Kaon condensation may play an important role in the structure of hadronic matter at densities greater than that of nuclear matter, as exist in the interior of neutron stars. We present the results of the first lattice QCD investigation of kaon condensation obtained by studying systems containing up to twelve negatively charged kaons. Surprisingly, the properties of the condensate that we calculate are remarkably well reproduced by leading order chiral perturbation theory. In our analysis, we also determine the three-kaon interaction from the multi-kaon systems and update our results for pion condensates.
We consider QCD at a nonzero chemical potential for strangeness. At a critical value of the chemical potential equal to the kaon mass, kaon condensation occurs through a continuous phase transition. We show that, when the isospin symmetry is exact in the Lagrangian, a Goldstone boson with a dispersion relation $E \sim p^2$ appears in the kaon condensed phase. At the same time, the number of the Goldstone bosons is less than the number of broken generators. Both phenomena are familiar in non-relativistic systems. We interpret our results in terms of a Goldstone boson counting rule found previou…
We show that it is possible to isolate a set of kaon fluctuations in lattice QCD. By means of the Hadron Resonance Gas (HRG) model, we calculate the actual kaon second-to-first fluctuation ratio, which receives contribution from primordial kaons and resonance decays, and show that it is very close to the one obtained for primordial kaons in the Boltzmann approximation. The latter only involves the strangeness and electric charge chemical potentials, which are functions of $T$ and $μ_B$ due to the experimental constraint on strangeness and electric charge, and can therefore be calculated on the…
We present the first lattice-QCD calculation of the kaon valence-quark distribution functions using the large-momentum effective theory (LaMET) approach. The calculation is performed with multiple pion masses with the lightest one around 220 MeV, 2 lattice spacings $a=0.06$ and 0.12 fm, $(M_π)_\text{min} L \approx 5.5$, and high statistics ranging from 11,600 to 61,312 measurements. We also calculate the valence-quark distribution of pion and find it to be consistent with the FNAL E615 experimental results, and our ratio of the $u$ quark PDF in the kaon to that in the pion agrees with the CERN…
In this work, we present the first results on the gluon parton distribution of the kaon from lattice quantum chromodynamics. We carry out the lattice calculation at pion mass around 310~MeV and two lattice spacings, 0.15 and 0.12~fm, using $2+1+1$-flavor HISQ ensembles generated by MILC Collaboration. The kaon correlators are calculated using clover fermions and momentum-smearing sources with maximum boost momentum around 2~GeV and high statistics (up to 324,000 measurements). We study the dependence of the resulting reduced Ioffe-time pseudo-distributions at multiple boost momenta and lattice…
In this paper, employing an all-to-all quark propagator technique, we investigate the kaon-nucleon interactions in lattice QCD. We calculate the S-wave kaon-nucleon potentials at the leading order in the derivative expansion in the time-dependent HAL QCD method, using (2+1)-flavor gauge configurations at the lattice spacing $a \approx 0.09$ fm on $32^3 \times 64$ lattices and the pion mass $m_π \approx 570$ MeV. We take the one-end trick for all-to-all propagators, which allows us to put the zero momentum hadron operators at both source and sink and to smear quark operators at the source. We f…
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 first lattice-QCD calculation of the kaon distribution amplitude using the large-momentum effective theory (LaMET) approach. The momentum-smearing technique has been implemented to improve signals at large meson momenta. We subtract the power divergence due to Wilson line to high precision using multiple lattice spacings. The kaon structure clearly shows an asymmetry of the distribution amplitude around $x=1/2$, a clear sign of its skewness. We also study the leading SU(3) flavor symmetry breaking relations for the pion, kaon and eta meson distribution amplitudes, and the result…
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 …
First simultaneous global QCD analysis of kaon and pion parton distributions with lattice QCD constraints
Argonne National Laboratory（阿贡国家实验室）；North Carolina State University（北卡罗来纳州立大学）；Jefferson Lab（杰弗逊实验室）；Helmholtz-Institut für Strahlen- und Kernphysik, University of Bonn（波恩大学亥姆霍兹辐射与核物理研究所）；Bethe Center for Theoretical Physics, University of Bonn（波恩大学贝特理论物理中心）
We summarize our lattice QCD determinations of the pion-pion, pion-kaon and kaon-kaon s-wave scattering lengths at maximal isospin with a particular focus on the extrapolation to the physical point and the usage of next-to-leading order chiral perturbation theory to do so. We employ data at three values of the lattice spacing and pion masses ranging from around 230 MeV to around 450 MeV, applying Luescher's finite volume method to compute the scattering lengths. We find that leading order chiral perturbation theory is surprisingly close to our data even in the kaon-kaon case for our entire ran…
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…
The different ground state energies of N-pion and M-kaon systems for N+M <=12 are studied in lattice QCD. These energies are then used to extract the various two- and three- body interactions that occur in these systems. Particular attention is paid to additional thermal states present in the spectrum because of the finite temporal extent. These calculations are performed using one ensemble of 2+1 flavor anisotropic lattices with a spatial lattice spacing a_s ~ 0.125 fm, an anisotropy factor ξ=a_s/a_t=3.5, and a spatial volume L^3 ~ (2.5 fm)^3. The quark masses used correspond to pion and kaon…
We calculate the kaon semileptonic form factors in lattice QCD with three flavors of dynamical overlap quarks. Gauge ensembles are generated at pion masses as low as 290 MeV and at a strange quark mass near its physical value. We precisely calculate relevant meson correlators using the all-to-all quark propagator. Twisted boundary conditions and the reweighting technique are employed to vary the momentum transfer and the strange quark mass. We discuss the chiral behavior of the form factors by comparing with chiral perturbation theory and experiments.
