Charged kaon condensation in high density quark matter

We show that at asymptotically high densities the “color-flavor-locked+neutral kaon condensate” phase of QCD develops a charged kaon condensate through the Coleman–Weinberg mechanism. At densities achievable in neutron stars a charged kaon condensate forms only for some (natural) values of the low energy constants describing the low-lying excitations of the ground state.     

Kaon production at subthreshold energies

We present a comprehensive investigation of subthreshold and threshold kaon production in the framework of the QMD model. The calculation shows that the kaon yield depends strongly on the nuclear equation of state (EOS) and subthreshold kaon experiments may therefore offer the up to now best possibility to determine this yet unknown property of nuclear matter. Whereas static equations of state are in quite good agreement with the data the more realistic momentum dependent EOS's underpredict the data by about a factor of three. Most kaons are produced in a two step process with an intermediate Δ, a process which is absent in NN collisions. Therefore the kaon yield is much higher than expected from the extrapolation of pp data. We discuss in detail the influence of the elementary kaon production cross section, the contribution of different production channels and the properties of the nuclear environment at the place where the kaon is produced. The decrease of the number of produced kaons per participant with decreasing participant number, which is also observed experimentally, has two sources: The nonmaxwellian momentum distribution for small participant numbers as well as a reduction of the ΔΔ channel. This finding is supported by the observed decrease of high momentum pions. We compare our results with other calculations and discuss in detail the theoretical and experimental uncertainties. They include the yet only vaguely known elementary kaon production cross section at the threshold, the lack of a quantum-mechanical treatment of the two step production process as well as the behaviour of the kaon (and therefore also of the kaon production threshold) in the nuclear environment.     

Kaon flow in heavy ion collisions

Using transport models that include explicitly the kaon degree of freedom, we have studied kaon flow, i.e., the average kaon transverse momentum as a function of rapidity, and the associated flow parameter in heavy ion collisions at both SIS and AGS energies. It is found that the pattern of kaon flow in heavy ion collisions is sensitive to the kaon potential used in the model and thus provides a useful means for studying the kaon properties in nuclear medium.     

重离子碰撞中产生的K介子的末态作用

推广了RVUU模型,计入了K介子的平均场势和K与核子的末态重散射.并用它模拟了每核子1GeV入射能量的两个Ca核碰撞的阈下K⁺产生.讨论了K⁺矢量势和K⁺末态重散射效应对K介子的末态性质的影响.计算结果表明,排斥的矢量势,与K⁺的末态重散射相似,明显地影响了末态K⁺动能谱,导致了实验室系中具有大动量的K⁺产额的增大.然而,排斥的K⁺矢量势的计入可观地减少了K⁺的末态重散射的影响.这说明,为了合理地评价K⁺能谱和角分布,K⁺同核子的这些末态作用都是不能忽略的.     

Kaon absorption from kaonic atoms and formation spectra of kaonic nuclei

We considered the kaon absorption from atomic states into the nucleus. We found that the nuclear density probed by the atomic kaon significantly depends on the kaon orbit. Then, we re-examined the meanings of the observed strengths of one-body and two-body kaon absorption, and investigated the effects to the formation spectra of kaon bound states by in-flight (K ^-, p) reactions. As a natural consequence, if the atomic kaon probes a smaller nuclear density, the ratio of the two-body absorption at nuclear center is larger than the observed value in kaonic atoms, and the depth of the imaginary potential is deeper even at smaller kaon energies as in kaonic nuclear states because of the large phase space for the two-body processes. This deeper imaginary potential makes the signals of kaonic nucleus formation more unclear in the (K ^-, p) spectra.     

重离子碰撞中K介子和π介子产生的统一动力学模拟

用RVUU模型统一地研究了重离子碰撞中产生的K介子和π介子的动力学过程.考虑了K产生和输运过程的介质效应,同时,计入了π在核物质中的传播.用它模拟了每核子1GeV入射能量的重离子碰撞中π产生和阈下K产生过程.讨论了核介质效应对π末态性质的影响,以及对K末态性质的联带影响.计算结果表明,吸引的π光学势,影响了末态π动量分布,使横动量分布中具有小动量的π产额增大,同时明显增大了K的产额,改变了K的动量分布.这说明要合理地评价重离子碰撞的探测信息,需要统一地研究K和π的这些末态动力学作用.     

Isospin effects on strangeness in heavy-ion collisions

Kaon properties are studied within the framework of a fully covariant transport approach. The kaon–nucleon potential is evaluated in two schemes, a chiral perturbative approach and an effective One-Boson-Exchange model. Isospin effects are explicitly accounted for in both models. The transport calculations indicate a significant sensitivity of momentum distributions and total yields of $K^{0,+}$ isospin states on the choice of the kaon–nucleon interaction. Furthermore, isospin effects are rather moderate on absolute kaon yields, but appear on strangeness ratios. This is an important issue in determining the high density symmetry energy from studies of strangeness production in heavy-ion collisions.     

