Femtoscopy is providing information on system size and its dynamics in heavy-ion collisions. At ultra-relativistic energies, such as those obtained at the LHC, significant production of pions, kaons and protons enables femtoscopic measurements for these particles. In particular the dependence of system size on pair momentum and particle type is interpreted as evidence for strong collective flow. Such phenomena are naturally modeled by hydrodynamics. We present calculations within the 3+1D hydrodynamic model coupled to statistical hadronization code THERMINATOR 2, corresponding to Pb--Pb collisions at $\sqrt{s_{\rm NN}}=$2.76 TeV. We obtain femtoscopic radii for pions, kaons, and protons, as a function of pair transverse momentum and collision centrality. We find that an approximate universal scaling of radii with pair transverse mass and final state event multiplicity is observed, and discuss the consequences for the interpretation of experimental measurements.
We provide, within the hydrokinetic model, a detailed investigation of kaon interferometry in $Pb+Pb$ collisions at LHC energy ($\sqrt{s_{NN}} = 2.76$ TeV). Predictions are presented for 1D interferometry radii of $K^0_SK^0_S$ and $K^{\pm}K^{\pm}$ pairs as well as for 3D femtoscopy scales in out, side and long directions. The results are compared with existing pion interferometry radii. We also make predictions for full LHC energy.
Non-identical particle femtoscopy measures the size of the system emitting particles ("radius") in heavy-ion collisions as well as the difference between mean emission space-time coordinates of two particle species ("emission asymmetry"). The system created in such collisions at the LHC behaves collectively and its dynamics is well described by hydrodynamic models. A significant emission asymmetry between pions and kaons, coming from collective flow, enhanced by contribution from flowing resonances is predicted. We present calculations within the (3+1)D viscous hydrodynamic model coupled to st…
The hydrokinetic model is applied to restore the initial conditions and space-time picture of the matter evolution in central Au+Au collisions at the top RHIC energy. The analysis is based on the detailed reproduction of the pion and kaon momentum spectra and femtoscopic data in whole interval of the transverse momenta studied by both STAR and PHENIX collaborations. A good description of the pion and kaon transverse momentum spectra and interferometry radii is reached with both initial energy density profiles motivated by the Glauber and Color Glass Condensate (CGC) models, however, at differe…
Three-dimensional analyses of the pion source revealed a heavy, non-Gaussian tail in the direction of the pair transverse momentum. The interpretation of these pion sources in terms of pure hydrodynamical evolution is, however, complicated by the strong contribution of feed-down from long-lived resonances to the source. On the other hand, kaons provide a much cleaner probe of the expanding fireball. Here we present a recent three-dimensional kaon correlation analysis using Cartesian harmonics decomposition technique. In contrary to pions, the three-dimensional source function of kaons is large…
A hadronic rescattering model with the proper hadronization time width as the free parameter is compared with charged pion and charged and neutral kaon femtoscopy measurements from the LHC ALICE experiment for sqrt{s}=7 TeV proton-proton collisions. Comparisons between the model and measurements are made for one-dimensional source parameters in several charged multiplicity and transverse particle pair momentum bins. It is found that a reasonable description of the measured source parameters by the model is obtained for a hadronization proper time width of 0.4 +- 0.1 fm/c, which is in agreement…
A simple method for the extraction of the times of maximal emission for kaons and pions using the combined fitting of their transverse momentum spectra and the longitudinal interferometry radii dependencies on the pair transverse mass $m_T$ is applied to Pb+Pb collisions at the LHC energy $\sqrt{s_{NN}}=5.02$ TeV. The method is based on the analytical formulas, that were earlier successfully utilized in the studies of Pb+Pb collisions at $\sqrt{s_{NN}}=2.76$ TeV. To test the method, the spectra, radii and particle radiation picture are calculated within the integrated hydrokinetic model (iHKM)…
We present new measurements of $Λ-Λ$ correlations, which are closely related to $H$-dibaryon: a six quark state predicted by Jaffe (1977), in Au+Au collisions at $\sqrt{s_{NN}}$ = 200 GeV from the STAR experiment. Fits to different potential models are discussed and extracted scattering length and effective range are also presented.We also present spherical harmonic decomposition of pion-kaon correlation function for 0-5% centrality in Au+Au collision at $\sqrt{s_{NN}} = 200$ GeV. In addition, we also discuss results from azimuthal HBT for beam energies 7.7-200 GeV.
