Reinhard Alkofer
Some of the difficulties arising when one tries to understand confinement as well as dynamical and anomalous chiral symmetry breaking are reviewed. Criteria to be fulfilled by a successful and complete picture of these phenomena are presented, and a few of the suggested explanations are listed.
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We study confinement and chiral symmetry breaking phase transitions for QCD and supersymmetric QCD. The method is based on some justified assumption regarding the behavior of the Green function relevant for the potential between two charges or a gap equation. We determine the number of flavors at which the transitions to confinement and chiral symmetry breaking take place. We find that whereas for chiral symmetry breaking the results are in perfect agreement with those in the literature for confinement the situation is more complex.
We discuss how saturation of unitarity would change phase structure of hadronic matter at very high temperatures emphasizing the role of the vacuum state with spontaneously broken chiral symmetry.
We give a brief overview of the problem of quark confinement in hadronic physics, and outline a few of the suggested explanations of the confining force.
Gribov's scenario of confinement caused by supercritical charges is described and the present status of Gribov's equation for the Green function of light quarks is discussed.
Spontaneous chiral symmetry breaking is accepted to occur in low energy hadronic physics, resulting in the several successful theorems of PCAC. On the other hand scalar confinement is suggested both by the spectroscopy of hadrons and by the string picture of confinement. However these two evidences are apparently conflicting, because chiral symmetry breaking requires a chiral invariant coupling to the quarks, say a vector coupling like in QCD. Here we reformulate the coupling of the quarks to the string, and we are able to comply with chiral symmetry breaking, using scalar confinement. The res…
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We study the phase diagram of QCD with the help of order parameters for chiral symmetry breaking and quark confinement. We also introduce a new order parameter for the confinement phase transition, which is related to the quark density. It is easily accessible by different theoretical approaches, such as functional approaches or lattice simulations. Its relation to the Polyakov loop expectation value is discussed and the QCD phase diagram is analysed. Our results suggest a close relation between the chiral and the confinement phase transition.
In the physical vacuum of QCD, the energy density of light-quark fields strongly coupled to slowly varying gluon fields can be negative, and so a condensate of pairs of quarks and antiquarks of nearly opposite momenta forms which breaks chiral symmetry, confines quarks, and makes gluons massive.
We illustrate why color deconfines when chiral symmetry is restored in gauge theories with quarks in the fundamental representation, and while these transitions do not need to coincide when quarks are in the adjoint representation, entanglement between them is still present.
The Lorentz nature of confinement in a heavy-light quarkonium is investigated. It is demonstrated that an effective scalar interaction is generated selfconsistently as a result of chiral symmetry breaking, and this effective scalar interaction is responsible for the QCD string formation between the quark and the antiquark.
The main features of QCD, e.g. confinement, chiral symmetry breaking, Regge trajectories are naturally and economically explained in the framework of the Field Correlator Method (FCM). The same method correctly predicts the spectrum of hybrids and glueballs. When applied to DIS and high-energy scattering it leads to the important role of higher Fock components in the Fock tower of moving hadron, containing primarily gluonic excitations.
The effective quark Lagrangian is derived from the QCD action by means of averaging over the vacuum fields. In the limit of large N_c and keeping for simplicity the lowest order gluonic correlator one obtains nonlinear equations for the quark propagator, exhibiting scalar confinement. Connection to the quark zero mode density is discussed.
We construct an effective model for the chiral field and the Polyakov loop in which we can investigate the interplay between the approximate chiral symmetry restoration and the deconfinement of color in a thermal SU(3) gauge theory with three flavors of massive quarks. The phenomenological couplings between these two sectors can then be related to the recent lattice data on the renormalized Polyakov loop and the chiral condensate close to the critical region.
