Pion-Photon TDAs in the NJL Model
A. Courtoy, S. Noguera
在NJL模型的形式下，将π介子视为Bethe-Salpeter意义下的束缚态，研究了π介子-光子跃迁分布振幅。得到的结果明确验证支持，和规则和多项式条件。PCAC的作用得到了强调。
The pion-photon Transition Distribution Amplitudes (TDAs) are studied, treating the pion as a bound state in the sense of Bethe-Salpeter, in the formalism of the NJL model. The results obtained explicitly verify support, sum rules and polynomiality conditions. The role of PCAC is highlighted.
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Charmonium production in association with a forward or backward pion in nucleon-antinucleon annihilation is one of the most promising reaction to access nucleon-to-pion transition distribution amplitudes (TDAs) at PANDA. We briefly review the description of this reaction in terms of πN TDAs within the collinear factorization approach and present the first results of dedicated feasibility studies for the PANDA experimental setup.
Pion-Photon Transition Distribution Amplitudes
讨论了新近引入的跃迁分布振幅（TDAs）对$π$ - $γ$跃迁的影响.给出了不同情况下$π$ - $γ$和$γ$ - $π$ TDAs之间的关系。比较了不同模型中$π$ - $γ$ TDAs的数值。GPD的功能扩展到TDA和PCAC的作用突出。我们给出了计算介子对产生的截面的方法。
Baryon-to-meson Transition Distribution Amplitudes (TDAs) appear as building blocks in the collinear factorized description of amplitudes for a class of hard exclusive reactions, prominent examples being hard exclusive pion electroproduction off a nucleon in the backward region and baryon-antibaryon annihilation into a pion and a lepton pair or a charmonium. Baryon-to-meson TDAs extend both the concepts of generalized parton distributions (GPDs) and baryon distribution amplitudes (DAs) encoding valuable complementary information on the hadronic structure. We review the basic properties of bary…
Baryon to meson transition distribution amplitudes (TDAs) extend the concept of generalized parton distributions. Baryon to meson TDAs appear as building blocks in the collinear factorized description of amplitudes for a class of hard exclusive reactions, prominent examples of which being hard exclusive meson electroproduction off a nucleon in the backward region and baryon-antibaryon annihilation into a meson and a lepton pair. We study the general properties of these objects following from the underlying symmetries of QCD. In particular, the Lorentz symmetry results in the polynomiality prop…
The extension of the concept of generalized parton distributions leads to the introduction of baryon to meson transition distribution amplitudes (TDAs), non-diagonal matrix elements of the nonlocal three quark operator between a nucleon and a meson state. We present a general framework for modelling nucleon to pion ($πN$) TDAs. Our main tool is the spectral representation for πN TDAs in terms of quadruple distributions. We propose a factorized Ansatz for quadruple distributions with input from the soft-pion theorem for πN TDAs. The spectral representation is complemented with a D-term like con…
Baryon to meson transition distribution amplitudes (TDAs), non-diagonal matrix elements of the nonlocal three quark operator between a nucleon and a meson state, extend the concept of generalized parton distributions. These non-perturbative objects which encode the information on three quark correlations inside the nucleon may be accessed experimentally in backward meson electroproduction reactions. We suggest a general framework for modelling nucleon to pion (pi N) TDAs employing the spectral representation for pi N TDAs in terms of quadruple distributions. The factorized Ansatz for quadruple…
Nucleon to meson transition distribution amplitudes (TDAs), non-diagonal matrix elements of nonlocal three quark operators between a nucleon and a meson states, arise within the collinear factorized description of hard exclusive electroproduction of mesons off nucleons in the backward direction. Below we address the problem of modelling pion to nucleon TDAs. We suggest a factorized Ansatz for quadruple distributions with input from the soft pion theorem for pi N TDAs. In order to satisfy the polynomiality property in its full form the spectral representation is complemented with a D-term like …
Pion Generalized Parton Distributions in the Non-Local NJL Model
在动量相关的夸克质量为$M(k)$的非定域NJL模型中计算了π介子的偏态部分子分布$H^I$。在正向极限下，$H^I$对应于部分子分布，而对于$t<0$，$H^I$与π电磁形状因子有关
The behavior of charged and neutral pion masses in the presence of a static uniform magnetic field is studied in the framework of the two-flavor Nambu-Jona-Lasinio (NJL) model. Analytical calculations are carried out employing the Ritus eigenfunction method. Numerical results are obtained for definite model parameters, comparing the predictions of the model with present lattice QCD (LQCD) results.
