We discuss a general diagrammatic description of n-point functions in the QCD instanton vacuum that resums planar diagrams, enforces gauge invariance and spontaneously broken chiral symmetry. We use these diagrammatic rules to derive the pion and kaon quasi-parton amplitude and distribution functions at leading order in the instanton packing fraction for large but finite momentum. The instanton and anti-instanton zero modes and non-zero modes are found to contribute to the quasi-distributions, but the latter are shown to drop out in the large momentum limit. The pertinent pion and kaon parton distribution amplitudes and functions are made explicit at the low renormalization scale fixed by the inverse instanton size. Assuming that factorization holds, the pion parton distributions are evolved to higher renormalization scales with one-loop DGLAP and compared to existing data.
We discuss the pion and kaon distribution amplitudes up to twist-3 in the context of the random instanton vacuum (RIV). We construct explicitly the pertinent quasi-pion and quasi-kaon distributions in the RIV, and analyze them in leading order in the diluteness factor, at a resolution fixed by the inverse instanton size. The distribution amplitudes (DA) follow from the large momentum limit. The results at higher resolution are discussed using QCD evolution, and compared to their asymptotic limits and some lattice results.
In this presentation, we briefly review recent investigations on pion and kaon structures from the instanton vacuum. Starting from the low-energy QCD partition function, we have computed the Gasser-Leutwyler low-energy constants, electromagnetic form factors of the pion and kaon, semileptonic decay form factors of the kaon, and light-cone distribution amplitues of the pion and kaon. The results are in good agreement with the experimental and empirical data.
We investigate the leading-twist light-cone distribution amplitudes for the pion and kaon based on the gauge-invariant nonlocal chiral quark model from the instanton vacuum in the presence of external axial-vector currents. We find that the nonlocal contribution from the gauge invariance has much effects on the pion distribution amplitudes, while it changes mildly the kaon ones. We also study the Gegenbauer moments of the distribution amplitudes and compare them with the empirical analysis of the CLEO data.
We investigate the leading-twist light-cone distribution amplitudes for the pion and kaon, based on the nonlocal chiral quark model from the instanton vacuum. Effects of explicit flavor SU(3)-symmetry breaking are taken into account. The Gegenbauer moments are computed, analyzed and compared with those of other models. The one-loop QCD evolution of the moments is briefly discussed. The transverse momentum distributions are also discussed for the pion and kaon light-cone wave functions.
We investigate the pion and kaon (pi^+, K^+, K^0) electromagnetic form factors in the space-like region: Q^2 ~< 1 GeV, based on the gauged low-energy effective chiral action from the instanton vacuum in the large N_c limit. Explicit flavor SU(3) symmetry breaking is taken into account. The nonlocal contributions turn out to be crucial to reproduce the experimental data. While the pion electromagnetic form factor is in good agreement with the data, the kaon one seems underestimated. We also calculate the electromagnetic charge radii for the pion and kaon: <r^2>_{pi^+}=0.455 fm^2, <r^2>_{K^+}=0.…
We investigate the kaon semileptonic decay (K_{l3}) form factors within the framework of the nonlocal chiral quark model from the instanton vacuum, taking into account the effects of flavor SU(3) symmetry breaking. We also consider the problem of gauge invariance arising from the momentum-dependent quark mass in the present work. All theoretical calculations are carried out without any adjustable parameter, the average instanton size (rho ~ 1/3 fm) and the inter-instanton distance (R ~ 1 fm) having been fixed. We also show that the present results satisfy the Callan-Treiman low-energy theorem …
Dense hadronic matter at low temperature is expected to be in crystal and at high density make a transition to a {\em chirally restored but color-confined} state which is a novel phase hitherto unexplored. This phase transition is predicted in both skyrmion matter in 4D and instanton matter in 5D, the former in the form of half-skyrmions and the latter in the form of half-instantons or dyons. We predict that when $K^-$'s are embedded in this half-skyrmion or half-instanton (dyonic) matter which may be reached not far above the normal density, there arises an enhanced attraction from the soft d…