We study the QCD phase diagram, in particular we study the critical points of the two main QCD phase transitions, confinement and chiral symmetry breaking. Confinement drives chiral symmetry breaking, and, due to the finite quark mass, at small density both transitions are a crossover, while they are a first or second order phase transition in large density. We study the QCD phase diagram with a quark potential model including both confinement and chiral symmetry. This formalism, in the Coulomb gauge hamiltonian formalism of QCD, is presently the only one able to microscopically include both a…
Schwinger-Dyson equations: Dynamical Chiral Symmetry Breaking and Confinement
本文对Schwinger-Dyson方程（QCD）的非微扰研究作了一个有代表性但不完全的评述。主要的焦点是夸克自能的研究，但胶子传播子和夸克-胶子顶点的研究也被讨论，因为它们对夸克自能很重要。本文的范围是应用这些方程研究动力学手征对称性破缺、夸克禁闭以及QCD的谱和动力学唯象。
Without any analytical assumption we solve the ladder QED2+1 in Minkowski space. Further, we transform Greens functions to the Temporal Euclidean space, wherein we show that in the special case of ladder QED2+1 the solution is fully equivalent to the Minkowski one. The obtained complex fermion propagator exhibits confinement because of the lack of the pole at the real timelike $q^2$ axis.
The critical behavior of non-order parameter fields is discussed. We show that relevant features of the deconfining phase transition can be determined by monitoring universal properties induced by the order parameter on the physical excitations. Some of the behaviors we uncover are already supported by lattice results.
We construct a self-consistent holographic QCD model which can realize two most important phenomena of QCD, i.e. chiral symmetry breaking and confinement. The model is formulated in the framework of graviton-dilaton-scalar system, where the dilaton field is of dimension-2 which might be dual to the dimension-2 gluon condensate and can lead to the linear confinement, while the scalar field corresponds to the quark anti-quark condensate and can explain the property of chiral dynamics. Within this framework, both Regge spectra of hadrons and the linear potential between quarks can be accommodated…
Hadron Production Ratios as Probes of Confinement and Freeze-Out
在热模型中分析了200 GeV/A能量中心S-A碰撞中的粒子产生。目前的数据表明，奇异粒子在比非奇异粒子更高的温度下冻结，并且奇异度饱和是不完全的。
Dual Ginzburg-Landau Theory for Quark Confinement and Dynamical Chiral-Symmetry Breaking
本文用对偶Ginzburg-Landau（DGL）理论研究了QCD的非微扰性质。在QCD-10凝聚真空中出现了线性夸克势。我们发现QCD凝聚对动力学手征对称性破缺起着至关重要的作用。我们还研究了有限温度下DGL理论中的QCD相变。
The standard chiral perturbation theory is known to predict much weaker effects in magnetic field, than found in numerical lattice data. To overcome this disagreement we are using the effective chiral confinement Lagrangian, $L_{ECCL}$, containing both chiral and quark degrees of freedom, in the presence of external magnetic field. Without magnetic fields $L_{ECCL}$ reduces to the ordinary chiral Lagrangian $L_{EC L}$, yielding in the lowest order $O(\partial_μφ)^2$ all known relations, and providing explicit numerical coefficients in the higher $O(p^4, p^6)$ orders. The inclusion of the magne…
We introduce a kinetical description of the hadronization of semi-deconfined quark matter produced in heavy ion collisions. A minimal microscopic model is considered in which the produced quarks and anti-quarks are redistributed into hadrons according to the additive quark model. Assuming thermalized quark matter and hadron matter we determine the appropriate parameters to describe the properties of both matter before and after hadronization. We find an adiabatic hadronization.
Production rates of dileptons and photons from the quark-gluon (QGP) phase are calculated taking into account effects of confinement and spontaneous chiral symmetry breaking (χSB) not far from the transition temperature $T_c$. We find that the production rates of dileptons with large momenta and of photons originating from the QGP around $T_c$ are suppressed by the χSB effect. We also discuss to what extent information about details of the chiral transition, such as its characteristic temperature range and the steepness of the crossover, are reflected in these quantities.
