Quark Gluon Condensate, Virtuality and Susceptibility of QCD Vacuum

We study vacuum of QCD in this work.The structure of non-local quark vacuum condensate,values ofvarious local quark and gluon vacuum condensates,quark-gluon mixed vacuum condensate,quark and gluon virtualityin QCD vacuum state,quark dynamical mass and susceptibility of QCD vacuum state to external field are predicted byuse of the solutions of Dyson Schwinger equations in'rainbow'approximation with a modeling gluon propagator andthree different sets of quark-quark interaction parameters.Our theoretical predictions are in good agreement with thecorrespondent empirical values used widely in literature,and many other theoretical calculations.The quark propagatorand self-energy functions are also obtained from the numerical solutions of Dyson-Schwinger equations.This work iscentrally important for studying non-perturbative QCD,and has many important applications both in particle andnuclear physics.

Tensor Susceptibilities of QCD Vacuum and Parameterized Quark Propagator

Based on the parameterized fully dressed quark propagator proposed by us, the tensor susceptibilities of QCD vacuum and quark vacuum condensates are investigated. Our predicted values of the tensor susceptibilities are in agreement with those predicted by many other theoretical models with QCD feature. The results also show that the tensor susceptibility of QCD vacuum strongly depends on flavor of quark but not sensitive to variation of quark vacuum condensates. However, the quark vacuum condensate is very sensitive to the change of cut-off-parameter μ^2 of the integration, that is, it depends on the separation point of perturbative and non-perturbative QCD region. The successful predictions clearly indicate the extensive validity of our parameterized fully dressed quark propagator used here.

Susceptibilities of QCD Vacuum from Renormalized Dyson-Schwinger Equations]

The pion and tensor vacuum susceptibilities are calculated in the framework of the renormalizable DysonSchwinger equations. A comparison with the results of other nonperturbative QCD approaches is given.

Dynamical Model of QCD Vacuum and Quark Confinement

The phase transition of a simple local gauge model is investigated in terms of the Nambu–Jona-Lasinio mechanism and it is pointed out that the physical vacuum of QCD is bound state of quark-antiquark pairs which can be viewed, generally, as a nearly perfect color dia-electric medium. An important relation between the vacuum expectation value of gauge fields and scalar fields is also derived by solving the Euler equation for the gauge fields. Based on this relation the gauge potential is given which can be used to explain the asymptotic behavior and confinement of quarks in a hadron, and at the same time the Yukawa potential of strong interaction can be given too.

The Pionic Deuterium and the Pion Tetrahedron Vacuum Polarization

A double-well potential model is proposed for the pionic deuterium that enables to calculate the energy split, the potential barrier height and estimate the pion tetrahedron edge length. We propose that pion tetrahedrons, πTd = ud~dũ, play a central role in the Yukawa interaction by enabling quark exchange reactions between protons and neutrons by tunneling through a potential barrier. A vacuum polarization Feynman diagram is proposed for the πTd having chains of fermion loops for the two valence quarks and anti-quarks connected by gluons. With a higher order vacuum polarization diagram, the d and u quark loops are interleaved and the chiral symmetry is broken dynamically. The proposed πTd vacuum polarization integral does not diverge in both the IR and UV limits and vanishes in the limit of an infinite pion tetrahedron condensate. We propose a new Delbruck scattering Feynman diagram that includes d and u quark and anti-quark interleaved loops. We further propose that conversion of gravitons to photons may occur via quark and anti-quark loops that describe the pion tetrahedrons dynamics in the vacuum and may also transfer gravitational waves.

The QCD Ground State Chiral Tetrahedron Symmetry

We propose that the exotic meson tetraquark ud~dũintroduced in previous papers, may be a pseudo-Goldstone boson having a tetrahedron geometry and symmetry. The transition from the neutral pion superposition of two free mesons, dd~ and uũ, to the tetrahedron geometry with optional two chiral states may be the symmetry breaking of the QCD ground state. The ud~dũtetrahedron mass may be calculated by measuring the β decay rate variability. We assume that electrons and positrons are composite particle exotic tetraquarks, dũdd~ for the electrons and ud~dd~ for the positrons and confined by the strong force. We propose that the QCD tetrahedrons play a central role in electron pairing mechanism in both chemical bond forming and superconductor Cooper pairs. We propose a hypothesis where the QCD ground state tetrahedrons play a central role in low energy physics where quark exchange reactions between particles and the QCD tetrahedrons via gluon junctions transfer all the forces. The QCD ground state ud~dũtetrahedrons hypothesis provides a symmetry breaking and a mass gap may be created by the ground state QCD tetrahedrons Bose-Einstein condensate.