We study the low $Q^2$ wave-functions of pions and kaons as an expansion in terms of hadron-like Fock state fluctuations. In this formalism, pion and kaon wave-functions are related one another. Consequently, the knowledge of the pion structure allows the determination of parton distributions in kaons. In addition, we show that the intrinsic (low $Q^2$) sea of pions and kaons are different due to their different valence quark structure. Finally, we analize the feasibility of a method to extract kaon's parton distribution functions within this approach and compare with available experimental da…
We investigate the parton distribution functions (PDFs) of the pion and the kaon by combining quantum chromodynamics (QCD) evolution with the basis light front quantization. The initial PDFs result from the light front wave functions obtained by diagonalizing the effective Hamiltonian consisting of the holographic QCD confinement potential, a complementary longitudinal confinement potential, and the color-singlet Nambu--Jona-Lasinio interactions. The valence-quark PDF of the pion, after QCD evolution, is consistent with the result from the E-0615 experiment at Fermilab. Meanwhile, the pion str…
We present pion and kaon parton distribution functions from a global QCD analysis of the experimental data within the framework of dynamical parton model. We use the DGLAP equations with parton-parton recombination corrections and the valence input of uniform distribution which maximizes the information entropy. At our input scale $Q_0^2$, there are no sea quark and gluon distributions. All the sea quarks and gluons of the pion and the kaon are completely generated from the parton splitting processes. The mass-dependent parton splitting kernel is applied for the strange quark distribution in t…
We revisit the global QCD analysis of parton-to-kaon fragmentation functions at next-to-leading order accuracy using the latest experimental information on single-inclusive kaon production in electron-positron annihilation, lepton-nucleon deep-inelastic scattering, and proton-proton collisions. An excellent description of all data sets is achieved, and the remaining uncertainties in parton-to-kaon fragmentation functions are estimated and discussed based on the Hessian method. Extensive comparisons to the results from our previous global analysis are made.
Naive parton picture for kaon color transparency in $A(e,e'K^+)$
Research Institute of Basic Science, Korea Aerospace University（韩国航空航天大学基础科学研究所）；Department of Physics and Engineering Physics, Yonsei University（延世大学物理与工程物理系）；Center for Exotic Nuclear Studies, Institute for Basic Science（基础科学研究院奇异核研究中心）
The separate quark flavour contributions to the pion and kaon valence quark distribution functions are studied, along with the corresponding electromagnetic form factors in the space-like region. The calculations are made using the solution of the Bethe-Salpeter equation for the model of Nambu and Jona-Lasinio with proper-time regularization. Both the pion and kaon form factors and the valence quark distribution functions reproduce many of the features of the available empirical data. The larger mass if the strange quark naturally explains the empirical fact that the ratio $u_{K^+}(x)/u_{π^+}(…
In this document, we present the global QCD analysis of parton-to-kaon fragmentation functions at next-to-leading order accuracy using the latest experimental information on single-inclusive kaon production in electron-positron annihilation, lepton-nucleon deep-inelastic scattering, and proton-proton collisions. An extended analysis of this work can be found in Ref.[1].
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…
We examine the relevance of the heavy quarks masses in the perturbative QCD description of hard interactions where charged kaons are produced in the final state. We extract a set of parton-to-kaon hadronization probabilities from a next to leading order QCD global analysis where a general mass variable flavor number scheme accounting for mass effects is implemented. We compare the results with those obtained in the massless approximation and also with those found in the case of final state pions. At variance with the very significant improvement found for the much more precise pion fragmentati…
The genuine twist-3 quark-gluon contributions to the Generalized Parton Distributions (GPDs) are estimated in the model of the instanton vacuum. These twist-3 effects are found to be parametrically suppressed relative to the ``kinematical'' twist-3 ones due to the small packing fraction of the instanton vacuum. We derive exact sum rules for the twist-3 GPDs.
