We calculate the signal rate of hypothetical heavy neutral leptons (HNL or sterile neutrinos) from kaon decays expected in the framework of the SHiP experiment. The kaons are produced in the hadronic shower initiated in the beam-dump mode by 400 GeV protons from CERN SPS. For a sufficiently light HNL (when the decays are kinematically allowed) we find kaon decays to be a noticeably richer source of HNL as compared to $D$-meson decays adopted in previous studies of the HNL phenomenology at SHiP. In particular, SHiP is capable of fully exploring the central part of the kinematically allowed region of the HNL mass and mixing with electron and muon neutrinos down to the lower cosmological bound. The latter is associated with HNL decays in the early Universe to energetic products rescattering off and thus destroying light nuclei produced at the primordial nucleosynthesis. A consistency of the HNL model with smaller mixing would require either a hierarchy -- much larger mixing of all the HNL with tau neutrino -- or non-standard cosmology and new ingredients in the HNL sector, closing the room for the minimal non-seesaw type I model with sterile neutrinos lighter than kaons.
Heavy Neutral Leptons (HNLs) are hypothetical particles predicted by many extensions of the Standard Model. These particles can, among other things, explain the origin of neutrino masses, generate the observed matter-antimatter asymmetry in the Universe and provide a dark matter candidate. The SHiP experiment will be able to search for HNLs produced in decays of heavy mesons and travelling distances ranging between $\mathcal{O}(50\text{ m})$ and tens of kilometers before decaying. We present the sensitivity of the SHiP experiment to a number of HNL's benchmark models and provide a way to calcu…
One of the main purposes of SHiP experiment is to shed light on neutrino mass generation mechanisms like the so-called seesaw. We consider a minimal type-I seesaw neutrino mass mechanism model with two heavy neutral leptons (right-handed or sterile neutrinos) with arbitrary masses. Extremely high active-sterile mixing angle requires a correlation between the phases of the Dirac neutrino couplings. Actual experimental limits on the half-life of neutrinoless double beta decay $0νββ$-rate on the active-sterile mixing angle are not significative for SHiP.
We present a comprehensive analysis of low-energy signals of hypothetical scalar leptoquark interactions in lepton and kaon transitions. We derive the most general effective four-fermion Lagrangian induced by tree-level scalar leptoquark exchange and identify the Wilson coefficients predicted by the five possible types of scalar leptoquarks. The current constraints on the leptoquark Yukawa couplings arising from lepton and kaon processes are worked out, including also loop-induced transitions with only leptons (or quarks) as external states. In the presence of scalar leptoquark interactions, w…
Recent results from the LHC's first run have revealed intriguing departures from lepton flavour universality in the semi-leptonic decays of $B$-mesons. We discuss the complementary role that rare kaon decays can provide in testing new physics explanations of these flavour anomalies. In the framework of minimal flavour violation, we relate the chiral low-energy constants involved in $K\toπ\ell\ell'$ and $K\to\ell\ell'$ ($\ell = μ\mbox{ or } e$) with the new physics Wilson coefficients of the $b\to s$ effective Hamiltonian. We comment on the determination of these low-energy constants at NA62 an…
We present a global analysis of leptonic and semileptonic kaon decay data, including all recent results published by the BNL-E865, KLOE, KTeV, ISTRA+ and NA48 experiments. This analysis, in conjunction with precise lattice calculations of the hadronic matrix elements now available, leads to a very precise determination of |Vus| and allows us to perform several stringent tests of the Standard Model.
SHiP is a proposed high-intensity beam dump experiment set to operate at the CERN SPS. It is expected to have an unprecedented sensitivity to a variety of models containing feebly interacting particles, such as Heavy Neutral Leptons (HNLs). Two HNLs or more could successfully explain the observed neutrino masses through the seesaw mechanism. If, in addition, they are quasi-degenerate, they could be responsible for the baryon asymmetry of the Universe. Depending on their mass splitting, HNLs can have very different phenomenologies: they can behave as Majorana fermions -- with lepton number viol…
We present here a study of the impact of a heavy neutrino (or heavy neutral lepton) on leptonic and semileptonic kaon decays. We used a simplified model consisting of 3 light neutrinos responsible for neutrino oscillations and a heavy sterile neutrino. We found that it can lead to large deviations from the Standard Model predictions for leptonic decays, in conflict with experimental measurements of $K_{e2}$ and the lepton universality test $R_K$. This allows to derive new constraints on the leptonic mixing for heavy sterile neutrinos. No tension was found when considering the semileptonic deca…
I discuss recent developments on non-leptonic and radiative kaon decays mainly related to direct CP-violation within the combined ChPT and 1/N_c expansion approaches. In particular, I review the status of K -> pi pi, epsilon_K', direct CP-violating K+ -> 3 pi Dalitz plot slope g and decay rate asymmetries, and the Standard Model prediction for Br(K_L -> pi0 e+ e-).