The $m_T$-dependencies of the femto-scales, the so-called interferometry and source radii, are investigated within the hydrokinetic model for different types of particle pairs - pion-pion, kaon-kaon, proton-proton and proton-lambda, - produced in Pb+Pb and $p+p$ collisions at the LHC. In particular, such property of the femto-scales momentum behavior as $m_T$-scaling is studied for the systems with (w) and without (w/o) intensive transverse flow, and also w and w/o re-scattering at the final afterburner stage of the matter evolution. The detail spatiotemporal description obtained within hydrok…
The hydrokinetic approach, that incorporates hydrodynamic expansion of the systems formed in A+A collisions and their dynamical decoupling, is applied to restore the initial conditions and space-time picture of the matter evolution in central Au+Au collisions at the top RHIC energy. The analysis is based on the detailed reproduction of the pion and kaon momentum spectra and femtoscopic data in whole interval of the transverse momenta studied by both STAR and PHENIX collaborations. The fitting procedure utilizes the two parameters: the maximal energy density at supposed thermalization time 1 fm…
The correlation function of two identical particles - pions or kaons - interacting via Coulomb potential is computed. The particles are emitted from an anisotropic particle's source of finite lifetime. In the case of pions, the effect of halo is taken into account as an additional particle's source of large spatial extension. The relativistic effects are discussed in detail. The Bowler-Sinyukov procedure to remove the Coulomb interaction is carefully tested. In the absence of halo the procedure is shown to work very well even for an extremely anisotropic source. When the halo is taken into acc…
We analyze the pion femtoscopy correlations in noncentral Au-Au and Pb-Pb collisions. The azimuthally sensitive Hanbury Brown-Twiss (HBT) method is used to extract the interferometry radii depending on the azimuthal angle with respect to the second and third-order event plane. The results are in semiquantitative agreement with the STAR collaboration data on the HBT radii with respect to the second-order reaction plane, with the preliminary PHENIX collaboration data on the HBT radii with respect to the third-order reaction plane in Au-Au collisions at 200GeV, and with the preliminary ALICE coll…
We review our studies of spectator-induced electromagnetic (EM) effects on charged pion emission in ultrarelativistic heavy ion collisions. These effects are found to consist in the electromagnetic {charge splitting} of pion directed flow as well as very large distortions in spectra and ratios of produced charged particles. As it emerges from our analysis, they offer sensitivity to the actual distance $d_E$ between the pion formation zone at freeze-out and the spectator matter. As a result, this gives a new possibility of studying the space-time evolution of dense and hot matter created in the…
Shedding Light on (Anti-)nuclei Production with Pion-Nucleus Femtoscopy
Key Laboratory of Nuclear Physics and Ion-beam Application (MOE), Institute of Modern Physics, Fudan University（核物理与离子束应用（教育部）重点实验室，现代物理研究所，复旦大学）；Shanghai Research Center for Theoretical Nuclear Physics, NSFC and Fudan University（上海理论核物理研究中心，国家自然科学基金委员会与复旦大学）；Cyclotron Institute and Department of Physics and Astronomy, Texas A&M University（回旋加速器研究所及物理与天文学系，德州农工大学）；School of Physics, East China Normal University（物理与电子科学学院，华东师范大学）
Kaon and Pion Fluctuations from Small Disoriented Chiral Condensates
原子核碰撞中Ω和反Ω重子产生的增强17 A GeV的能量可以通过许多小的无序手性凝聚体区域的形成来解释。这种解释意味着中性和带电的K介子以及π介子必须表现出新的同位旋波动。我们计算了这些区域中中性π介子和K介子的分数分布。然后，我们提出了强大的统计观测值，可用于提取新的波动在RHIC和LHC的π介子和K介子测量的背景贡献。
The structure of hadrons is described well by the Nambu--Jona-Lasinio (NJL) model, which is a chiral effective quark theory of QCD. In this work we explore the electromagnetic structure of the pion and kaon using the three-flavor NJL model, including effects of confinement and a pion cloud at the quark level. In the calculation there is only one free parameter, which we take as the dressed light quark ($u$ and $d$) mass. In the regime where the dressed light quark mass is approximately $0.25\,$GeV, we find that the calculated values of the kaon decay constant, current quark masses, and quark c…