Using the effective potential formalism, we study dynamical chiral symmetry breaking (D$χ$SB) in the dual Ginzburg-Landau (DGL) theory, where the color confinement is brought by monopole condensation. The effective potential as a function of infrared quark mass is found to have double-well structure, which leads to spontaneous breaking of chiral symmetry. To examine the role of confinement, we divide the effective potential into the confinement part and others, which correspond to the confinement term and other (Yukawa, Coulomb) terms of the gluon propagator in the DGL theory. It is found that…
We address the old difficulty in accommodating the scalar quark-antiquark confining potential together with chiral symmetry breaking. We develop a quark confining potential inspired in the QCD scalar flux tube. The coupling to quarks consists in a double vector vertex. We study the Dirac and spin structure of this potential. In the limit of massless quarks the quark vertex is vector. Nevertheless symmetry breaking generates a new scalar quark vertex. In the heavy quark limit the coupling is mostly scalar. We solve the mass gap equation and find that this potential produces spontaneous chiral s…
Chiral dynamics is investigated using the chiral confining Lagrangian (CCL), previously derived from QCD with confinement interaction. Based on the calculations of the quark condensate, which is defined entirely by confinement in the zero quark mass limit, one can assert that chiral symmetry breaking occurs not spontaneously but is predetermined by confinement. The expansion of the CCL provides the GMOR relations and the effective chiral Lagrangian, which is used to provide the masses and decay constants of all chiral mesons, including $η,η'$. For the latter one needs to define a non-chiral co…
Spontaneous Breaking of Chiral Symmetry as a Consequence of Confinement
我们表明，在大- $N$展开中的主导阶，格点量子色动力学激发的大距离线性上升限制势导致非局域四夸克相互作用，实现自发破缺的手征对称性（SBCS），以同样的方式Nambu-Jona-Lasinio模型。动力学夸克质量$m$代表了带隙方程的解，它与弦张力$σ$的平方根成正比，并且在大- $N$展开式$m=2 \sqrtσ/π$中的首阶处具有$σ=0.27$ GeV $^2$的形式。Nambu-Jona-Lasinio唯象常数$G_1$是导致SBCS的主要因素，它用弦的张力和约束半径来表示。
An effective Lagrangian for the light quark in the field of a static source is derived systematically using the exact field correlator expansion. The lowest Gaussian term is bosonized using nonlocal colorless bosonic fields and a general structure of effective chiral Lagrangian is obtained containing all set of fields. The new and crucial result is that the condensation of scalar isoscalar field which is a usual onset of chiral symmetry breaking and is constant in space-time, assumes here the form of the confining string and contributes to the confining potential, while the rest bosonic fields…
Without any analytical assumption we solve the ladder QED2+1 in Minkowski space. Obtained complex fermion propagator exhibits confinement in the sense that it has no pole. Further, we transform Greens functions to the Temporal Euclidean space, wherein we show that in the special case of ladder QED2+1 the solution is fully equivalent to the Minkowski one. Obvious invalidity of Wick rotation is briefly discussed. The infrared value of the dynamical mass is compared with other known approaches, e.g. with the standard Euclidean calculation.
Dyons in QCD: Confinement and Chiral Symmetry Breaking
讨论了$SU(2)$胶子动力学的双子经典解.给出了不同规范下双子解的精确形式，解决了双子稀气体组成的非平凡问题。经典的（反）双子之间的相互作用被认为是解析和数值。结合个别双子解的拓扑性质讨论了双子气体中的禁闭。给出了双子气体的费米零模，并证明了双子气体的手征对称性破缺。
We discuss how the inclusion of singular gauge fields in the partition function for QCD can lead to a domain-like picture for the QCD vacuum by virtue of specific conditions on quantum fluctuations at the singularities. With a simplified model of hyperspherical domain regions with interiors of constant field strength we calculate the basic parameters of the QCD vacuum, the gluon condensate, topological susceptibility, string constant and quark condensate, and briefly discuss confinement of dynamical quarks and gluons.
The effective chiral Lagrangian in both nonlocal form $L_{ECCL}$ and standard local form $L_{ECL}$ are derived in QCD using the confining kernel, obtained in the vacuum correlator formalism. As a result all coefficients of $L_{ECL}$ can be computed via $q\bar q$ Green's functions. In the $p^2$ order of $L_{ECL}$ one obtains GOR relations and quark decay constants $f_a$ are calculated $a=1,...8$, while in the $p^4$ order the coefficients $L_1, L_2, L_3,L_4, L_5, L_6$ are obtained in good agreement with the values given by data. The chiral quark model is shown to be a simple consequence of $L_{E…
We study the correlation between confinement and dynamical chiral-symmetry breaking (D$χ$SB) in the dual Ginzburg-Landau (DGL) theory using the effective potential formalism. The DGL theory is an infrared effective theory based on the dual Higgs mechanism, and provides the nonperturbative gluon propagator, which leads to the linear quark potential. The screening effect for the confining potential can be obtained by introducing the infrared cutoff corresponding to the hadron size. We formulate the effective potential for D$χ$SB in the DGL theory, and find the vacuum instability against quark co…
An overview of some issues discussed is given, including the following ones: (i) the mechanism of confinement, (ii) the structure of the string, (iii) non-perturbative glue in vacuum and hadrons, and (v) quark-hadron duality. In doing so I try to indicate issues important for JLab. Finally I discuss another issue debated during this conference, namely (vi) whether one can use some common effective potential for description of various hadrons, using heavy quarkonia as an example.