Recent results on the search of bound kaonic states in nuclei with FINUDA

An overview of the results achieved so far by the FINUDA experiment in the search of kaon–nuclear bound systems is presented.     

K介子协变动力学及其准粒子模型的性质

简要综述了中高能重离子碰撞中K介子的产生及研究进展。重点介绍了K介子协变动力学模型, 并在此框架内分析了中高能重离子碰撞中K+介子以及与其伴随产生的Λ超子的集体流特征。 结果表明: 协变动力学模型能够很好地给出K+介子和Λ超子的微分直接流。 相对而言, 软势给出的集体流与实验值符合更好。同时, 通过对不同输运模型中K介子准粒子模型的基本属性进行对比分析, 明确了协变动力学模型中K介子准粒子模型的质量及能量随核物质密度的变化特征, 以及周围核子的运动对于K介子基本属性的影响。In the present paper, we briefly review the progress in the study of kaon production in heavy\|ion collisions at intermediate and high energies and introduce the covariant kaon dynamics model. The collective flows of positively charged kaon and the lambda hyperon associated produced with kaon are studied in the framework of the dynamics. It shows that the directed differential flow of K+ meson and Λ hyperon can be reasonably reproduced in the covariant kaon dynamics model. The calculated results with soft equation of nuclear matter are in better agrement with experimental data. Meawhile, a detailed comparison of the properites of different quasi\|particle models in various transport model and the influence of nucleon’s movement on the effective mass and energy of the quasi\|particle in the covariant kaon dynamics model are discussed.     

通过基矢光前量子化方法研究K介子

为研究K介子的性质,通过基矢光前量子化(BLFQ)方法获得K介子的光前波函数(LFWF)。使用的光前哈密顿量中包含了动能项、横向与纵向禁闭势以及夸克-胶子相互作用,其中横向禁闭势借鉴了光前全息量子色动力学(LFHQCD)模型的禁闭势。基矢空间包括领头阶与次领头阶的Fock空间。在前期工作的基础上,只引入了奇异夸克的质量作为唯一额外参数,使K>介子的质量与实验值相匹配。基于K介子领头阶Fock空间的LFWF,计算了K介子的部分子分布振幅(PDA),其结果与量子色动力学(QCD)微扰论在零夸克质量近似下计算的结果相近。本工作得到的K介子的电磁形状因子(FF)与欧洲核子中心(CERN)超级质子同步加速器 (SPS)以及费米国家加速器实验室(FNAL)的实验结果一致。从领头阶Fock空间的LFWF计算出的电磁半径与粒子物理数据表(PDG)的实验值相近。计算出的K介子部分子分布函数(PDF),QCD演化后,在实验能标下的K介子和$ \pi $介子中价夸克u的PDF之比与CERN-NA-003的实验数据在整体趋势上大体相符。此外,在计算出的K介子PDF中,价夸克携带的纵向动量之比,$ \langle x_{uv}\rangle/\langle x_{sv}\rangle $,约为$ 2/3 $,这个数值与Bethe-Salpeter equation(BSE)模型以及密西根州立大学格点QCD(MSULat)模型的计算结果相近。还计算了K介子的结构函数,发现与BLFQ考虑有效 Nambu–Jona-Lasinio相互作用(BLFQ-NJL)模型的结果有显著差别。K介子的结构函数有望在将来的电子离子对撞机(EIC)实验中得到观测与检验。     

Generalized form factors and spin structures of the kaon

We investigate the spin structure of the kaon, based on the nonlocal chiral quark model from the instanton vacuum. We first revisit the electromagnetic form factors of the pion and kaon, improving the results for the kaon. We evaluate the generalized tensor form factors of the kaon in order to determine the probability density of transversely polarized quarks inside the kaon. We consider the effects of flavor SU(3) symmetry breaking, so that the probability density of the up and strange quarks are examined in detail. It is found that the strange quark behaves differently inside the kaon in comparison with the up quark.     

中子星物质中的K介子凝聚与三体核力效应

利用Brueckner-Hartree-Fock方法，计算了β稳定中子星物质的状态方程以及三体核力的影响，特别是研究了三体核力对中子星物质中K介子凝聚的影响. 结果表明三体核力对β稳定中子星物质中出现K介子凝聚的临界密度以及中子星物质中各种粒子所占的比例均有重要影响. 三体核力的主要作用是降低了中子星物质中出现K介子凝聚的临界密度并使K凝聚相中的核物质更加接近于对称核物质.     

φ production in In–In collisions at 158 A GeV

The NA60 experiment has measured muon pair production in In–In collisions at 158 AGeV at the CERN SPS. This paper presents a high statistics measurement of φ→μ μ meson production. Differential spectra, yields, mass and width are measured as a function of centrality and compared to previous measurements in other colliding systems at the same energy. The width of the rapidity distribution is found to be constant as a function of centrality, compatible with previous results. The decay muon polar angle distribution is measured in several reference frames. No evidence of polarization is found as a function of transverse momentum and centrality. The analysis of the p _T spectra shows that the φ has a small radial flow, implying a weak coupling to the medium. The T _eff parameter measured in In–In collisions suggests that the high value observed in Pb–Pb in the kaon channel is difficult to reconcile with radial flow alone. The absolute yield is compared to results in Pb–Pb collisions: though significantly smaller than measured by NA50 in the muon channel, it is found to exceed the NA49 and CERES data in the kaon channel at any centrality. The mass and width are found to be compatible with the PDG values at any centrality and at any p _T : no evidence for in-medium modifications is observed.     