Using realistic quark propagators and meson Bethe-Salpeter amplitudes based on the Dyson-Schwinger equations, we calculate the pion and kaon's valence parton distribution functions (PDF) through the modified impulse approximation. The PDFs we obtained at hadronic scale have the purely valence characteristic and exhibit both dynamical chiral symmetry breaking and SU(3) flavor symmetry breaking effects. A new calculation technique is introduced to determine the valence PDFs with precision. Through NLO DGLAP evolution, our result is compared with pion and kaon valence PDF data at experimental sca…
A study of energy behavior of the pion spectra and interferometry scales is carried out for the top SPS, RHIC and for LHC energies within the hydrokinetic approach. The main mechanisms that lead to the paradoxical, at first sight, dependence of the interferometry scales with an energy growth, in particular, a decrease $R_{out}/R_{side}$ ratio, are exposed. The hydrokinetic predictions for the HBT radii at LHC energies are compared with the recent results of the ALICE experiment.
Borrowing the structures of the hydrogen atom, molecular ion, and diatomic molecule, we predict the nature of a new type of hydrogenlike charm-pion or charm-kaon matter that could be obtained by replacing the proton and electron in hydrogen matter with a charmed meson and a pion or a kaon, respectively. We find that the spectra of the atom, molecular ion, and diatomic molecule can be obtained simultaneously with the Coulomb potential for the hydrogen, the charm-pion, and the charm-kaon systems. The predicted charm-pion matter also allows us to explore the mass shift mediated by the strong inte…
Effects of charge symmetry breaking associated with the $u$ and $d$ quark mass difference in the elastic form factors of the pion and kaon are presented. We use a confining version of the Nambu--Jona-Lasinio model. The pion and kaon are described as a dressed quark and antiquark bound states governed by the Bethe-Salpeter equation, and exhibit the properties of Goldstone bosons, with the pion mass difference given by $m_{π^{+}}^2 - m_{π^{0}}^2 \propto (m_u -m_d)^2$ as demanded by dynamical chiral symmetry breaking. We found significant charge symmetry breaking effects for realistic current qua…
We have calculated the Bjorken-x dependence of the kaon and pion valence quark distributions in a statistical model. Each meson is described by a Fock state expansion in terms of quarks, antiquarks and gluons. Although Drell-Yan experiments have measured the pion valence quark distributions directly, the kaon valence quark distributions have only been deduced from the measurement of the ratio $\bar{u}_K(x)/\bar{u}_π(x)$. We show that, using no free parameters, our model predicts the decrease of this ratio with increasing x.
Quasi-elastic knockout of pions and kaons from nucleons by high-energy electrons and quark microscopy of "soft" meson degrees of freedom in the nucleon
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.
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…
In the present work the Mott effect for pions and kaons is described within a Beth- Uhlenbeck approach on the basis of the PNJL model. The contribution of these degrees of freedom to the thermodynamics is encoded in the temperature dependence of their phase shifts. A comparison with results from $N_f = 2 + 1$ lattice QCD thermodynamics is performed.
We describe expressions for pion and kaon dressed-quark distribution functions that incorporate contributions from gluons which bind quarks into these mesons and hence overcome a flaw of the commonly used handbag approximation. The distributions therewith obtained are purely valence in character, ensuring that dressed-quarks carry all a meson's momentum at a characteristic hadronic scale and vanishing as $(1-x)^2$ when Bjorken-$x\to 1$. Comparing such distributions within the pion and kaon, it is apparent that the size of SU(3)-flavour symmetry breaking in meson parton distribution functions i…
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…
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 talk we present our recent studies for the unpolarized fragmentation functions for the pion and kaon, employing the nonlocal chiral quark model, which manifests the nonlocal interaction between the quarks and pseudoscalar mesons, in the light-cone frame. It turns out that the nonlocal interaction produces considerable differences in comparison to typical local-interaction models.