Assuming a Gaussian approximation for the QCD gluodynamics, all the nonperturbative physics can be encoded into two parameters: the gluon correlation length $T_g$ and the gluon condensate $G_2$. These parameters are sufficient in order to describe the heavy-heavy quark nonperturbative interaction. In this work we adopt the same framework in order to study heavy-light bound states in the non-recoil limit. Spontaneous chiral symmetry breaking and a confining chiral non-invariant interaction emerge quite naturally. The gap equation is solved and discussed. In particular a relation between the lig…
This work presents a new phenomenological description of QCD vacuum where the color background field is depicted by a constant parallel vector with amplitude proportional to $σ\sim 0.28 GeV^2$. The familiar Regge relation can be derived directly in a classic meaning. A new mass formula of hadrons are conjectured to give a very consistent description of hadron mass spectra. The lower bounds of the baryon mass are determined to be $\sqrt{3σ}$ for nucleon and $\sqrt{5σ}$ for isospin-3/2 baryon. In the meanwhile, the mass-square differences of $1 {}^3 S_1$ and $1 {}^1 S_0$ meson states are obtaine…
The scalar confinement in QCD is shown to produce the nonzero quark condensate for any current quark mass. Mechanisms for the Chiral Symmetry breaking and for the nonzero quark condensates are revealed. For the light and strange flavors the condensates are essentially chiral (proportional to (string tension)$^{3/2}$). The expressions for the quark condensates are obtained as a sum over non-chiral meson states, and, using the operator product expansion, as an explicit expression that involves the confining string tension and the current quark mass. The numerical results are fairly close to the …
Singular gauge fields in the partition function for QCD can lead to a domain-like picture for the QCD vacuum by virtue of constraints on quantum fluctuations at the singularities. With a simple model of hyperspherical domains with interiors of constant field strength we show that the main features of gluon condensation and an area law for static quarks can be realised.The Dirac operator in such a background is exactly soluble. Chirality properties of the solutions show agreement with recent lattice results.
We address the question of the Lorentz nature of the effective interquark interaction in QCD which leads to the formation of the QCD string between colour charges. In particular, we start from a manifestly vectorial fundamental interaction mediated by gluons and demonstrate that, as soon as chiral symmetry is broken spontaneously, the effective interquark interaction acquires a selfconsistently generated scalar part which is eventually responsible for the formation of the QCD string. We demonstrate this explicitly for a heavy-light quarkonium, using the approach of the Schwinger-Dyson-type equ…
Two models which generate the supersymmetric Grand Unification Scale from the strong dynamics of an additional gauge group are presented. The particle content is chosen such that this group confines with chiral symmetry breaking. Fields that are usually introduced to break the Grand Unified group appear instead as composite degrees of freedom and can acquire vacuum expectation values due to the confining dynamics. The models implement known solutions to the doublet-triplet splitting problem. The SO(10) model only requires one higher dimensional representation, an adjoint. The dangerous coloure…
In this paper the spectrum of quark-antiquark systems, including light mesons and tachyons, is studied in the true vacuum and in the chiral invariant vacuum. The mass gap equation for the vacua and the Salpeter-RPA equation for the mesons are solved for a simple chiral invariant and confining quark model. At T=0 and in the true vacuum, the scalar and pseudoscalar, or the vector and axial vector are not degenerate, and in the chiral limit, the pseudoscalar groundstates are Goldstone bosons. At T=0 the chiral invariant vacuum is an unstable vacuum, decaying through an infinite number of scalar a…