Pion light cone wave function in the non-local NJL model
我们用简单的瞬子激发的NJL型模型计算了超前扭转π介子光锥的波函数。该模型包括在夸克环中使用动量相关的夸克质量，进入波函数的定义。结果是解析的，直到某个代数方程的解。各种属性，包括依赖的π波函数的kT进行了讨论。由此产生的kT积分波函数不是渐近的，并与最近的分析CLEO数据。
The behavior of charged pion masses in the presence of a static uniform magnetic field is studied in the framework of the two-flavor NJL model, using a magnetic field-independent regularization scheme. Analytical calculations are carried out employing the Ritus eigenfunction method, which allows us to properly take into account the presence of Schwinger phases in the quark propagators. Numerical results are obtained for definite model parameters, comparing the predictions of the model with present lattice QCD results.
Differential distributions in the $π_0π_0γ$ system created in the annihilation channel of an electron-positron collision are considered. The energy fractions of the pions (Dalitz-plot) distribution are presented in a general form and in approximation of intermediate vector mesons (excited and ordinary ones).It is pointed out that in relevant experiments the generalized polarizability of the neutral pion can be measured. Numerical illustrations are presented.
Pion and photon beam initiated backward charmonium or lepton pair production
本文综述了利用近后向区域π介子与光子束引发的硬遍举反应研究核子TDAs的方法，通过核子交换模型和双参数模型估计了J-PARC、JLab、EIC及EicC条件下轻子对与$J/ψ$产生的截面。
On pion correction to quark mass in next-leading order of mean-field expansion in NJL model
在Nambu-Jona-Lasinio模型中，采用四维截断正则化和次领先平均场展开的维度解析正则化，计算了夸克质量修正.分析计算表明，π介子对夸克质量的修正等于零。比较两种正则化的结果可以看出，Nambu-Jona-Lasinio模型的π介子对夸克质量的修正为零是与正则化无关的事实。
NJL model on the light cone and pion structure function
在光锥上建立了NJL模型。利用1/N展开法求解费米约束，导出了有效的4-费米拉格朗日量。利用拉格朗日函数研究了Pionic性质，并证明了与等时公式的形式等价性。讨论了两种光锥变量的正则化方案：不变质量截断方案的推广和横向动量截断方案。结果表明，第一个是等价的协变3-动量截止（色散截止）格式的等时公式。作为应用，研究了π介子的结构函数在这两种正则化方案。
Parton Distributions Functions of Pion, Kaon and Eta pseudoscalar mesons in the NJL model
利用Pauli-Villars正则化方法在NJL模型中得到了赝标π、K和eta介子的部分子分布，并根据LO和NLO演化进行了分析，在Q^2 = 4 GeV^2下得到了π介子的价海夸克和胶子部分子分布，并与该尺度下已有的参数化结果进行了比较。令人惊讶的是，NLO阶效应与LO阶效应相比很小。价分布与实验分析吻合得很好，但胶子和海的分布在高x区域较软，在低x区域较硬。
Pion and vacuum properties in the nonlocal NJL model
我们用动量相关的夸克质量建立了非定域NJL模型，并计算了旋度为2和3的π介子光锥波函数。主导扭转波函数不是渐近的，与新的CLEO数据吻合得很好。利用扭曲3波函数的归一化条件计算夸克凝聚。提出了一个计算胶子凝聚的公式。胶子凝聚的数值与唯象值很好地吻合，而夸克凝聚的数值大于$-(250$ MeV $)^3$的唯象值。利用$k_T^2$矩与混合凝聚之间的关系，估计了5维混合夸克胶子凝聚。
The charge pion polarizability is calculated in the Nambu-Jona-Lasinio model, where the quark loops (in the mean field approximation) and the meson loops (in the $1/N_c$ approximation) are taken into account. We show that quark loop contribution dominates, because the meson loops strongly conceal each other. The sigma-pole contribution $(m^2_σ-t)^{-1}$ plays the main role and contains strong t-dependence of the effective pion polarizability at the region $|t|\geq 4M_π^2$. Possibilities of experimental test of this sigma-pole effect in the reaction of Coulomb Nuclear Scattering are estimated fo…
In the framework of the Nambu--Jona-Lasino (NJL) model, we study the effect of an intense external uniform magnetic field on neutral and charged pion masses and decay form factors. In particular, the treatment of charged pions is carried out on the basis of the Ritus eigenfunction approach to magnetized relativistic systems. Our analysis shows that in the presence of the magnetic field three and four nonvanishing pion-to-vacuum hadronic form factors can be obtained for the case of the neutral and charged pions, respectively. As expected, it is seen that for nonzero magnetic field the $π^0$ mes…