We investigate the twist-3 pion and kaon distribution amplitudes of the pseudoscalar (phi^p_{pi,K}) and pseudotensor (phi^{sigma}_{pi,K}) types, based on the effective chiral action from the instanton vacuum. Effects of flavor SU(3) symmetry breaking are explicitly taken into account. The Gegenbauer moments and the moments of the distribution amplitudes (<xi^m>) are also computed. Our results are summarized as follows: a^p_{2,pi} ~ 0.4, a^p_{1,K} ~ 0.02 and a^p_{2,K} ~ 0.14, and a^{sigma}_{2,pi} ~ 0.02 and a^{sigma}_{1,K} ~ a^{sigma}_{2,K} ~ 0; <xi^2>^p_π ~ <xi^2>^p_K ~ 0.37 and <xi>^p_K ~ 0, …
In a model of hadrons in which the hadron wave function at low $Q^2$ is represented by a hadron-like Fock state expansion, we calculate the $π$ and $K$ parton distribution functions by comparing to experimental data. We show that the model gives an accurate description of available data and, in addition, gives a clear prediction of the initial flavors to be considered at the low $Q^2$ scale where perturbative evolution starts
Multiple scattering and induced parton splitting lead to a medium modification of the QCD evolution for jet fragmentation functions and the final hadron spectra. Medium-induced parton splittings not only lead to energy loss of leading partons and suppression of leading hadron spectra, but also modify the flavor composition of a jet due to induced flavor conversion via gluon emission, quark pair production and annihilation. Through a numerical study of the medium-modified QCD evolution, leading $K^-$ strange meson spectra are found to be particularly sensitive to the induced flavor conversion i…
We investigate the parton-distribution functions (PDFs) for the positively charged pion and kaon at a low-renormalization scale ~ 1 GeV. To this end, we employ the gauge-invariant effective chiral action from the nonlocal chiral-quark model, resulting in that the vector currents are conserved. All the model parameters are determined phenomenologically with the normalization condition for PDF and the empirical values for the pseudoscalar-meson weak-decay constants. We consider the momentum dependence of the effective quark mass properly within the model calculations. It turns out that the leadi…
We investigate the parton distribution functions (PDFs) of the pion and kaon from the eigenstates of a light-front effective Hamiltonian in the constituent quark-antiquark representation suitable for low-momentum scale applications. By taking these scales as the only free parameters, the valence quark distribution functions of the pion, after QCD evolving, are consistent with the E615 experiment at Fermilab. In addition, the ratio of the up quark distribution in the kaon to that in the pion also agrees with the NA3 experimental result at CERN.
We show that the instanton-induced inelastic processes, leading to multi-gluon production in in high-energy parton-parton scattering, are considerably enhanced over the quasi-elastic ones, by a factor of 100. The basic instanton-induced inelastic contribution cause the parton-parton cross section to increase as ${\rm ln} {s}$, and their Poisson resummation in hadron-hadron scattering yield a regge-type cross section. The pomeron slope and intercept due to instanton-induced contributions are evaluated. We show that the small intercept is due to the diluteness of the instantons in the QCD vacuum…
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.
The circle compactification of the 6-dim (2,0) superconformal theory of $A_{N-1}$ type leads the 5-dim SU(N) maximally supersymmetric gauge theory. Instanton solitons embody Kaluza-Klein modes and are conjectured to be composed of partonic constituents. We realize such a parton of 1/N instanton topological charge at the intersection of magnetic flux sheets. After a further compactification with nontrivial Wilson line expectation value, instantons or calorons have been shown to be split into fundamental monopoles of fractional instanton charge. In the symmetric phase with trivial Wilson line ex…
We present a detailed assessment of uncertainties in parton-to-pion and parton-to-kaon fragmentation functions obtained in recent global QCD analyses of single-inclusive hadron production data at next-to-leading order accuracy. We use the robust Lagrange multiplier approach for determining uncertainties to validate the applicability of the simpler but approximate Hessian method. Extensive comparisons of the results obtained within both methods are presented for the individual parton-to-pion and kaon fragmentation functions. We provide Hessian eigenvector sets of pion and kaon fragmentation fun…
Parton distributions of pseudoscalar pi,K and eta mesons obtained within the NJL model using the Pauli-Villars regularization method are analyzed in terms of LO and NLO evolution, and the valence sea quark and gluon parton distributions for the pion are obtained at Q^2 = 4 GeV^2 and compared to existing parametrizations at that scale. Surprisingly, the NLO order effects turn out to be small compared to the LO ones. The valence distributions are in good agreement with experimental analyses, but the gluon and sea distributions come out to be softer in the high-x region and harder in the low-x re…