The extension of the Standard Model with two gauge-singlet Majorana fermions can simultaneously explain two beyond-the-Standard-model phenomena: neutrino masses and oscillations, as well as the origin of the matter-antimatter asymmetry in the Universe. The parameters of such a model are constrained by the neutrino oscillation data, direct accelerator searches, big bang nucleosynthesis, and requirement of successful baryogenesis. We show that the combination of all these constraints still leaves an allowed region in the parameter space below the kaon mass. This region can be probed by the furth…
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…
High-intensity proton beams impinging on a fixed target or beam dump allow to probe new physics via the production of new weakly-coupled particles in hadron decays. The CERN SPS provides opportunities to do so with the running NA62 experiment and the planned SHiP experiment. Reconstruction of kaon decay kinematics (beam mode) allows NA62 to probe for the existence of right-handed neutrinos and dark photons with masses below 0.45 GeV. Direct reconstruction of displaced vertices from the decays of new neutral particles (dump mode) will allow NA62 and SHiP to probe right-handed neutrinos with mas…
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 present a global analysis of leptonic and semileptonic kaon decays data, including all recent results by BNL-E865, KLOE, KTeV, ISTRA+, and NA48. Experimental results are critically reviewed and combined, taking into account theoretical (both analytical and numerical) constraints on the semileptonic kaon form factors. This analysis leads to a very accurate determination of Vus and allows us to perform several stringent tests of the Standard Model.
We discuss rare kaon decays that violate charged-lepton flavour conservation in supersymmetric theories with and without R parity, in view of possible experiments using an intense proton source as envisaged for a neutrino factory. In the Minimal Supersymmetric Standard Model, such decays are generated by box diagrams involving charginos and neutralinos, but the limits from μ-> e γ, μ-e conversion and Δm_K constrain the branching ratios to challengingly small values. However, this is no longer the case in R-violating theories, where such decays may occur at tree level at rates close to the pres…
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…
Recent anomalies in the decays of $B$ mesons and the Higgs boson provide hints towards lepton flavor (universality) violating physics beyond the Standard Model. We observe that four-fermion operators which can explain the $B$-physics anomalies have corresponding analogs in the kaon sector, and we analyze their impact on $K\toπ\ell \ell'$ and $K\to\ell \ell'$ decays $(\ell=μ,e)$. For these processes, we note the corresponding physics opportunities at the NA62 experiment. In particular, assuming minimal flavor violation, we comment on the required improvements in sensitivity necessary to test th…
In the Standard Model extended by sterile neutrinos, modified W-l-nu couplings arise, which are able to induce a tree-level enhancement to lepton flavour universality violation in kaon decays. The additional mixing between the active neutrinos and the sterile ones can generate deviations from unitarity in the leptonic mixing matrix for charged currents. We reconsidered this idea in the context of the inverse seesaw and evaluated its impact on the well measured ratio $R_K$. We show that the current experimental bound can be saturated in agreement with the different experimental and observationa…
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.
We present an overview of searches fo violation of lepton flavor universality with focus on low energy precision probes using pions, kaons, tau leptons, and nuclear beta decays. The current experimental results are reviewed, the theoretical status within the context of the Standard Model is summarized, and future prospects (both experimental and theoretical) are discussed. We review the implications of these measurements for physics beyond the Standard Model by performing a global model-independent fit to modified $W$ couplings to leptons and four-fermion operators. We also discuss new physics…
In this talk I describe work on computing non-leptonic matrix elements consistently with both long and short distance contributions included. On the simpler example of the $π^+$-$π^0$ mass difference I explain in detail the matching procedure and the difference between various low-energy models. I then explain the new difficulties in non-leptonic Kaon decays and how the matching here can in principle be done in the same way when scheme dependences are correctly accounted for. In the end I summarize the results J. Prades and I obtain for the $ΔI=1/2$ rule and $B_6$.