Coupling of pion condensate, chiral condensate and Polyakov loop in an extended NJL model
将带有Polyakov环的Nambu Jona-Lasinio模型推广到有限同位旋化学势的情形，其特征是π凝聚、手征凝聚和Polyakov环同时耦合.通过最小化系统的热力学势，研究了π凝聚体、手征凝聚体和Polyakov环随温度和同位旋化学势的变化。由此产生的$(T,μ_I)$相图研究重点的临界点和Polyakov回路动力学。确定了π超流性相变的三临界点，并且在高同位旋化学势区，同位旋对称性恢复的相变与Polyakov环的交叉相变完全一致.这些结果与格点量子色动力学的实验结果一致。
In this work, a compilation of effective electromagnetic field couplings to pions and constituent quarks and their effective interactions derived previously, including corrections to the NJL model, is presented. The particular case of a weak external magnetic field along the $\hat{z}$ direction is considered shortly and effective coupling constants are redefined to incorporate the weak-$B_0$ dependence. They correspond to corrections to well known pion-constituent quark couplings and to the NJL and vector NJL effective couplings that break isospin and chiral symmetries.
We present a thorough analysis of unpolarized Drell-Yan (DY) pair production in pion-nucleus scattering. On the nucleus side, we use nuclear parton distributions along with parametrisations of the nucleon partonic transverse distribution available in the literature. Partonic longitudinal and transverse distributions of the pion are those obtained in a recent calculation in a Nambu-Jona Lasinio (NJL) framework, with Pauli-Villars regularization. The scale of the NJL model is fixed by a comparison between NLO predictions based on NJL evolved pion distributions and rapidity differential DY cross …
Pion Properties in the 1/N_c-corrected NJL model
在Nambu-Jona-Lasinio（NJL）模型中，考虑1/N_c修正，研究了介子涨落对π传播子的影响.由于模型的不可重整化性，我们必须用一个独立的截断参数Lambda_M来正则化介子环。而对于中等的λ_M值，π介子性质的变化只是定量的，我们遇到了较大的λ_M值的强不稳定性。
We study pion condensation and the phase structure in a two-flavor Nambu-Jona-Lasinio model in the presence of baryon chemical potential $μ$ and isospin chemical potential $μ_I$at zero and finite temperature. There is a competition between the chiral condensate and a Bose-Einstein condensate of charged pions. In the chiral limit, the chiral condensate vanishes for any finite value of the isospin chemical potential, while there is a charged pion condensate that depends on the chemical potentials and the temperature. At the physical point, the chiral condensate is always nonzero, while the charg…
The Pion-Photon Transition Distribution Amplitudes in the Nambu-Jona Lasinio Model
我们定义的π介子光子跃迁分布振幅（TDA）的场论形式主义从协变Bethe-Salpeter方法的束缚态的测定。我们应用我们的形式主义的Nambu-JonaLasinio模型，作为一个现实的理论的π介子。得到的矢量和轴向TDAs满足一般考虑所需的所有功能。特别地，求和规则和多项式条件被明确地验证。数值证明了向量TDA多项式展开式中的奇系数在手征极限下为零。PCAC的作用和π极的存在得到了明确的证明。
In this paper we investigate the phase structure of a (1+1) and (3+1)-dimensional quark model with four-quark interaction and in the presence of baryon ($μ_B$), isospin ($μ_I$) and chiral isospin ($μ_{I5}$) chemical potentials. It is shown that the chemical potential $μ_{I5}$ promotes the appearance of the charged PC phase with nonzero baryon density. Results of both models are qualitatively the same, this fact enhances one's confidence in %the faith in the obtained predictions. It is established that in the large-$N_c$ limit ($N_c$ is the number of colored quarks) there exists a duality corre…