Virtualities of quark and gluon in QCD vacuum

The non-local vacuum condensates of quantum chromodynamics (QCD) describe the distributions of quarks and gluons in the non-perturbative QCD vacuum state. Physically, this means that vacuum quarks and gluons have a nonzero mean-squared momentum in the vacuum, called virtuality. The quark virtuality is given by the ratio of the local quark-gluon mixed vacuum condensate to the quark local vacuum condensate. The gluon virtuality is expressed by gluon vacuum condensates and four-quark vacuum condensates. We study the two virtualities by solving Dyson-Schwinger Equations and calculating quark and gluon vacuum condensates. Our theoretical results for quark virtuality are in good agreement with many other theoretical model predictions such as QCD sum rules and lattice QCD calculations. Our calculation on gluon virtuality is initial and the results are quite interesting.

Evidence for False Vacuum States inside the Cores of Massive Pulsars and the Ramification on the Measurements of Their True Masses

Based on the theory and observations of glitching pulsars, we show that the ultra-cold supranuclear dense matter inside the cores of massive pulsars should condensate in vacua, as predicated by non-perturbative QCD. The trapped matter here forms false vacuums embedded in flat spacetimes and completely disconnected from the outside world. Although the vacuum expectation value here vanishes, the masses and sizes of these incompressible superfluid cores are set to grow with cosmic times, in accord with the Onsager-Feynman superfluidity analysis. We apply our scenario to several well-studied pulsars, namely the Crab, Vela, PSR J0740+6620 and find that the trapped mass-contents in their cores read {0.15,0.55,0.64}, implying that their true masses are {1.55,2.35,2.72} , respectively. Based thereon, we conclude that: 1) The true masses of massive pulsars and neutron stars are much higher than detected by direct observations and, therefore, are unbounded from above, 2) The remnant of the merger event in GW170817 should be a massive NS harbouring a core with 1.66 .

Non-Uniform Pion Tetrahedron Aether and Electron Tetrahedron Model

We propose that the QCD vacuum pion tetrahedron condensate density vary in space and drops to extremely low values in the Kennan, Barger and Cowie (KBC) void in analogy to earth’s atmospheric density drop with elevation from earth. We propose a formula for the gravitation acceleration based on the non-uniform pion tetrahedron condensate. Gravity may be due to the underlying microscopic attraction between quarks and antiquarks, which are part of the vacuum pion tetrahedron condensate. We propose an electron tetrahedron model, where electrons are comprised of tetraquark tetrahedrons, and . The quarks determine the negative electron charge and the or quarks determine the electron two spin states. The electron tetrahedron may perform a high frequency quark exchange reactions with the pion tetrahedron condensate by tunneling through the condensation gap creating a delocalized electron cloud with a fixed spin. The pion tetrahedron may act as a QCD glue bonding electron pairs in atoms and molecules and protons to neutrons in the nuclei. Conservation of valence quarks and antiquarks is proposed.

QCD真空凝聚和参数化的夸克传播子

基于整体色对称模型,用完全穿衣服参数化的夸克传播子研究了量子色动力学(QCD)真空的性质,预言了各种表征QCD真空的凝聚值。其结果与其他唯象QCD理论模型的预言是一致的。结果清楚地表明了参数化的夸克传播子是成功和可靠的。讨论了计算QCD真空凝聚值时积分截断参数的问题,提出了一个避免计算的结果对截断参数强烈依赖的物理方法。

Non-perturbative Aspects of QCD and Parameterized Quark Propagator

Based on the Global Color Symmetry Model, the non-perturbative Q, CD vacuum is investigated in the parameterized fully dressed quark propagator. Our theoretical predictions for various quantities characterized the QCD vacuum are in agreement with those predicted by many other phenomenologieal QCD inspired models. The successful predictions clearly indicate the extensive validity of our parameterized quark propagator used here. A detailed discussion on the arbitrariness in determining the integration cut-off parameter ofμ in calculating QCD vacuum condensates and a good method, which avoided the dependence of calculating results on the cut-off parameter is also strongly recommended to readers.