We present a calculation of the kaon $B$-parameter, $B_K$, using lattice QCD. We use improved staggered valence and sea fermions, the latter generated by the MILC collaboration with $N_f=2+1$ light flavors. To control discretization errors, we use four different lattice spacings ranging down to $a\approx 0.045\;$fm. The chiral and continuum extrapolations are done using SU(2) staggered chiral perturbation theory. Our final result is $\hat{B}_K = 0.727 \pm 0.004 (\text{stat}) \pm 0.038 (\text{sys})$, where the dominant systematic error is from our use of truncated (one-loop) matching factors.
We present calculations of the decay constants and kaon B-parameter $B_K$ as the first stage of RBC Collaboration's quenched numerical simulations using DBW2 gauge action and domain-wall fermions. Some of potential systematic errors and consistency to previous works are discussed.
We report on our calculation of the kaon semileptonic form factors in Nf=2+1 lattice QCD. Chiral symmetry is exactly preserved by using the overlap quark action for a straightforward comparison with chiral perturbation theory (ChPT). We simulate three pion masses down to 290 MeV at a single lattice spacing of 0.11 fm and at a strange quark mass very close to its physical value. The form factors near zero momentum transfer are precisely calculated by using the all-to-all propagator and twisted boundary conditions. We compare the normalizations and slopes of the form factors with ChPT and experi…
We present a lattice QCD calculation of the axial $γW$-box diagrams relevant for the kaon semileptonic decays. We utilize a recently proposed method, which connects the electroweak radiative corrections in Sirlin's representation to that in chiral perturbation theory. It allows us to use the axial $γW$-box correction in the SU(3) limit to obtain the low energy constants for chiral perturbation theory. From first principles our results confirm the previously used low energy constants provided by the minimal resonance model with a significant reduction in uncertainties.
In this short review, I present the recent lattice computations of kaon weak matrix elements relevant to $K \to ππ$ decays and neutral kaon mixing. These matrix elements are key to the theoretical determination of the CP violation parameters $ε$ and $ε'$ . Impressive progress have been achieved recently, in particular the first realistic computation of $ε'/ε$ with physical kinematics has been reported in [1]. The novelty is the $ΔI = 1/2$ channel, whereas the $ΔI = 3/2$ contribution is now computed at several values of the lattice spacing and extrapolated to the continuum limit. I will also pr…
We present the first results for neutral kaon mixing using 2+1 flavors of domain wall fermions. A new approach is used to extrapolate to the physical up and down quark masses from our numerical studies with pion masses in the range 240 -- 420 MeV; only $SU(2)_L \times SU(2)_R$ chiral symmetry is assumed and the kaon is not assumed to be light. Our main result is $B_K^{\bar{\rm MS}}(2 \mathrm{GeV}) = 0.524(10)(28)$ where the first error is statistical and the second incorporates estimates for all systematic errors.
We introduce four-point functions in the hadronic ladder resummation approach to large $N_c$ QCD Green functions. We determine the relevant one to calculate the $B_K$ kaon parameter in the chiral limit. This four-point function contains both the large momenta QCD OPE and the small momenta ChPT at NLO limits, analytically. We get $\hat B_K^χ= 0.38 \pm 0.15$. We also give the ChPT result at NLO for the relevant four-point function to calculate $B_K$ outside the chiral limit, while the leading QCD OPE is the same as the chiral limit one.