The influence of the magnetic field on the pion superfluidity and the phase structure is analyzed in the framework of the two-flavor Nambu--Jona-Lasinio(NJL) model. To do this, we first derive the thermodynamic potential from the Lagrangian density of the NJL model in the mean field approximation. Using this thermodynamic potential, we get the gap equation of the chiral condensate and the pion condensate. The effect of external magnetic field on the pion condensate is not simple promotion or suppression, which we will discuss in detail in the paper. It is shown that the tricritical point on th…
We present an analysis of unpolarized Drell-Yan pair production in pion-nucleus scattering with a particular focus into the pion dynamics. The study consists in analyzing the effect of the partonic longitudinal and, especially, transverse distributions of the pion in a Nambu--Jona-Lasinio (NJL) framework, with Pauli-Villars regularization. In order to consistently take into account the QCD evolution effects, we have estimated the hadronic scale corresponding to the NJL model's degrees of freedom through a minimization procedure at NLO: The NLO evolved pion distributions have been compared to r…
The deconfinement phase transition, hadronization and the NJL model
量子色动力学的一个可靠预言是，在足够高的温度和/或密度下，强子物质应该经历热力学相变，变成物质的色消限态--通常称为夸克-胶子等离子体（QGP）。在低能有效量子色动力学（QCD）理论中，人们通常讨论手征跃迁，手征跃迁存在一个明确的序参量。用Nambu-JonaLasinio（NJL）模型研究了热夸克物质介质中π介子和K介子的离解。π介子和K介子的衰变宽度很大，但在远高于手征（或解除禁闭）跃迁的临界温度的温度下是有限的，K介子的衰变宽度要大得多。因此，在如此高温下，π介子甚至K介子（密度比π介子低）都可以与夸克和胶子共存。在此前提下，我们研究了夸克-胶子等离子体中的强子化过程，并着重讨论了这一过程是否对可接受的低能有效QCD理论有所启示。
The processes $τ^- \to π^- π^0 ν_τ$ and $e^{+}e^{-} \to π^{+} π^{-}$ are considered within the chiral Nambu--Jona-Lasinio model with taking into account the pion final state interactions beyond the leading $1/N_c$ approximation. The contribution of the loop correction caused by a $ρ$ meson exchange between the pions, which gives the main contribution in the P-wave channel, is caclulated. The results for both processes are in a satisfactory agreement with experimental data.
Pion Structure Function in the Nambu and Jona-Lasinio model
在Nambu和Jona-Lasinio（NJL）模型下研究了π介子的结构函数。在Bjorken极限下，计算了虚光子与π介子靶的前向散射振幅，得到了低能强子尺度下π介子的价夸克分布.利用Altarelli-Parisi方程将计算的分布函数演化到实验动量尺度。所得分布与实验结果吻合较好。我们还计算了K介子结构函数，并与实验结果进行了比较。
Pion and kaon condensation in a 3-flavor NJL model
我们分析了三味Nambu-Jona-Lasinio模型在有限温度$T$和化学势$μ_u, μ_d, μ_s$下的相图。我们研究了π介子和K介子凝聚的竞争，提出了一种仅由轻夸克有限密度导致K介子凝聚的物理情形。
Backward DVCS on the pion in Sullivan processes
本工作在共线QCD因子化框架下，基于光前波函数重叠的TDAs方法，系统研究了Sullivan过程中π介子后向DVCS的测量可行性，并预估了未来中美电子-离子对撞机的截面。
The properties of two-flavored massive Nambu--Jona-Lasinio model in (1+1)-dimensional spacetime are investigated in the presence of isospin and quark number chemical potentials. The consideration is performed in the large-$N_c$ limit, where $N_c$ is the number of colored quarks. It is shown in the framework of this model that charged pion condensation phenomenon of dense quark/hadron isotopically asymmetric matter is rather a spatially inhomogeneous than a homogeneous one.