The Polyakov loop is the appropriate deconfinement order parameter for Yang-Mills theories without quarks or with quarks in the adjoint representation of the gauge group. However it is not a physical state of the theory so the information regarding the center group symmetry must be transferred to the physical states. We briefly review how this transfer of information takes place. When adding quarks the center group is no longer a symmetry for matter in the fundamental representation. This feature allows us to explain why color deconfines when chiral symmetry is restored in hot gauge theories w…
A description of the Roper using the chiral chromodielectric model is presented and the transverse $A_{1/2}$ and the scalar $S_{1/2}$ helicity amplitudes for the electromagnetic Nucleon--Roper transition are obtained for small and moderate $Q^2$. The sign of the amplitudes is correct but the model predictions underestimate the data at the photon point. Our results do not indicate a change of sign in any amplitudes up to $Q^2\sim1$ GeV$^2$. The contribution of the scalar meson excitations to the Roper electroproduction is taken into account but it turns out to be small in comparison with the qu…
Employing functional approaches the infrared behaviour of Landau gauge QCD vertex functions is investigated. Results for the ghost-gluon, three-gluon and quark-gluon vertex functions are presented. As can be analytically shown a linear rising potential between heavy quarks is generated by infrared singularities in the dressed quark-gluon vertex. The selfconsistent mechanism that generates these singularities implies the existence of scalar Dirac amplitudes of the full vertex and the quark propagator. These amplitudes can only be present when chiral symmetry is broken, either explicitly or dyna…
Properties of chiral Born-Infeld Theory proposed as the model for shock-wave fireball production in the hadron-hadron collisions was studied. The role of the shock-waves in the multi-particle production was discussed.
A qualitative mechanism for the emergence of domain structured background gluon fields due to singularities in gauge field configurations is considered, and a model displaying a type of mean field approximation to the QCD partition function based on this mechanism is formulated. Estimation of the vacuum parameters (gluon condensate, topological susceptibility, string constant and quark condensate) indicates that domain-like structures lead to an area law for the Wilson loop, nonzero topological susceptibility and spontaneous breakdown of chiral symmetry. Gluon and ghost propagators in the pres…
Gribov Confinement and Chiral Perturbation Theory
我讨论了Gribov的禁闭理论的手征动力学。在临界耦合$α_s^c$下，轻夸克真空经历了一系列相变，这些相变在手征微扰理论的应用中应予以考虑。Gribov理论提供了一个简单的解释的值的π核子σ项，而不需要调用一个大的奇怪的夸克成分的核子。
Two crucial properties of QCD, confinement and chiral symmetry breaking, cannot be understood within the context of conventional Feynman perturbation theory. Non-perturbative phenomena enter the theory in a fundamental way at both the classical and quantum level. Over the years a coherent qualitative picture of the interplay between chiral symmetry, quantum mechanical anomalies, and the lattice has emerged and is reviewed here.
Chiral symmetry and many-body nonleptonic decays of heavy hadrons
我们认为，类似于手征有效拉格朗日量最近在涉及Goldstone玻色子的重强子半轻子衰变中的许多应用，手征对称性也可以应用于重强子的多体非轻子衰变。作为例子，我们建立了底强子典型多体非轻子衰变的手征有效哈密顿量。我们讨论的最低阶的贡献来自这样的哈密顿量。我们强调，这种方法的广泛应用是可能的。
An approach to QCD vacuum as a medium describable in terms of statistical ensemble of almost everywhere homogeneous Abelian (anti-)self-dual gluon fields is reviewed. These fields play the role of the confining medium for color charged fields as well as underline the mechanism of realization of chiral $SU_{\mathrm L}(N_f)\times SU_{\mathrm R}(N_f)$ and $U_{\mathrm A}(1)$ symmetries. Hadronization formalism based on this ensemble leads to manifestly defined quantum effective meson action. Strong, electromagnetic and weak interactions of mesons are represented in the action in terms of nonlocal …
I give a summary of Section E of the sixth edition of the Conference "Quark confinement and the hadron spectrum". Papers were presented on different subjects, from spectroscopy, including pentaquarks and hadron structure, to new physics effects (non commutative field theories, supersymmetry and extra dimensions) and the problem of color confinement, both in ordinary Yang-Mills models and in supersymmetric Yang-Mills.