Heavy neutral leptons ($N$) below the kaon mass are severely constrained by cosmology and lab-based searches for their decays in flight. If $N$ interacts via an additional force, $N\toνe^+e^-$ decays are enhanced and cosmological limits can be avoided. We show that the T2K and MicroBooNE neutrino experiments provide the best limits on the mixing of $N$ with muon-neutrinos, outperforming past-generation experiments, previously thought to dominate. We constrain models with electromagnetically-decaying and long-lived $N$, such as in a transition-magnetic-moment portal and in a leptophilic axion-l…
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.…
We investigate lepton-number-violating decays $K^\mp \rightarrow π^\pm l^\mp l^\mp$ in the presence of sterile neutrinos. We consider minimal interactions with Standard-Model fields through Yukawa couplings as well as higher-dimensional operators in the framework of the neutrino-extended Standard Model Effective Field Theory. We use $SU(3)$ chiral perturbation theory to match to mesonic interactions and compute the lepton-number-violating decay rate in terms of the neutrino masses and the Wilson coefficients of higher-dimensional operators. For neutrinos that can be produced on-shell, the deca…
In the chiral limit, the $D=6$ contribution to the Operator Product Expansion (OPE) of the $\mathrm{VV-AA}$ correlator of quark currents only depends on two vacuum condensates, which can be related to hadronic matrix elements associated to CP violation in non-leptonic kaon decays. We use those relations to determine $\langle(ππ)_{I=2}|\mathcal{Q}_{8}|K\rangle$, using the updated ALEPH spectral functions. Alternatively, we use those relations in the opposite direction. Taking the values of the matrix elements from the lattice to obtain the $D=6$ vacuum elements provides a new short-distance con…
We study the scaling with the number of colours, $N_c$, of the weak amplitudes mediating kaon mixing and decay. We evaluate the amplitudes of the two relevant current-current operators on the lattice for $N_c=3-7$. We conclude that the subleading $1/N_c$ corrections in $\hat{B}_K$ are small, but those in the $K \rightarrow ππ$ amplitudes are large and fully anti-correlated in the $I=0, 2$ isospin channels. We briefly comment on the implications for the $ΔI=1/2$ rule.
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…
In this talk, I first motivate the use of Chiral Perturbation Theory in the context of Lattice QCD. In particular, I explain how partially quenched QCD, which has, in general, unequal valence- and sea-quark masses, can be used to obtain real-world (i.e. unquenched) results for low-energy constants. In the second part, I review how Chiral Perturbation Theory may be used to overcome theoretical difficulties which afflict the computation of non-leptonic kaon decay rates from Lattice QCD. I argue that it should be possible to determine at least the O(p^2) weak low-energy constants reliably from nu…
We study single kaon production off the nucleon induced by electrons (positrons) i.e. $e^-(e^+) + N \rightarrow ν_e (\bar ν_e) + \bar K (K) + N^\prime$ at low energies. The possibility of observing these processes with the high luminosity beams available at TJNAF and Mainz is discussed, taking into account that the strangeness conserving electromagnetic reactions have a higher energy threshold for $\bar K (K)$ production. The calculations are done using a microscopic model that starts from the SU(3) chiral Lagrangians, includes background terms and the resonant mechanisms associated to the low…
The weak leptonic decays $π^\pm\toμ^\pmν_μ(\barν_μ), π^\pm\to e^\pmν_e(\barν_{e}), K^\pm\toμ^\pmν_μ(\barν_μ)$ and $K^\pm\to e^\pm ν_e(\barν_{e})$ are investigated within the framework of the SU(3) Nambu-Jona-Lasinio model, in the vacuum and in quark matter in $β$ equilibrium. It is found that, at low densities, the decay rates of the charge multiplets, that are decoupled in this kind of flavor asymmetric matter, are affected differently. As the density increases, these decay rates become closer and show a tendency to vanish. This shows that weak interactions are strongly influenced by the medi…
The kaon sector is characterised by several processes which are under active investigation across different experiments. In this work, we present the global picture that emerges from a study of the different decay modes. We begin by revisiting the theoretical component of these decays and providing up-to-date predictions of the Standard Model as well as the corresponding uncertainties. Several new features emerge, in particular for $K_{S,L}\to μ\barμ$, and are presented in considerable detail. This offers an ideal platform for extracting the parameter space supported by the existing data. Moti…
New measurements in leptonic kaon and pion decays: experimental and theoretical perspectives
Deutsches Elektronen-Synchrotron DESY（德国电子同步加速器）；Horia Hulubei National Institute for R&D in Physics and Nuclear Engineering（霍里亚·胡卢贝伊核物理与核工程研发国家研究所）；INFN, Laboratori Nazionali di Frascati（意大利国家核物理研究院弗拉斯卡蒂国家实验室）；Institut für Physik, Humboldt-Universität zu Berlin（柏林洪堡大学物理研究所）
