 collaboration. Predictions for the $K\raπμ^{+}μ^{-}$ modes are also obtained. We f…
Rare kaon decays are an important testing ground of the electroweak flavor theory: They can provide new signals of CP-violating phenomena. The interplay of long-distance QCD effects in strangeness-changing transitions can be analyzed with Chiral Perturbation Theory techniques. In particular, two rare kaon decays are analyzed: The first decay, K_L -> pi0 e+e-, is being searched for as a signal of direct Delta S = 1 CP violation. We provide a thorough updating of the analysis of the three components of the decay: 1) Direct CP violation, 2) CP violation through the mass matrix and 3) CP-conservin…
With anomalies found in cosmic ray observations and unsolved questions of the Standard Model of particle physics like the discrepancy in the muon's anomalous magnetic moment, the idea of an U(1) extension of the Standard Model arose. This extension allows for the interaction of Dark Matter by exchange of a photon-like massive force carrier $A'$ not included in the Standard Model. We discuss the possibility to constrain the dark photon parameter space by using data taken from rare kaon decays. Therefore we analyze the decay $K\rightarrow μνA'$ as a signal process and calculate the expected Stan…
We review the current status of the field of rare kaon decays. The study of rare kaon decays has played a key role in the development of the standard model, and the field continues to have significant impact. The two areas of greatest import are the search for physics beyond the standard model and the determination of fundamental standard-model parameters. Due to the exquisite sensitivity of rare kaon decay experiments, searches for new physics can probe very high mass scales. Studies of the k->pnn modes in particular, where the first event has recently been seen, will permit tests of the stan…
We entertain the possibility that scalar leptoquarks (LQs) generate consequential effects on the strangeness-changing decays of hyperons and kaons involving missing energy carried away by a pair of invisible fermions. Although such processes have suppressed rates in the standard model (SM), they could get significant enhancement in the presence of the LQs. In order to respect the available data on the kaon modes $K\toπν\barν$ and increase the rates of the hyperon decays substantially at the same time, two different scalar LQs are needed. If the LQs have Yukawa couplings solely to SM fermions, …
The rare kaon decays K_L -> pi^0 nu {bar nu}, K^+ -> pi^+ nu {bar nu}, K_L -> pi^0 e^+ e^- and K_L -> pi^0 mu^+ mu^- are theoretically very clean and, being strongly CKM suppressed, highly sensitive to New Physics (NP). Recent Flavour Physics analyses show that they represent unique probes for revealing NP effects and to provide information on the NP flavour structure. After a brief discussion of the main properties that make rare K decays so promising and of the basic ideas of the most interesting NP models, we review the results of recent phenomenological analyses both within and beyond the …
The rare kaon decays $K\toπν\barν$ are strongly suppressed in the standard model and widely regarded as processes in which new phenomena, not predicted by the standard model, may be observed. Recognizing such new phenomena requires precise standard model prediction for the braching ratio of $K\toπν\barν$ with controlled uncertainty for both short-distance and long-distance contributions. In this work we demonstrate the feasibility of lattice QCD calculation of the long-distance contribution to rare kaon decays with the emphasis on $K^+\toπ^+ν\barν$. Our methodology covers the calculation of bo…
New SAPHIR p(gamma,K+)Lambda total cross section data show a resonance structure at a total c.m. energy around 1900 MeV. We investigate this feature with an isobar model and find that the structure can be well explained by including a new D_{13} resonance at 1895 MeV. Such a state has been predicted by a relativistic quark model at 1960 MeV with significant gamma-N and K-Lambda branching ratios. We demonstrate how the measurement of the photon asymmetry can be used to further study this resonance. In addition, verification of the predicted large decay widths into the eta-N and eta'-N channels …
We show that long distance contributions to the rare decays K -> pi nu nu-bar and K -> pi l+ l- can be computed using lattice QCD. The proposed approach requires well established methods, successfully applied in the calculations of electromagnetic and semileptonic form factors. The extra power divergences, related to the use of weak four-fermion operators, can be eliminated using only the symmetries of the lattice action without ambiguities or complicated non-perturbative subtractions. We demonstrate that this is true even when a lattice action with explicit chiral symmetry breaking is employe…
Conventionally for observable $n-{\bar n}$ oscillation through Pati-Salam intermediate gauge symmetry in $SO(10)$, the canonical seesaw mechanism is also constrained by $M_R \sim M_C \le 10^6$ GeV which yields light neutrino masses much larger than the neutrino oscillation data. Recently, this difficulty has been evaded via inverse seesaw mechanism, but with proton lifetime far beyond the experimentally accessible limits. In the present work, adopting the view that we may have only a TeV scale $Z^{\prime}$ gauge boson, we show how a class of non-SUSY $SO(10)$ models allow experimentally verifi…
The present status of Kaon physics is summarized from a theory point of view. Focus is laid on $ΔS=2$, $ΔS=1$ as well as on rare Kaon decays, where progress has been made for instance in the case of $\varepsilon_K$ and $K_S\to μ^+μ^-$. Furthermore, several New Physics scenarios are discussed in the context of rare Kaon decays and other Kaon observables.
We introduce and discuss basic topics in the theory of kaons and charmed particles. In the first part, theoretical methods in weak decays such as operator product expansion, renormalization group and the construction of effective Hamiltonians are presented, along with an elementary account of chiral perturbation theory. The second part describes the phenomenology of the neutral kaon system, CP violation, $\varepsilon$ and $\varepsilon'/\varepsilon$, rare kaon decays ($K\toπν\barν$, $K_L\toπ^0 e^+e^-$, $K_L\toμ^+μ^-$), and some examples of flavour physics in the charm sector.
In this overview, I discuss some of the open issues in Kaon physics. After briefly touching on lattice calculations of Kaon dynamics and tests of CPT, my main focus of attention is on epsilon prime over epsilon and on constraints on the CKM model. The impact of rare K- decays and of experiments with B-mesons for addressing the issue of CP-violation is also discussed. The importance of looking for signals of flavor-conserving CP violating phases is emphasized.
Results are presented for the two-body decays of mesons into light neutralinos and from the first complete calculation of the loop-induced decays of kaons to pions plus light neutralinos and of B mesons to kaons plus light neutralinos. The branching ratios are shown to be strongly suppressed within the MSSM with minimal flavor violation, and no bounds on the neutralino mass can be inferred from experimental data, i.e. a massless neutralino is allowed.
We analyze the rare kaon decays $K_L \to π^0 ν\bar ν$, $K^+ \to π^+ ν\bar ν$, $K_L \to π^0 e^+ e^-$ and $K_L \to μ^+ μ^-$ in conjunction with the CP violating ratio $ε'/ε$ in a general class of supersymmetric models in which $Z$- and magnetic-penguin contributions can be substantially larger than in the Standard Model. We point out that radiative effects relate the double left-right mass insertion to the single left-left one, and that the phenomenological constraints on the latter reflect into a stringent bound on the supersymmetric contribution to the $Z$ penguin. Using this bound, and those …