With the isovector coupling constants adjusted to reproduce the physical pion mass and lattice QCD results in baryon-free quark matter, we have carried out rigourous calculations for the pion condensate in the 3-flavor Nambu-Jona-Lasinio model, and studied the 3-dimensional QCD phase diagram. With the increasing isospin chemical potential $μ_I$, we have observed two nonzero solutions of the pion condensate at finite baryon chemical potentials $μ_B$, representing respectively the pion superfluid phase and the Sarma phase, and their appearance and disappearance correspond to a second-order (firs…
The Nambu--Jona-Lasinio (NJL) - Jet model provides a sound framework for calculating the fragmentation functions in an effective chiral quark theory, where the momentum and isospin sum rules are satisfied without the introduction of ad hoc parameters. Earlier studies of the pion fragmentation functions using the NJL model within this framework showed qualitative agreement with the empirical parameterizations. Here we extend the NJL-Jet model by including the strange quark. The corrections to the pion fragmentation functions and corresponding kaon fragmentation functions are calculated using th…
Pion Observables in the Extended NJL Model with Vector and Axial-Vector Mesons
将矢量介子和轴矢量介子的Nambu和Jona-Lasinio模型的动量空间玻色化方法应用于$ππ$散射。与以往文献中的情况不同，我们利用手征对称性的线性和非线性实现，充分考虑了介子顶点的动量依赖性，得到了$ππ$的散射振幅.我们展示了这两种方法之间的完全物理等效性。详细讨论了该模型中的手征展开过程。得到了夸克质量、π介子质量和常数$f_π$的手征展开式。将低能量$ππ$相移与可用数据进行比较。我们还研究了π介子的标量形状因子。
In this paper, we study the possibility of an inhomogeneous quark condensate in the 1+1 dimensional Nambu-Jona-Lasinio model in the large-$N_c$ limit at finite temperature $T$ and quark chemical potential $μ$ using dimensional regularization. The phase diagram in the $μ$--$T$ plane is mapped out. At zero temperature, an inhomogeneous phase with a chiral-density wave exists for all values of $μ>μ_c$. Performing a Ginzburg-Landau analysis, we show that in the chiral limit, the critical point and the Lifschitz point coincide. We also consider the competition between a chiral-density wave and a co…
The NJL-jet model provides a sound framework for calculating the fragmentation func- tions in an effective chiral quark theory, where the momentum and isospin sum rules are satisfied without the introduction of ad hoc parameters [1]. Earlier studies of the pion fragmentation func- tions using the Nambu-Jona-Lasinio (NJL) model within this framework showed good qualitative agreement with the empirical parameterizations. Here we extend the NJL-jet model by including the strange quark. The corrections to the pion fragmentation function and corresponding kaon fragmen- tation functions are calculat…
In this paper we investigate the phase structure of a (1+1)-dimensional quark model with four-quark interaction and in the presence of baryon ($μ_B$), isospin ($μ_I$) and chiral isospin ($μ_{I5}$) chemical potentials. Spatially inhomogeneous chiral density wave (for chiral condensate) and single wave (for charged pion condensate) approaches are used. It is established that in the large-$N_c$ limit ($N_c$ is the number of colored quarks) there exists a duality correspondence between the chiral symmetry breaking phase and the charged pion condensation (PC) one. Moreover, it is shown that inhomog…
In this paper the phase structure of dense quark matter has been investigated in the presence of baryon, isospin and chiral isospin chemical potentials in the framework of (3+1)-dimensional Nambu--Jona-Lasinio model with two quark flavors. It has been shown that in the large-$N_{c}$ limit ($N_{c}$ is the number of colors of quarks) there exists a duality correspondence between the chiral symmetry breaking phase and the charged pion condensation one. The key conclusion of our studies is the fact that chiral isospin chemical potential generates charged pion condensation in dense quark matter wit…
