22 LaTeX pages, 11 ps figures, plenary talk at the XXVI International Symposium on Lattice Field Theory, July 14-19, 2008, Williamsburg, VA, USA. v2. References and discussion added in Sec. 5. Discussions in Sec. 2 and 2.1 improved. Two criteria in Sec. 3.1 slightly modified and resulting changes implemented. World averages unchanged. v3. Typos corrected
I critically review recent lattice QCD results relevant for kaon phenomenology, as well as the methods that are used to obtain them. The focus is on calculations with N_f=2 and N_f=2+1 flavors of sea quarks. Concerning methodology, the subjects covered include a discussion of how best to extrapolate and/or interpolate results to the physical quark-mass point, a scheme for assessing the extent to which a lattice QCD calculation includes the various effects required to compute a given quantity reliably and a procedure for averaging lattice results. The phenomenological topics that I review comprise leptonic and semileptonic kaon decays, as well as neutral kaon mixing and CP violation in K->ππdecays.
We present a progress update on the calculation of beyond the standard model (BSM) kaon mixing matrix elements at the physical point. Simulations are performed using 2+1 flavour domain wall lattice QCD with the Iwasaki gauge action at 3 lattice spacings and with pion masses ranging from 430 MeV to the physical pion mass.
We calculate the kaon semileptonic form factors using the two sets of the PACS10 configuration, whose physical volumes are more than (10 fm)$^4$ at the physical point. The lattice spacings are 0.063 and 0.085 fm. The configurations were generated using the Iwasaki gauge action and $N_f=2+1$ stout-smeared nonperturbatively $O(a)$-improved Wilson quark action. From the momentum transfer dependence of the form factors, we evaluate the slope and curvature for the form factors at the zero momentum transfer. Furthermore, we calculate the phase space factor, which is used to obtain $|V_{us}|$ through…
We present preliminary results for the calculation of the Kaon Bag parameter $B_K$ in $N_f=2+1$ lattice QCD, using Möbius Domain Wall Fermion ensembles generated by the RBC-UKQCD collaboration. This computation is done directly at physical meson masses, so that we do not have to rely on chiral perturbation theory or any other mass extrapolation. In parallel, the four-quark operator is renormalised through the Rome-Southampton technique. Finally, we compare our value with previous results and draw some conclusions about the remaining dominant contributions in our error budget.
We present results from a calculation of beyond the standard model (BSM) kaon mixing including data physical with light quark masses. We simulate $N_f=2+1$ QCD with Iwasaki gauge and domain wall fermion action on 8 ensembles, spanning 3 lattice spacings and pion masses from the physical value up to 430MeV. The ratio of the BSM to standard model (SM) matrix elements are extracted from the correlation functions and renormalised using the RI-SMOM Rome-Southampton method with non-exceptional kinematics. The results at the physical point continuum limit are found by performing a simultaneous contin…
We review recent progress in calculating kaon spectrum, pseudoscalar meson decay constants, $B_K$, $ε'/ε$, $K\to ππ$ matrix elements, kaon semileptonic form factors, and moments of kaon distribution amplitudes on the lattice. We also address the issue of how best to improve the staggered fermion formulation for the action and operators.
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.
The CKM matrix element $|V_{us}|$ can be extracted from the experimental measurement of semileptonic $K\toπ$ decays. The determination depends on theory input for the corresponding vector form factor in QCD. We present a preliminary update on our efforts to compute it in $N_f=2+1$ lattice QCD using domain wall fermions for several lattice spacings and with a lightest pion mass of about $170\,\mathrm{MeV}$. By using partially twisted boundary conditions we avoid systematic errors associated with an interpolation of the form factor in momentum-transfer, while simulated pion masses near the physi…
I review recent lattice results in kaon physics, particularly in the determination of V_{us} and the B_K parameter of K^0-\bar{K}^0 mixing. I use lattice data to argue for the need of developing SU(2)_L \times SU(2)_R chiral perturbation theory for kaon physics and discuss some recent progress in achieving this. In particular it is shown that for K_{\ell 3} decays at q^2=0 (where q is the momentum transfer between the kaon and the pion), the chiral logarithms can be calculated in spite of the fact that the external pion carries half the energy of the kaon (in the kaon's rest frame), because th…
Parton physics from a heavy-quark operator product expansion: Dynamical lattice QCD calculation of moments of the pion and kaon light-cone distribution amplitudes
Institute of Physics, National Yang Ming Chiao Tung University（国立阳明交通大学物理研究所）；Center for Theoretical Physics - A Leinweber Institute, Massachusetts Institute of Technology（麻省理工学院理论物理中心-莱纳伯研究所）；University of Maryland（马里兰大学）；RIKEN Center for Computational Science（理化学研究所计算科学中心）；Chung-Yuan Christian University（中原大学）；Argonne National Laboratory（阿贡国家实验室）
We compute pseudoscalar meson masses and decay constants using staggered quarks on lattices with three flavors of sea quarks and lattice spacings $\approx 0.12$ fm and $\approx 0.09$ fm. We fit partially quenched results to ``staggered chiral perturbation theory'' formulae, thereby taking into account the effects of taste-symmetry violations. Chiral logarithms are observed. From the fits we calculate $f_π$ and $f_K$, extract Gasser-Leutwyler parameters of the chiral Lagrangian, and (modulo rather large perturbative errors) find the light and strange quark masses.