Role of the Coulomb interaction in the flow and the azimuthal distribution of kaons from heavy ion reactions

Coulomb final-state interaction of positive charged kaons in heavy ion reactions and its impact on the kaon transverse flow and the kaon azimuthal distribution are investigated within the framework of QMD (quantum molecular dynamics) model. The Coulomb interaction is found to tend to draw the flow of kaons away from that of nucleons and lead to a more isotropic azimuthal distribution of kaons in the target rapidity region. The recent FOPI data have been analyzed by taking into account both the Coulomb interaction and a kaon in-medium potential of the strong interaction. Although the effect of the kaon Coulomb potential on the kaon flow and azimuthal distribution is much smaller than that of the strong potential, it is found to be visible, and therefore, should be taken into account if one wants to extract unambiguous information about the kaon strong potential in nuclear matter from the kaon flow and azimuthal distribution data.     

Influence of Chiral Mean Field on Kaon In-plane Flow in Heavy Ion Collisions

The influence of the chiral mean field on the K⁺ in-plane flow in heavy ion collisions at SIS energy is investigated within covariant kaon dynamics. For the kaon mesons inside the nuclear medium a quasi-particle picture including scalar and vector fields is adopted and compared to the standard treatment with a static potential. It is confirmed that a Lorentz force from spatial component of the vector field provides an important contribution to the in-medium kaon dynamics and strongly counterbalances the influence of the vector potential on the K⁺ in-plane flow. The calculated results show that the new FOPI data can be reasonably described using the Brown & Rho parametrization, which partly takes into account the correction of higher order contributions in the chiral expansion. This indicates that one can abstract the information on the kaon potential in a nuclear medium from the analysis of the K⁺ in-plane flow.     

Kaon properties in (proto-)neutron star matter

The modification of kaon and antikaon properties in the interior of (proto-)neutron stars is investigated using a chiral SU(3) model. The parameters of the model are fitted to nuclear-matter saturation properties, baryon octet vacuum masses, hyperon optical potentials and low-energy kaon-nucleon scattering lengths. We study the kaon/antikaon medium modification and explore the possibility of antikaon condensation in (proto-)neutron star matter at zero as well as finite temperature/entropy and neutrino content. The effect of hyperons on kaon and antikaon optical potentials is also investigated at different stages of the neutron star evolution.     

Evidence for time-reversal violation?

The experiment CPLEAR at CERN has measured an asymmetry between the transition rates of the antikaon to kaon process, and its reverse, kaon to antikaon. The present note shows, based on a criterion by Wolfenstein, that this observation constitutes direct evidence for time-reversal violation. Experiments at FNAL (KTEV) and CERN (NA48) have measured a T-odd asymmetry in the K_L decay. Based on an analysis by Sehgal and van Leusen, it is demonstrated that this asymmetry is well described by a (hypothetical) kaon time evolution, which is time-reversal invariant.Received: 8 January 2004, Published online: 11 May 2004     

Calculations of some properties of the kaon

The wave functions of the bound state of the charged kaon are obtained from Bethe-Salpeter equation with the phenomenological vector-vector-type flat-bottom potential. The physical spacelike electromagnetic form factor of the charged kaon is calculated from the wave functions. The radius of the kaon is given from the electromagnetic form factor. The decay constant f _K of the kaon is estimated by the relationship between the decay constant and the normalization factor derived from the axial-vector Ward identity. All calculated results give a good fit to the experimental values.     

Hot Nuclear Matter Equation of State and Finite Temperature Kaon Condensation

We perform a systematic calculation of the equation of state of asymmetric nuclear matter at finite temperature within the framework of the Brueckner-Hartree-Fock approach with a microscopic three-body force. When applying it to the study of hot kaon condensed matter, we find that the thermal effect is more profound in comparison with normal matter, in particular around the threshold density. Also, the increase of temperature makes the equation of state slightly stiffer through suppression of kaon condensation.     

高密核物质中核子的运动对于K介子的等效质量和能量的影响

本文对比分析了目前用于研究K介子产生与演化的不同动力学模型中,高温高密核物质中K⁺介子和K^-介子的等效质量和它所感受到的平均场.所得结果显示:在关于K介子的一般的平均场理论中,所定义的K⁺介子的等效质量随着核物质密度的增大而增加, K^-介子的等效质量随着核物质密度的增大而减小;但在K介子演化的协变动力学模型中,所采用的K⁺介子和K^-介子等效质量是随着核物质密度的增大都是减小的 关键词： 高密核物质 K介子 等效质量 核子运动