In this paper we investigate the phase structure of a (1+1)-dimensional schematic quark model with four-quark interaction and in the presence of baryon ($μ_B$), isospin ($μ_I$) and chiral isospin ($μ_{I5}$) chemical potentials. It is established that in the large-$N_c$ limit ($N_c$ is the number of colored quarks) there exists a duality correspondence between the chiral symmetry breaking phase and the charged pion condensation (PC) one. The role and influence of this property on the phase structure of the model are studied. Moreover, it is shown that the chemical potential $μ_{I5}$ promotes th…
We investigate pion and sigma meson correlations in hot quark matter within a modified NJL model. Special emphasis is on the transformation of mesonic bound states to resonances (Mott dissociation) when due to the partial chiral symmetry restoration with increasing temperature the threshold of quark-antiquark continuum states drops below the meson mass at the corresponding Mott temperature. The description is based on evaluating the polarization functions for quark-antiquark (meson) correlations as a function of the temperature and the results can be represented by introducing modulus and phas…
Kaon gravitational form factors and mechanical structure in a three-flavor NJL model
在适当时间正则化三味NJL模型中，计算K介子引力形状因子，对比其与π介子的结果，分析味对称性破缺对K介子力学结构的影响，明确C项投影约化对维持π介子低能定理的必要性。
The recently developed Nambu-Jona-Lasinio (NJL) - Jet model is used as an effective chiral quark theory to calculate the quark fragmentation functions to pions, kaons, nucleons, and antinucleons. The effects of the vector mesons rho, K* and phi on the production of secondary pions and kaons are included. The fragmentation processes to nucleons and antinucleons are described by using the quark-diquark picture, which has been shown to give a reasonable description of quark distribution functions. We incorporate effects of next-to-leading order (NLO) in the Q^2 evolution, and compare our results …
Exploring backward pion electroproduction in the scaling regime
我们使用的过渡分布振幅（TDAs），进入描述的p -> pi 0过渡，和质子分布振幅（DA）在软π极限估计的大小的振幅向后电生产的pi 0在大Q2之间的一般关系。
We evaluate the valence double parton distribution (dPDF) of the pion in the Nambu--Jona-Lasinio model. At the low-energy quark-model scale and in the chiral limit a particularly simple factorized form $D(x_1,x_2, \vec{q}) = δ(1-x_1-x_2) F(\vec{q})$ follows, where $x_{1,2}$ denote the longitudinal momentum fractions of the valence quark and antiquark, and $\vec{q}$ is their relative transverse momentum. For $\vec{q}=\vec{0}$ our result complies to the Gaunt-Sterling sum rules. We carry out the necessary dDGLAP evolution to higher scales via the Mellin moments and explore its impact on the corr…
Dimensional reduction and the generalized pion in a magnetic field within the NJL model
本研究在NJL模型中研究磁场下中性π介子质量，发现反常磁矩符号与电荷相反且小于组分质量，构造两个广义π介子并证明其Goldstone性质被维度约化破坏，质量下降为红外动力学残余。
Production of a pion in association with a high-Q2 dilepton pair in antiproton-proton annihilation at GSI-FAIR
我们计算了反p p -> l+ l-pi 0的正向截面和大轻子对不变质量的正向截面.在这个运动学区域中，主导扭转振幅分解为短程矩阵元、长程主导反质子分布振幅和质子到π介子跃迁分布振幅（TDA）。使用这些TDAs的手性限制启发的建模，我们得到了这个截面的第一个估计，从而证明了这个过程可以在GSI-FAIR测量。
In this talk we present investigation of the phase structure of a (1+1)-dimensional quark model with four-quark interaction and in the presence of baryon ($μ_B$), isospin ($μ_I$) and chiral isospin ($μ_{I5}$) chemical potentials. Spatially homogeneous and inhomogeneous (chiral density wave (for chiral condensate) and single wave (for charged pion condensate)) condensates are considered. It is established that in the large-$N_c$ limit ($N_c$ is the number of colored quarks) there exists a duality correspondence between the chiral symmetry breaking phase and the charged pion condensation one. Th…
Isospin asymmetry is the well-known property of dense quark matter, which exists in the compact stars and is produced in heavy ion collisions. On the other hand, the chiral imbalance between left- and right-handed quarks is another highly anticipated phenomenon that could occur in the dense quark matter. To investigate quark matter under these conditions, we take into account baryon -- $μ_B$, isospin -- $μ_I$ and chiral isospin -- $μ_{I5}$ chemical potentials and study QCD phase portrait using NJL$_4$ model generalized to two massive quarks that could condense into the pion condensation. We ha…
Improved phenomenology of $πN$ transition distribution amplitudes