强子内部激发和QCD真空在核热力学行为上的效应

对于非常高的温度,基于一个混合相模型,研究了强子的内部激发和QCD真空在核子系统的热力学行为上的效应。结果表明这两个效应带来了一个合理的相变图象,它重大地改变了系统的热力学行为。

重夸克偶素中的非微扰QCD效应(英文)

在势模型的框架下，通过粲夸克偶素及底夸克偶素能谱的计算，研究了由高维夸克胶子凝聚描述的非微扰ＱＣＤ效应结果表明：六维算符真空凝聚仍有明显的贡献；单圈微扰修正在散射和湮灭过程中的贡献几乎相同。

A New Theory Exploring the Internal Structure of Quarks

This paper introduces a novel theoretical model that reimagines the internal structure of quarks as superfluid vortices formed during the Quark Epoch of the Big Bang. The proposed theory challenges the traditional view of quarks as point-like entities without internal structure, offering instead a hydrodynamic perspective that aligns with the principles of quantum chromodynamics (QCD). By considering quarks as vortices in a frictionless superfluid vacuum, the model provides new insights into their mass, charge, spin, and interactions. The formalism presented in this work utilizes hydrodynamic principles to model quarks as irrotational circular vortices, calculating key properties such as charge radius, mass, and density. The calculations are grounded in the application of vortex dynamics, including the evaluation of circulation, vorticity, and the balance of forces within the quantum fluid. The resulting quark radius and mass are shown to be consistent with known experimental ranges, providing a strong validation of the vortex-based formalism. The theory also explores the implications of this vortex model on the stability of quarks within protons and neutrons, and how quark-antiquark pairs (mesons) and three-quark structures (baryons) can be understood as interactions between these vortices. Additionally, the model predicts specific quark properties such as charge radius and density, which are consistent with experimental observations and current understandings of subatomic particle physics. Furthermore, this approach elucidates the strong force’s role as an interaction between these vortices, mediated by gluons in the quantum fluid. The proposed model not only aligns with existing experimental data but also paves the way for further exploration into the complex behaviors of quarks and their role in the fundamental structure of matter.

Prediction of Cosmological Constant Λ in Veneziano Ghost Theory of QCD

Based on the Veneziano ghost theory of QCD, we estimate the cosmological constant Λ, which is related to the vacuum energy density, , by =8πG . In the recent Veneziano ghost theory is given by the absolute value of the product of the local quark condensate and quark current mass: =(2NfH/m)*c|mq<0|:qq:|0>|.By solving Dyson-Schwinger Equations for a dressed quark propagator, we found the local quark condensate;-(235 MeV)3, the generally accepted value. The quark current mass is mq 4.0 Mev. This gives the same result for as found by previous authors, which is somewhat larger than the observed value. However, when we make use of the nonlocal quark condensate, =g(x), with g(x) estimated from our previous work, we find Λ is in a good agreement with the observations.

非定域夸克真空的结构和Kisslinger函数

夸克的真空凝聚是量子色动力学(QCD)研究中一个非常重要的问题。用完全穿衣服的夸克传播子研究了QCD真空性质和夸克的真空结构。计算了定域夸克的真空凝聚值,预言了夸克的真空结构。其结果与文献中的经验值相符合,也与Dyson-Schwinger方程解一致。说明参数化的夸克传播子是成功和可靠的。

Does There Exist Only One Solution of the Dyson-Schwinger Equation for the Quark Propagator in the Case of Non-Zero Current Quark Mass

It is shown on general ground that there exist two qualitatively distinct solutions of the Dyson-Schwinger equation for the quark propagator in the case of non-zero current quark mass. One solution corresponds to the “Nambu- Goldstone” phase and the other one corresponds to the “Wigner” phase in the chiral limit.

Modified Approach for Calculating Four-Quark Condensates

By differentiating the dressed quark propagator with respect to a variable background field, the linear response of the dressed quark propagator in the presence of the background field can be obtained. From this general method, using the vector background tield as an illustration, we extract a general formula for the four-quark condensate （0： q（0）γμq（0）q（0）γμq（0） ： ｜0）. This formula contains the corresponding fully dressed vector vertex. We use this formula to analyze the factorization problem of the four-quark condensate and show that in the bare vertex approximation factorization holds exactly.

Vacuum condensates of QCD

We study the properties of QCD vacuum state in this paper. The values of various local quark vacuum condensates, quark-gluon mixed vacuum condensates, and the structure of non-local quark vacuum condensate are predicted by the solution of Dyson-Schwinger Equations in ＂rainbow＂ approximation with three sets of different parameters for effective gluon propagator. The light quark virtuality is also obtained in a consistent way. Our all theoretical results here are in good agreement with the empirical values used widely in literature and many other theoretical calculations.

Linear Chemical Potential Dependence of Two-Quark Condensate

By differentiating the inverse dressed quark propagator at finite chemical potential μ with respect to μ, the linear response of the dressed quark propagato r to the chemical potential can be obtained, From this we extract a modelindependent formula for the linear chemical potential dependence of the in-medium two-quark condensate and show by two independent methods （explicit calculation and Lorentz covariance arguments） that the first-order contribution in μ to the in-medium two-quark condensate vanishes identically. Therefore if one wants to study the in-medium two-quark condensate one should expand to at/east the second order in the chemical potential μ.