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 present the current status of a non-perturbative lattice calculation of the moments of the pion and kaon distribution amplitudes by the RQCD collaboration. Our investigation is carried out using $N_f=2+1$ dynamical, non-perturbatively O(a)-improved Wilson fermions on the CLS ensembles with 5 different lattice spacings and pion masses down to the physical pion mass. A combined continuum and chiral extrapolation to the physical point is performed along two independent quark mass trajectories simultaneously. We employ momentum smearing in order to decrease the contamination by excited states a…
We present results for the interaction of two kaons at maximal isospin. The calculation is based on 2+1+1 flavour gauge configurations generated by the ETM Collaboration (ETMC) featuring pion masses ranging from about 230 MeV to 450 MeV at three values of the lattice spacing. The elastic scattering length $a_0^{I=1}$ is calculated at several values of the bare strange quark and light quark masses. We find $M_K a_0 =-0.397(11)(_{-8}^{+0})$ as the result of a chiral and continuum extrapolation to the physical point. This number is compared to other lattice results.
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…
CKM-unitarity, direct and indirect CP-violation and the ΔI=1/2 rule in full lattice QCD are the focus of this talk. To this end I will discuss and compare recent lattice results for leptonic, semi-leptonic and non-leptonic decays of the kaon and neutral kaon mixing and I will motivate current best estimates f_K/f_π=1.198(10), f_+^{Kπ}(0)=0.964(5) and \hat{B}_K=0.720(39). Moreover new theoretical advances that will improve the quality of these computations in the future will be discussed.
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.
I calculate the kaon B-parameter with a lattice simulation in quenched approximation. The lattice simulation uses an action possessing exact lattice chiral symmetry, an overlap action. Computations are performed at two lattice spacings, about 0.13 and 0.09 fm (parameterized by Wilson gauge action couplings beta=5.9 and 6.1) with nearly the same physical volumes and quark masses. I describe particular potential difficulties which arise due to the use of such a lattice action in finite volume. My results are consistent with other recent lattice determinations using domain-wall fermions.
We present preliminary results of a study of Delta S = 2 matrix elements originating from physics beyond the Standard Model. Using 2+1 flavour Domain Wall Fermions we obtain the non-perturbative renormalisation (mixing) matrix in the RI scheme. We also discuss plans for the chiral extrapolation of the renormalised matrix elements in a partially quenched set-up.
We present the first calculation of the kaon semileptonic form factor with sea and valence quark masses tuned to their physical values in the continuum limit of 2+1 flavour domain wall lattice QCD. We analyse a comprehensive set of simulations at the phenomenologically convenient point of zero momentum transfer in large physical volumes and for two different values of the lattice spacing. Our prediction for the form factor is f+(0)=0.9685(34)(14) where the first error is statistical and the second error systematic. This result can be combined with experimental measurements of K->pi decays for …
Most of the analytic approaches which are used at present to understand the low energy hadronic interactions in Particle Physics, get their inspiration from QCD in the limit of a large number of colors $N_c$. I first illustrate this with the example of the left--right correlation function which is an excellent theoretical laboratory. Next, I present the list of observables which have been computed using a large--$N_c$ QCD approach. Finally, I discuss in some detail examples which are relevant to lattice QCD, in the sense that we can make comparisons.
New precise data in B physics and theoretical developments in K physics lead us to reconsider the weak K^0-\bar{K}^0 transition from a large-N_c viewpoint, N_c being the number of colors. In this framework, we infer an upper limit on \hat{B}_K and the Kaon indirect CP violation.