We analyze the decays $K\toπ\ellν$ and $P\to\ellν$ ($P=K,π$, $\ell=e,\,μ$) using a low-energy Effective-Field-Theory approach to parametrize New Physics and study the complementarity with baryon $β$ decays. We then provide a road map for a global analysis of the experimental data, with all the Wilson coefficients simultaneously, and perform a fit leading to numerical bounds for them and for $V_{us}$. A prominent result of our analysis is a reinterpretation of the well-known $V_{ud}-V_{us}$ diagram as a strong constraint on new physics. Finally, we reinterpret our bounds in terms of the $SU(2)_…
In this paper, we have investigated the charged kaons decay at the lowest order in the presence of a circularly polarized laser field. To be more precise, we have examined the leptonic decay of both positive (matter) and negative (antimatter) kaon which weakly decay via the exchange of $W$ boson. Indeed, we have derived the expression of the leptonic decay width, the leptonic branching ratio, the leptonic ratio and the charged kaon lifetime by using the decay matrix approach. In addition, by using numerical computation, we have presented and discussed how the laser field influences these physi…
The origin of the baryon asymmetry of the Universe (BAU) is one of the major puzzles beyond the Standard Model. Detecting the particles responsible for the generation of the BAU would enormously boost our understanding of physics of the early Universe. Here we demonstrate that searches for displaced vertices at ATLAS, CMS and LHCb allow detecting heavy neutral leptons (HNL) with parameters that can simultaneously lead to the successful generation of the BAU and explain the masses and oscillations of active neutrinos. The combination of a dedicated LHC search program and a complementary Intensi…
I review lattice quantum chromodynamics as relevant to the kaon system. Topics covered include the pseudoscalar masses and decay constants, the chiral effective lagrangian, $f_K/f_π$, semi-leptonic kaon decay form factors, and the neutral kaon oscillation parameter $B_K$.
The recent significant progress on both the experimental and theoretical sides on the study of leptonic and semileptonic kaon decays allows to precisely test the Standard Model. Here we present results for the determination of Vus from experimental data, the comparison between the values of Vus obtained from data on semileptonic and leptonic kaon decays, and tests of lepton universality in semileptonic kaon decays.
SHiP is a newly proposed fixed-target experiment at the CERN SPS with the aim of searching for hidden particles that interact very weakly with SM particles. The work presented in this document investigates SHiP's physics reach in the parameter space of the Neutrino Minimal Standard Model ($ν$MSM), which is a theory that could solve most problems left open by the Standard Model with sterile neutrinos. A model introducing an extra $U(1)$ symmetry in the hidden sector, providing a natural candidate for dark matter, is also explored. This work shows that the SHiP experiment can improve by several …
SHiP is a new general purpose fixed target experiment at the CERN SPS designed to complement LHC experiments in the search for new physics. In its initial phase, the $400$ GeV proton beam extracted from the SPS will be dumped on a heavy target with the aim of integrating $2\times10^{20}$ pot in 5 years. Shielded by an active muon shield, a dedicated detector, based on a long decay volume followed by a spectrometer and particle identification detectors, will allow probing a variety of models with light long-lived exotic particles with masses below $\mathcal{O}(10)\; \mathrm{GeV}/{c^2}$. The mai…
We present a determination of the ratio of kaon and pion leptonic decay constants in isosymmetric QCD (isoQCD), $f_K / f_π$, making use of the gauge ensembles produced by the Extended Twisted Mass Collaboration (ETMC) with $N_f = 2 + 1 + 1$ flavors of Wilson-clover twisted-mass quarks, including configurations close to the physical point for all dynamical flavors. The simulations are carried out at three values of the lattice spacing ranging from $\sim 0.068$ to $\sim 0.092$ fm with linear lattice size up to $L \sim 5.5$~fm. The scale is set by the PDG value of the pion decay constant, $f_π^{i…
The confinement mechanism proposed earlier by the author is employed for to compute the decay constants $f_P$ corresponding to leptonic decays $P\to l^\pm+ν_l$, $l=μ, e$, where $P$ stands for any meson from $π^\pm$, $K^\pm$. For this aim the weak axial form factor of $P$-meson is nonperturbatively calculated. The study entails estimates for parameters of the confining SU(3)-gluonic field in charged pions and kaons. The corresponding estimates of the gluon concentrations, electric and magnetic colour field strengths are also adduced for the mentioned field at the scales of the mesons under cons…
During the last few years, new experimental and theoretical results have allowed ever-more-stringent tests of the Standard Model to be performed using kaon decays. This overview of recent progress includes updated results for the evaluation of the CKM matrix element V_us from kaon decay data and related tests of CKM unitarity and gauge and lepton universality.