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…
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 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 …
We discuss the recent progress in the study of semileptonic kaon and pion decays, including new experimental results, improved electroweak radiative corrections, form factor calculations and isospin-breaking effects. As a result, we obtain $|V_{us}|=0.22309(40)(39)(3)$ from kaon semileptonic decays and $|V_{us}/V_{ud}|=0.22908(66)(41)(40)(2)(1)$ from the ratio between the kaon and pion semileptonic decay rates. We report an apparent violation of the top-row Cabibbo-Kobayashi-Maskawa matrix unitarity at a $3.2\sim 5.6σ$ level, and a discrepancy at a $2.2σ$ level between the value of $|V_{us}/V_…
The CMS experiment at the Large Hadron Collider has recently presented data on the average transverse momentum of protons, kaons and pions as a function of particle multiplicity. We relate the particle multiplicity to saturation momentum using recently published computations of the interaction radius determined from the theory of the Color Glass Condensate. We show that the pp and the pA experimental data scale in terms of these saturation momenta. Computing transverse momentum spectra for identified particles using Boltzmann-type distributions and relating different associated multiplicities …
Non-universality of color transparency onset in pion and kaon electroproduction
Center for Exotic Nuclear Studies, Institute for Basic Science（基础科学研究所奇异核研究中心）；Research Institute of Basic Science, Korea Aerospace University（韩国航空大学基础科学研究所）；Department of Physics and Engineering Physics, Yonsei University（延世大学物理与工程物理系）
We present a calculation of the connected-diagram contributions to the first three non-trivial Mellin moments for the pion and kaon, extracted using local operators with up to 3 covariant derivatives. We use one ensemble of gauge configurations with two degenerate light, a strange and a charm quark ($N_f$=2+1+1) of maximally twisted mass fermions with clover improvement. The ensemble has a pion mass $\sim$260 MeV, and a kaon mass $\sim$530 MeV. We reconstruct the $x$-dependence of the PDFs via fits to our results, and find that our lattice data favor a $(1-x)^2$-behavior in the large-$x$ regio…
We study the contributions from the connected and disconnected contraction diagrams to the pion-kaon scattering amplitude within the framework of SU$(4|1)$ partially-quenched chiral perturbation theory. Combining this with a finite-volume analysis, we demonstrate that a lattice calculation of the easier computable connected correlation functions is able to provide valuable information of the noisier disconnected correlation functions, and may serve as a theory guidance for the future refinement of the corresponding lattice techniques.
In this paper we study the gluon and valence quark distributions in the pion and kaon in nuclear medium for various nuclear densities as well as in vacuum within the Nambu--Jona-Lasinio (NJL) model with the help of the proper-time regularization scheme which simulates a confinement of QCD. The nuclear medium effect is also determined in the same model for the symmetric nuclear matter. We then analyze the gluon and valence quark distributions for the bound pion and kaon in symmetric nuclear matter as well as those in vacuum. We find that the valence quark and gluon distributions in vacuum have …
Large Hadron Collider (LHC) had produced a vast amount of high precision data for high energy heavy ion collision. We attempt here to study (i) transverse momenta spectra, (ii) $K/π$, $p/π$ ratio behaviours, (iii)rapidity distribution, and (iv) the nuclear modification factors of the pion, kaon and antiproton produced in $p+p$ and $Pb+Pb$ collisions at energy $\sqrt{s_{NN}}$ = 2.76 TeV, on the basis of Sequential Chain Model (SCM). Comparisons of the model-based results with the measured data on these observables are generally found to be modestly satisfactory.
Within the three-flavor PNJL and EPNJL chiral quark models we have obtained pseudoscalar meson properties in quark matter at finite temperature $T$ and baryochemical potential $μ_B$. We compare the meson pole (Breit-Wigner) approximation with the Beth-Uhlenbeck (BU) approach that takes into account the continuum of quark-antiquark scattering states when determining the partial densities of pions and kaons. We evaluate the kaon-to-pion ratios along the (pseudo-)critical line in the $T-μ_B$ plane as a proxy for the chemical freezeout line, whereby the variable $x=T/μ_B$ is introduced that corres…