We report the first calculation using physical light-quark masses of the electromagnetic form factor $V(z)$ describing the long-distance contributions to the $K^+\toπ^+\ell^+\ell^-$ decay amplitude. The calculation is performed on a 2+1 flavor domain wall fermion ensemble with inverse lattice spacing $a^{-1}=1.730(4)$GeV. We implement a Glashow-Iliopoulos-Maiani cancellation by extrapolating to the physical charm-quark mass from three below-charm masses. We obtain $V(z=0.013(2))=-0.87(4.44)$, achieving a bound for the value. The large statistical error arises from stochastically estimated quar…
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…
The rare kaon decay $K^+\toπ^+ν\barν$ is an ideal process in which to search for signs of new physics and is the primary goal of the NA62 experiment at CERN. In this paper we report on a lattice QCD calculation of the long-distance contribution to the $K^+\toπ^+ν\barν$ decay amplitude at the near-physical pion mass $m_π=170$ MeV. The calculations are however, performed on a coarse lattice and hence with a lighter charm quark mass ($m_c^{\bar{\mathrm{MS}}}(\mbox{3 GeV})=750$ MeV) than the physical one. The main aims of this study are two-fold. Firstly we study the momentum dependence of the amp…
We present results for matrix elements of $ΔS=2$ four-fermion operators arising generically in models of new physics. These are needed to constrain such models using the measured values of $\varepsilon_K$ and $ΔM_K$. We use lattice QCD with 2+1 flavors of improved staggered fermions on lattices generated by the MILC collaboration. We extrapolate to the continuum from three lattice spacings ranging down to $a\approx 0.045\;$fm. Total errors are $\sim 5-6%$, arising primarily from our use of one-loop matching between lattice and continuum operators. For two of the matrix elements, our results di…
In this short presentation I emphasize the increased importance of kaon flavour physics in the search for new physics (NP) that we should witness in the rest of this decade and in the next decade. The main actors will be the branching ratios for the rare decays $K^+\rightarrowπ^+ν\barν$ and $K_{L}\rightarrowπ^0ν\barν$, to be measured by NA62 and KOTO, and their correlations with the ratio $\varepsilon'/\varepsilon$ on which recently progress by lattice QCD and large $N$ dual QCD approach has been made implying a new flavour anomaly. Further correlations of $K^+\rightarrowπ^+ν\barν$, $K_{L}\rig…
We discuss weak kaon decays in a scenario in which the Standard Model is extended by massive sterile fermions. After revisiting the analytical expressions for leptonic and semileptonic decays we derive the expressions for decay rates with two neutrinos in the final state. By using a simple effective model with only one sterile neutrino, compatible with all current experimental bounds and general theoretical constraints, we conduct a thorough numerical analysis which reveals that the impact of the presence of massive sterile neutrinos on kaon weak decays is very small, less than $1\%$ on decay …
Kaon physics provides a unique opportunity to identify new flavour and CP violating interactions beyond the Standard Model (SM). In the SM, implied by the hierarchical structure of the CKM matrix and the GIM mechanism, flavour changing neutral current processes are most strongly suppressed in the kaon sector while the suppression is much less effective in the B meson systems. Thus their theoretical cleanness makes rare K decays, in particular the K -> pi nu anti-nu system, extremely well suited to look for deviations from their tiny SM values. Despite the increasingly stringent constraints on …
We present a new calculation of the K->pi semileptonic form factor at zero momentum transfer in domain wall lattice QCD with Nf=2+1 dynamical quark flavours. By using partially twisted boundary conditions we simulate directly at the phenomenologically relevant point of zero momentum transfer. We perform a joint analysis for all available ensembles which include three different lattice spacings (a=0.09-0.14fm), large physical volumes (m_pi*L>3.9) and pion masses as low as 171 MeV. The comprehensive set of simulation points allows for a detailed study of systematic effects leading to the predict…
The decays and mixing of $K$ mesons are remarkably sensitive to the weak interactions of quarks and leptons at high energies. They provide important tests of the standard model at both first and second order in the Fermi constant $G_F$ and offer a window into possible new phenomena at energies as high as 1,000 TeV. These possibilities become even more compelling as the growing capabilities of lattice QCD make high-precision standard model predictions possible. Here we discuss and attempt to forecast some of these capabilities.