Standard lattice calculations in kaon physics are based on the evaluation of matrix elements of local operators between two single-hadron states or a single-hadron state and the vacuum. Recent progress in lattice QCD has gone beyond these standard observables. I will review the status and prospects of lattice kaon physics with an emphasis on non-leptonic $K\toππ$ decay and long-distance processes including $K^0$-$\overline{K^0}$ mixing and rare kaon decays.
We study the discovery prospect of different three body lepton number violating~(LNV) meson decays $M_{1}^{-}\to\ell_{1}^{-}\ell_{2}^{-}M_{2}^{+}$ in the framework of right handed~(RH) neutrino extended Standard Model~(SM). We consider a number of ongoing experiments, such as, NA62 and LHCb at CERN, Belle II at SuperKEK, as well as at the proposed future experiments, SHiP, MATHUSLA and FCC-ee. The RH Majorana neutrino $N$ mediating these meson decays provides a resonant enhancement of the rates, if the mass of $N$ lies in the range $(100\, \text{MeV}-6\, \text{GeV})$. We consider the effect of…
I review lattice calculations and results for hadronic parameters relevant for kaon physics, in particular the vector form factor f+(0) of semileptonic kaon decays, the ratio fK/fpi of leptonic decay constants and the kaon bag parameter BK. For each lattice calculation a colour code rating is assigned, by following a procedure which is being proposed by the Flavianet Lattice Averaging Group (FLAG), and the following final averages are obtained: f+(0)=0.962(3)(4), fK/fpi = 1.196(1)(10) and \hat BK = 0.731(7)(35). In the last part of the talk, the present status of lattice studies of non-leptoni…
Recent results and future prospects of the particle physics experiments with neutral and charged K-meson (kaon) decays are reviewed. Topics include CP violation, rare decays, leptons in kaon decays, tests of CPT and quantum mechanics, radiative decays, hadrons in kaon decays, basic observables, Vus and CKM unitarity, and exotic searches. Experimental techniques developed for the kaon decay experiments are discussed.
Theoretical aspects of kaon and muon decays are reviewed. In particular, three topics on kaon and muon decays, namely $K \to πν\barν$ processes, T violation in $K^+ \to π^0μ^+ ν$ decay and lepton flavor violation in muon decay are considered. Theoretical backgrounds and possible significance on new physics searches by these processes are discussed.
We report on the status of our dynamical simulations of a $SU (N_c )$ gauge theory with $N_c=3-6$ and $N_f =4$ fundamental fermions. These ensembles can be used to study the Large $N_c$ scaling of weak matrix elements in the GIM limit $m_c=m_u$, that might shed some light on the origin of the $ΔI=1/2$ rule. We present preliminary results for the $K \to π$ matrix elements in the $N_c=3$ dynamical simulations, where we observe a significant effect of the quark loops that goes in the direction of enhancing the ratio of $A_0/A_2$ amplitudes. Finally, we present the relevant NLO Chiral Perturbation…
We review a novel model-independent approach to the analysis of new-physics effects in the $s\to u\ell^-\barν$ transitions. We apply it to (semi)leptonic kaon decays and study their complementarity with pion and hyperon $β$ decays or with collider searches of new physics.