本文开发了一个灵活的唯象模型来描述核子-π介子跃迁分布振幅（$πN$ TDAs），基于双分量因子化假设并考虑阈值产生定理约束与前向极限贡献，用于研究后向区域反应的截面与极化不对称性，并考察了预测对建模假设的敏感性。
The properties of two-flavored massless Nambu-Jona-Lasinio model in (1+1)-dimensional $R^1\times S^1$ spacetime with compactified space coordinate are investigated in the presence of isospin and quark number chemical potentials $μ_I$, $μ$. The consideration is performed in the large $N_c$ limit, where $N_c$ is the number of colored quarks. It is shown that at $L=\infty$ ($L$ is the length of the circumference $S^1$) the pion condensation (PC) phase with {\it zero quark number density} is realized at arbitrary nonzero $μ_I$ and for rather small values of $μ$. However, at arbitrary finite values…
Meson Properties in the 1/N_c-corrected NJL model
在Nambu-Jona-Lasinio模型下研究了介子的性质。我们包括介子环修正，它是通过次领先顺序的系统1/N_c展开产生的。我们表明，我们的计划是符合手征对称性，特别是与Goldstone定理和Gell-Mann Oakes Renner关系。数值部分着重于π介子和ρ介子部分。对于后者，1/N_c-校正是至关重要的，以便包括占主导地位的rho -> pi π-衰变通道，而首阶近似仅包含非物理的q \bar q-衰变通道。我们表明，一个令人满意的描述的π电磁形状因子可以得到。强子模型的异同进行了讨论。
Pion Structure at High and Low Energies in Chiral Quark Models
本文在手征夸克模型的框架下评述了π介子的低能和高能性质。特别强调的是把最简单的版本SU（2）NJL模型作为原型。强调了规范不变性在这类计算中的作用。结果被用作微扰QCD演化方程的初始条件。在首阶，夸克模型的尺度是$μ_0 \sim 320 {\rm MeV} $，由π介子分布函数和π介子分布振幅确定。
In this paper we investigate in the large-$N_c$ limit ($N_c$ is the number of colored quarks) the phase structure of a massless (1+1)-dimensional quark model with four-quark interaction and in the presence of baryon ($μ_B$), isospin ($μ_I$) and chiral isospin ($μ_{I5}$) chemical potentials as well as at nonzero temperature. It is established that chiral isospin chemical potential leads to the generation of charged pion condensation (PC) in dense (nonzero baryon density) and chiral asymmetric quark matter for a wide range of isospin densities. It is shown that there exists a duality corresponde…
The weak decay of the kaon to two pions is studied within the NJL Model. Using the standard effective weak Hamiltonian, both the decay amplitude arising from an intermediate state σ-meson and the direct decay amplitude are calculated. The effect of final state interactions is also included. When the matching scale is chosen such that the decay amplitude with isospin I=2 is close to its experimental value, the σ-meson contributes more than 85% of the total I=0 amplitude. This supports recent suggestions that the σ-meson should play a vital role in explaining the ΔI= 1/2 rule in this system.
In this paper the phase structure of the dense quark matter has been investigated in the presence of baryon $μ_B$, isospin $μ_I$, chiral $μ_{5}$ and chiral isospin $μ_{I5}$ chemical potentials in the framework of Nambu--Jona-Lasinio model. It has been shown that in the large-$N_{c}$ limit ($N_{c}$ is the number of quark colours) there exist three duality correspondences in the model. The first duality is between the chiral symmetry breaking and the charged pion condensation phenomena. And there are two new dualities that hold only for chiral symmetry breaking and charged pion condensation phen…
We investigate the screening masses of neutral pions and sigma mesons in hot and magnetized quark matter in the framework of a two-flavor lattice-improved Nambu-Jona-Lasinio (NJL) model with a magnetic field dependent coupling constant, which is determined by utilizing the results from lattice QCD simulations. Since such model can well reproduce inverse magnetic catalysis (IMC), by comparing with the standard NJL model, we systemically analyze the impacts of IMC on the temperature and magnetic field dependences of the longitudinal and transverse screening masses of the chiral partners, i.e. π^…
The temperature behaviour of the pion width in the hadronic phase is investigated in the framework of the NJL model. The contribution to the width from the pion-pion collision is considered with a scalar sigma-meson as an intermediate state. It is shown that the pion width significantly broadens at $T>0.1$ GeV. Using the two-step iteration method, suggested by Kadanoff and Baym, the pion spectral function in a hot pion gas is calculated at different temperatures.
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