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)_…
We present the state-of-the-art lattice QCD calculation of the pion and kaon light-cone distribution amplitudes (DAs) using large-momentum effective theory. The calculation is done at three lattice spacings $a\approx\{0.06,0.09,0.12\}$ fm and physical pion and kaon masses, with the meson momenta $P_z = \{1.29,1.72,2.15\}$ GeV. The result is non-perturbatively renormalized in a recently proposed hybrid scheme with self renormalization, and extrapolated to the continuum as well as the infinite momentum limit. We find a significant deviation of the pion and kaon DAs from the asymptotic form, and …
The FLAG working group reviews lattice results relevant for pion and kaon physics with the aim of making them easily accessible to the particle physics phenomenology community. The set of quantities considered so far comprises light quark masses, kaon and pion form factors, the kaon mixing parameter, and low energy constants of SU(2)_L X SU(2)_R and SU(3)_L X SU(3)_R chiral perturbation theory.
After years of silence we should witness in the rest of this decade and in the next decade the revival of kaon flavour physics. This is not only because of the crucial measurements of the branching ratios for the rare decays $K^+\toπ^+ν\barν$ and $K_{L}\to π^0ν\barν$ by NA62 and KOTO that being theoretically clean and very sensitive to new physics (NP) could hint for new phenomena even beyond the reach of the LHC without any significant theoretical uncertainties. Indeed simultaneously the advances in the calculations of perturbative and in particular non-perturbative QCD effects in $\varepsilo…
Kaon flavour physics has played in the 1960s and 1970s a very important role in the construction of the Standard Model (SM) and in the 1980s and 1990s in SM tests with the help of CP violation in $K_L\toππ$ decays represented by $\varepsilon_K$ and the ratio $\varepsilon'/\varepsilon$. In this millennium this role has been taken over by $B_{s,d}$ and $D$ mesons. However there is no doubt that in the coming years we will witness the return of kaon flavour physics with the highlights being the measurements of the theoretically clean branching ratios for the rare decays $K^+\rightarrow π^+ν\barν$…
We compute the hadronic matrix elements of the four-quark operators relevant for $K^0-{\bar K^0}$ mixing beyond the Standard Model. Our results are from lattice QCD simulations with $n_f=2+1$ flavours of domain-wall fermion, which exhibit continuum-like chiral-flavour symmetry. The simulations are performed at two different values of the lattice spacing ($a\sim0.08$ and $a\sim 0.11 \, \fm $) and with lightest unitary pion mass $\sim 300\, \MeV$. For the first time, the full set of relevant four-quark operators is renormalised non-perturbatively through RI-SMOM schemes; a detailed description o…
We discuss the reduction of errors in the calculation of the form factor $f_+^{K π}(0)$ with HISQ fermions on the $N_f=2+1+1$ MILC configurations from increased statistics on some key ensembles, new data on ensembles with lattice spacings down to 0.042 fm and the study of finite-volume effects within staggered ChPT. We also study the implications for the unitarity of the CKM matrix in the first row and for current tensions with leptonic determinations of $\vert V_{us}\vert$.
Using the tadpole improved clover Wilson quark action on small, coarse and anisotropic lattices, $KN$ scattering length in the I=1 channel is calculated within quenched approximation. The results are extrapolated towards the chiral and physical kaon mass region. Finite volume and finite lattice spacing errors are also analyzed and a result in the infinite volume and continuum limit is obtained which is compatible with the experiment and the results from Chiral Perturbation Theory.
Using the tadpole improved Wilson quark action on small, coarse and anisotropic lattices, $Kπ$ scattering length in the $I=3/2$ channel is calculated within quenched approximation. The results are extrapolated towards the chiral and physical kaon mass region. Finite volume and finite lattice spacing errors are also analyzed and a result in the infinite volume and continuum limit is obtained. Our result is compared with the results obtained using Roy equations, Chiral Perturbation Theory, dispersion relations and the experimental data.
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…
We describe two recent developments of the radiative correction theory in semileptonic beta decays. For neutron, a novel dispersive analysis of the $γW$-box diagram making use of neutrino scattering data leads to an improved precision and a shifted central value of $V_{ud}$; for kaon, an appropriate combination of meson form factors, lattice QCD inputs and chiral perturbation theory gives a much-improved determination of the radiative corrections in semileptonic kaon decays. These new calculations help to unveil/sharpen a series of anomalies in the measurements of $V_{ud}$ and $V_{us}$ that ma…
A rainbow-ladder truncation of QCD's Dyson-Schwinger equations, constrained by existing applications to hadron physics, is employed to compute the valence-quark parton distribution functions of the pion and kaon. Comparison is made to pi-N Drell-Yan data for the pion's u-quark distribution and to Drell-Yan data for the ratio u_K(x)/u_π(x): the environmental influence of this quantity is a parameter-free prediction, which agrees well with existing data. Our analysis unifies the computation of distribution functions with that of numerous other properties of pseudoscalar mesons.