Pion and kaon structural properties provide insights into the emergence of mass within the Standard Model and attendant modulations by the Higgs boson. Novel expressions of these effects, in impact parameter space and in mass and pressure profiles, are exposed via $π$ and $K$ generalised parton distributions, built using the overlap representation from light-front wave functions constrained by one-dimensional valence distribution functions that describe available data. Notably, e.g. $K$ pressure profiles are spatially more compact than $π$ profiles and both achieve near-core pressures of simil…
We phenomenologically study whether partonic collisions responsible for the growth of hadron-hadron cross sections at high energy can be ascribed to instanton-induced processes. Although non-perturbative in nature, these interactions occur at the semi-hard scale $Q\sim 1-2$ GeV, and should therefore be described using information from deep inelastic leptonic scattering on the partonic constituents in nucleons, pions, and photons. After considering shadowing corrections in nucleon-nucleon scattering, we fix a free instanton tail suppression parameter and determine the effective quark-quark cros…
We obtain the pion and the kaon parton distribution functions from the eigenstates of a light front effective Hamiltonian in the constituent quark-antiquark representation suitable for low-momentum scale applications. By taking these scales as the only free parameters, the valence quark distribution functions of the pion, after QCD evolution, are consistent with the data from the FNAL-E615 experiment. The ratio of the up quark distribution of the kaon to that of the pion also agrees with the CERN-NA3 experiment. Supplemented by known parton distribution functions for the nucleons, we further o…
We present the generalized parton distributions (GPDs) for the valence quarks of the pion and the kaon in both momentum space and position space within the basis light-front quantization framework. These GPDs are obtained from the eigenvectors of a light-front effective Hamiltonian consisting of the holographic quantum chromodynamics (QCD) confinement potential, a complementary longitudinal confinement potential, and the color-singlet Nambu-Jona--Lasinio interactions for the valence quarks of mesons. We then calculate the generalized form factors of the pion and the kaon from the moments of th…
I discuss the instanton-induced contributions to the coefficient functions in front of parton densities. They correspond to the spherically symmetric particle production at the level of $10^{-2}-10^{-5}$ of the total cross section of deep inelastic scattering from the parton.
We investigate the tomographical structure of pion and kaon in light cone quark model (LCQM). In particular, we study the parton distribution amplitude (PDA) of pion and kaon. We obtain the parton distribution function (PDF) and the generalized parton distributions (GPDs) of the pion and kaon. The valence quark PDA and PDF of pion, after QCD evolution, are found to be consistent with the data from the E791 and the E615 experiments at Fermilab, respectively. Further, we investigate the transverse momentum distributions (TMDs) of pion and kaon. We also discuss the unpolarized TMD evolution for p…
We determine the leading Fock state light front wave functions (LFWFs) of the pion and kaon via light front projections of the covariant Bethe-Salpeter wave function. Using these LFWFs we study the multi-dimensional images of the valence quarks in the pion and kaon that are provided by their generalized parton distribution functions (GPDs) and transverse momentum dependent parton distribution functions (TMDs). Moments of the GPDs are taken to obtain the electromagnetic and gravitational form factors of the pion and kaon, and comparisons to available experimental and lattice data are made. High…
We compute all kaon and pion parton distribution amplitudes (PDAs) to twist-three and find that only the pseudotensor PDA can reasonably be approximated by its conformal limit expression. At terrestrially accessible energy scales, the twist-two and pseudoscalar twist-three PDAs differ significantly from those functions commonly associated with their forms in QCD's conformal limit. In all amplitudes studied, SU(3) flavour-symmetry breaking is typically a 13% effect. This scale is determined by nonperturbative dynamics; namely, the current-quark-mass dependence of dynamical chiral symmetry break…
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）
New fragmentation functions (FFs) are extracted from a NLO QCD fit to the preliminary COMPASS data on pion and kaon multiplicities. It is shown that the new kaon FFs are very different from those of De Florian at al. (DSS) and Hirai et al. (HKNS). The sensitivity of the extracted polarized PDFs to the new FFs is discussed.