We give a progress report of our new $a^{-1}\approx 3$ GeV quenched calculation of kaon matrix elements with domain-wall fermion and DBW2 gauge action. Our smaller lattice spacing allows us to address the effect of charmed quark on the lattice. We show preliminary results of $B_K$ renormalized non-perturbatively and $K\toπ$ matrix elements.
Monopole and photon contributions to Wilson loops are calculated using Monte-Carlo simulations of SU(2) QCD in the maximally abelian gauge. The string tensions of SU(2) QCD are well reproduced by extended monopole contributions alone.
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.
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 …
Next-to-next-to-leading order QCD corrections to pion (kaon)-induced exclusive Drell-Yan process
South China Normal University（华南师范大学）；Guangdong Basic Research Center of Excellence for Structure and Fundamental Interactions of Matter（广东省物质结构与基本相互作用卓越研究中心）；Guangdong Provincial Key Laboratory of Nuclear Science（广东省核科学重点实验室）；École polytechnique, Institut Polytechnique de Paris（巴黎综合理工学院，巴黎理工学院）；Zhengzhou University（郑州大学）；Institute of High Energy Physics, Chinese Academy of Sciences（中国科学院高能物理研究所）；School of Physical Sciences, University of Chinese Academy of Sciences（中国科学院大学物理科学学院）
An effective monopole action is derived from vacuum configurations after abelian projection in the maximally abelian gauge in $SU(2)$ QCD. Entropy dominance over energy of monopole loops is seen on the renormalized lattice with the spacing $b>b_c\simeq 5.2\times10^{-3} Λ_L^{-1}$ when the physical volume of the system is large enough. QCD confinement may be interpreted as the (dual) Meissner effect due to the monopole condensation.
We discuss the computation of the kaon and D meson masses in the N_f = 2+1+1 twisted mass lattice QCD setup, where explicit heavy flavor and parity breaking occurs at finite lattice spacing. We present three methods suitable in this context and verify their consistency.
We present a calculation of the kaon form factors in two-flavor QCD with the non-perturbatively $O(a)$-improved Wilson quark action. In order to achieve a few percent accuracy in the study of SU(3) breaking effects, we use a set of double ratios of the matrix elements, with which the bulk of the statistical fluctuation and the multiplicative renormalization factors cancel.
We calculate the neutral kaon mixing parameter B_K in unquenched lattice QCD using asqtad-improved staggered sea quarks and domain-wall valence quarks. We use the "2+1" flavor gauge configurations generated by the MILC Collaboration, and simulate with multiple valence and sea quark masses at two lattice spacings of a ~ 0.12 fm and a ~ 0.09 fm. We match the lattice determination of B_K to the continuum value using the nonperturbative method of Rome-Southampton, and extrapolate B_K to the continuum and physical quark masses using mixed action chiral perturbation theory. The "mixed-action" method…
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 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…
We consider the dependence of the pion and kaon decay constants on the up, down and strange quark masses in QCD with strict isospin symmetry. The role of dynamical vector meson degrees of freedom is scrutinized in terms of an effective chiral Lagrangian for vector mesons. Applying a set of low-energy parameters as determined previously from QCD lattice data on the masses of the light vector mesons from PACS-CS, QCDSF-UKQCD and HSC we compute its implications on the pion and kaon decay constants for QCD lattice ensembles of HPQCD, CLS and ETMC. It is shown that with Gasser-Leutwyler L_4 and L_5…
The kaon B parameter is calculated in quenched lattice QCD with the Wilson quark action. The mixing problem of the Δs=2 four-quark operators is solved non-perturbatively with full use of chiral Ward identities, and this method enables us to construct the weak four-quark operators exhibiting good chiral behavior. We find B_K(NDR, 2GeV)=0.562(64) in the continuum limit, which agrees with the value obtained with the Kogut-Susskind quark action.
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.
It is proven that dual superconductivity of QCD vacuum in the confining phase is an intinsic property, independent on the choice of the abelian projection used to define the monopoles.
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…
In Ref [1] we have presented the results of an exploratory lattice QCD computation of the long-distance contribution to the $K^+\toπ^+ν\barν$ decay amplitude. In the present paper we describe the details of this calculation, which includes the implementation of a number of novel techniques. The $K^+\toπ^+ν\barν$ decay amplitude is dominated by short-distance contributions which can be computed in perturbation theory with the only required non-perturbative input being the relatively well-known form factors of semileptonic kaon decays. The long-distance contributions, which are the target of thi…
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.