A self-consistent holographic QCD model is proposed which can realize both chiral symmetry breaking and confinement, two most important phenomena of QCD. It is pointed out that the model can accommodate both Regge spectra of hadrons and the linear potential between quarks. The model is formulated in the framework of graviton-dilaton-scalar system, where the dilaton field is dual to the dimension-2 gluon condensate and can lead to the linear confinement, while the scalar field corresponds to the quark anti-quark condensate and can explain the property of chiral dynamics.
We discuss HERA data on the high energy behavior of the total gamma*p cross section and on diffraction in deep inelastic scattering. We outline their novelty in comparison with diffraction in high energy hadron hadron scattering. As a physical picture, we propose an interpretation in terms of QCD radiation at small and large distances: a careful study of the transition between the two extremes represents a new approach to the QCD confinement problem.
Inhomogeneous confinement and chiral symmetry breaking induced by imaginary angular velocity
本文研究虚转动下高温夸克-胶子物质，发现超过阈值虚角速度时出现非均匀禁闭，并确认在微扰禁闭相中发生自发手征对称性破缺。
We remind the chiral doubling scenario [1,2] for hadrons built of heavy and light quarks. Then we recall arguments why new states D_s(2317),D_s(2460),D_0(2308) and D_1^'(2427) should be viewed as chiral partners of D_s,D_s^*,D and D^*,respectively. We summarize with the list of predictions based on chiral doubling scenario for other heavy-light hadrons.
We analytically study the relation between quark confinement and spontaneous chiral-symmetry breaking in QCD. In terms of the Dirac eigenmodes, we derive some formulae for the Polyakov loop, its fluctuations, and the string tension from the Wilson loop. We also investigate the Polyakov loop in terms of the eigenmodes of the Wilson, the clover and the domain wall fermion kernels, respectively. For the confinement quantities, the low-lying Dirac/fermion eigenmodes are found to give negligible contribution, while they are essential for chiral symmetry breaking. These relations indicate no direct …
Color Confinement, Quark Pair Creation and Dynamical Chiral-Symmetry Breaking in the Dual Ginzburg-Landau Theory
我们利用对偶Ginzburg-Landau理论研究了非微扰QCD的色禁闭、$q$ - $\bar q$对的产生和动力学手征对称性破缺，其中QCD-手征凝聚对红外区的非微扰动力学起着至关重要的作用.由于双迈斯纳效应的存在，在猝灭近似下，在长距离范围内得到了表征夸克禁闭的线性静态夸克势。我们得到了类似于超导物理中单位长度涡旋能量的弦张力的简单表达式。本文从$q$ - $\bar q$对的产生或强子弦的切割所引起的红外屏蔽效应出发，研究了轻夸克对夸克禁闭势的动力学效应。通过使用用于$q$ - $\bar q$对产生的Schwinger公式来估计电势的屏蔽长度。我们在胶子传播子中的强长程关联因子中引入相应的红外截止作为轻夸克的动力学效应，得到了一个包含屏蔽效应的红外区夸克势的紧致公式.我们利用Schwinger-Dyson方程研究了动力学手征对称性破缺，其中胶子传播子包含与
We demonstrate that $SO(N_{c})$ gauge theories with matter fields in the vector representation confine due to monopole condensation and break the $SU(N_{F})$ chiral symmetry to $SO(N_{F})$ via the quark bilinear. Our results are obtained by perturbing the ${\cal N}=1$ supersymmetric theory with anomaly-mediated supersymmetry breaking.
We study the QCD phase diagram, in particular we study the critical points of the two main QCD phase transitions, confinement and chiral symmetry breaking. Confinement drives chiral symmetry breaking, and, due to the finite quark mass, at small density both transitions are a crossover, while they are a first or second order phase transition in large density. We study the QCD phase diagram with a quark potential model including both confinement and chiral symmetry. This formalism, in the Coulomb gauge hamiltonian formalism of QCD, is presently the only one able to microscopically include both a…
We evaluate the impact of an external magnetic field on the chiral symmetry and confinement-deconfinement transition temperatures by using a vector-vector contact interaction model for quarks regularized so as to include an explicit confining scale in the corresponding gap equation. Exploring the evolution of the chiral condensate and the confining scale with temperature $T$ and magnetic field strength $eB$ ($e$ represents the fundamental electric charge), we determine the pseudo-critical temperatures for the chiral ($T_c^χ$) and deconfinement ($T_c^c$) transitions from their inflection points…
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