The only experimental information on the parton distribution of kaons was obtained from the scarce kaon-induced Drell-Yan cross section data. From these data, evidence for a valence $u$ quark distribution of kaon softer than that of pion was found. We study the feasibility to extract kaon's valence quark distribution via the existing kaon-induced J/psi production data. We compare the NA3 data on the K- / pi- and K+ / pi+ ratios for J/psi production on a platinum target with theoretical calculations based on the color-evaporation model. We show that the NA3 data on J/psi production provide an i…
Clear windows onto emergent hadron mass (EHM) and modulations thereof by Higgs boson interactions are provided by observable measures of pion and kaon structure, many of which are accessible via generalised parton distributions (GPDs). Beginning with algebraic GPD Ansaetze, constrained entirely by hadron-scale $π$ and $K$ valence-parton distribution functions (DFs), in whose forms both EHM and Higgs boson influences are manifest, numerous illustrations are provided. They include the properties of electromagnetic form factors, impact parameter space GPDs, gravitational form factors and associat…
Algebraic Ansaetze for the Poincaré-covariant Bethe-Salpeter wave functions of the pion and kaon are used to calculate their light-front wave functions (LFWFs), parton distribution amplitudes (PDAs), quasi-PDAs (qPDAs), valence parton distribution functions (PDFs), and quasi-PDFs (qPDFs). The LFWFs are broad, concave functions; and the scale of flavour-symmetry violation in the kaon is roughly 15%, being set by the ratio of emergent masses in the $s$-and $u$-quark sectors. qPDAs computed with longitudinal momentum $P_z =1.75\,$GeV provide a semiquantitatively accurate representation of the obj…
Strangeness was discovered roughly seventy years ago, lodged in a particle now known as the kaon, $K$. Kindred to the pion, $π$; both states are massless in the absence of Higgs-boson couplings. Kaons and pions are Nature's most fundamental Nambu-Goldstone modes. Their properties are largely determined by the mechanisms responsible for emergent mass in the standard model, but modulations applied by the Higgs are crucial to Universe evolution. Despite their importance, little is known empirically about $K$ and $π$ structure. This study delivers the first parameter-free predictions for all $K$ d…
We compute the kaon's valence-quark (twist-two parton) distribution amplitude (PDA) by projecting its Poincare'-covariant Bethe-Salpeter wave-function onto the light-front. At a scale ζ=2GeV, the PDA is a broad, concave and asymmetric function, whose peak is shifted 12-16% away from its position in QCD's conformal limit. These features are a clear expression of SU(3)-flavour-symmetry breaking. They show that the heavier quark in the kaon carries more of the bound-state's momentum than the lighter quark and also that emergent phenomena in QCD modulate the magnitude of flavour-symmetry breaking:…
We compute the distribution amplitudes of the pion and kaon in the light-front constituent quark model with the symmetric quark-bound state vertex function. In the calculation we explicitly include the flavor-SU(3) symmetry breaking effect in terms of the constituent quark masses of the up (down) and strange quarks. To calculate the kaon parton distribution functions~(PDFs), we use both the conditions in the light-cone wave function, i.e., when $\bar{s}$ quark is on-shell, and when $u$ quark is on-shell, and make a comparison between them. The kaon PDFs calculated in the two different conditio…
One of the biggest challenges in contemporary physics is understanding the origin and dynamics of the internal structure of hadrons which, at a fundamental level, is described by quantum chromodynamics (QCD). Taking great prominence amongst hadrons are pions and kaons which, despite being the lightest hadrons in nature, their very existence is intimately connected to those mechanisms responsible for almost all of the mass of the visible matter. In this manuscript we discuss many aspects of the pion and kaon structure via light front wave functions and generalized parton distributions, and a co…
We investigate the various distributions explaining multi-dimensional structure of kaon at the level of its constituents ($u$ and $\bar{s}$) using the light-cone quark model. The overlap form of wavefunctions associated with the light-cone quark model is adopted for the calculations. The generalized parton distributions(GPDs)of $u$ and $\bar{s}$ quarks are presented for the case when the momentum transfer in the longitudinal direction is non-zero. The dependence of kaon GPDs is studied in terms of variation of quark longitudinal momentum fraction, momentum transfer in longitudinal direction an…
Pion and Kaon PDFs via Infrared-Safe Evolution augmented by $J/ψ$ Data Constraints
Guizhou University of Finance and Economics（贵州财经大学）；Institute of Modern Physics, Chinese Academy of Sciences（中国科学院近代物理研究所）；University of Chinese Academy of Sciences（中国科学院大学）
In this work, we investigate the gluon distribution functions for the pion and kaon, in addition to the improved result of the valence-quark ones, in the gauge-invariant nonlocal chiral-quark model (NL$χ$QM), in which the momentum dependence of the quark interactions is properly taken into account. We then analyze the gluon distribution functions, generated dynamically through the splitting functions in the DGLAP QCD evolution. By comparing with the recent lattice QCD results and JAM global analyses, it is found that the present numerical results for the gluon parton distribution functions for…