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.
The disorder parameter $<μ>$ for the condensation of monopoles in QCD is estimated analytically in terms of gauge invariant field strength correlators. The continuum limit is discussed.
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 a study of $B$-parameters for generic $ΔS=2$ four-quark operators in domain wall QCD. Our calculation covers all the $B$-parameters required to study the neutral kaon mixing in the standard model (SM) and beyond it. We evaluate one-loop renormalization factors of the operators employing the plaquette and Iwasaki gauge actions. Numerical simulations are carried out in quenched QCD with both gauge actions on $16^3\times 32\times 16$ and $24^3\times 32\times 16$ at the lattice spacing $1/a\approx 2$GeV. We investigate the relative magnitudes of the non-SM $B$-parameters to the SM one, …
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…
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 use a lattice thermal partition functional to study Abelian monopole condensation in full QCD with $N_f=2$ staggered fermions. We present preliminary results on $16^3\times4$ and $32^3\times4$ lattices.
We present results of a large-scale simulation for the Kaon B parameter $B_K$ in quenched lattice QCD with the Kogut-Susskind quark action. Calculating $B_K$ at 1% statistical accuracy for seven values of lattice spacing in the range $a\approx 0.24-0.04$ fm on lattices up to $56^3\times 96$, we verify a quadratic $a$ dependence of $B_K$ theoretically predicted. Strong indications are found that, with our level of accuracy, $α_{\bar{MS}}(1/a)^2$ terms arising from our one-loop matching procedure have to be included in the continuum extrapolation. We present $B_K$(NDR, 2 GeV)=0.628(42) as our fi…
Recent studies of confinement based on the idea of abelian monopole condensation are reviewed briefly. Emphasis is placed on the approach to get the effective monoole action using the blockspin transformation on the dual lattice. The trajectory obtained looks to be the renormalized one in $SU(2)$ QCD. A disorder parameter of confinement is constructed. Monopole condensation occurs also in $SU(3)$ QCD.
We present the status of on-going calculations of the $K\toπlν$ and $D\to K(π) lν$ semileptonic form factors at $q^2=0$. These form factors are important for the determination of the CKM matrix elements $\lvert{V_{us}}\rvert$ and $\lvert{V_{cs(d)}}\rvert$ respectively. This work uses the HISQ action for both valence quarks and sea quarks on MILC $N_f=2+1+1$ configurations. We employ twisted boundary conditions to calculate the form factors at zero momentum transfer directly. The $K\toπ$ results are an update to previously published results with new data at the physical point. The $D\to K(π)$ r…
We study the KN interactions in the I(J^π)=0(1/2^-) and 1(1/2^-) channels and associated exotic state Θ^+ from 2+1 flavor full lattice QCD simulation for relatively heavy quark mass corresponding to m_π=871 MeV. The s-wave KN potentials are obtained from the Bethe-Salpeter wave function by using the method recently developed by HAL QCD (Hadrons to Atomic nuclei from Lattice QCD) Collaboration. Potentials in both channels reveal short range repulsions: Strength of the repulsion is stronger in the I=1 potential, which is consistent with the prediction of the Tomozawa-Weinberg term. The I=0 poten…
We present numerical results for the kaon B-parameter, B_K, determined in the quenched approximation of lattice QCD. Our simulations are performed using domain-wall fermions and the renormalization group improved, DBW2 gauge action which combine to give quarks with good chiral symmetry at finite lattice spacing. Operators are renormalized non-perturbatively using the RI/MOM scheme. We study scaling by performing the simulation on two different lattices with a^{-1} = 1.982(30) and 2.914(54) GeV. We combine this quenched scaling study with an earlier calculation of B_K using two flavors of dynam…
The order parameter for monopole condensation is computed in terms of gauge invariant field strength correlators. Important properties emerge of the correlators in the confined phase, which could not be extracted by existing numerical determinations on the lattice.
We compare two competing conjectures of the color confinement in QCD, the monopole condensation and the Abelian dominance, and show that it is the monopole condensation which is responsible for the confinement. To demonstrate this we present a new gauge invariant integral expression of the one-loop QCD effective action which has no infra-red divergence. With this we show that, just as the GSO-projection restores the supersymmetry and modular invariance in NSR string theory, the color reflection invariance ("the C-projection") assures the gauge invariance and the stability of the monopole conde…
