Mesons in the Eguchi Kawai model

Fermions in the fundamental representation of theSU(N) gauge group are incorporated into the Eguchi Kawai reduction scheme. The proof for the equivalence of reduced and extended theories is given. This equivalence can be used, to calculate chiral condensate and meson propagators from the fermion matrix of a partially reduced TEK model.     

Spin-motive force and orbital-motive force: from magnon Bose-Einstein condensation to chiral Weyl superfluids

Spin-motive geometric force acting on electrons in metallic ferromagnets is extended to spin-motive force in magnon Bose-Einstein condensate, which is represented by phase-coherent precession of magnetization, and to the orbital-motive force in superfluid ³He-A. In ³He-A there are two contributions to the orbitalmotive force. One of them comes from the chiral nature of this liquid. Another one originates from chiral Weyl fermions living in the vicinity of the topologically protected Weyl points, and is related to the phenomenon of chiral anomaly.     

The first PDF moments for three dynamical flavors in BChPT

We present a calculation of generalized baryon form factors in the framework of three-flavor covariant baryon chiral perturbation theory at leading one-loop order, necessary for the calculation of the first moments of generalized parton distribution functions. The formulae we derive can be used to guide the chiral extrapolation of three-flavor lattice calculations of the corresponding QCD matrix elements.     

Observations on the Wilson fermions in the ϵ regime

We make several observations concerning the low quark mass region with Wilson fermions and how this is connected with the ? regime in the continuum. A transition from tiny cutoff effects to rather large discretization errors would take place in general with Wilson fermions if we lower the quark mass at finite lattice spacing. We argue that these two regions exhibit rather different behaviours concerning the coupling between cutoff effects and zero-modes. We interpolate between these two regimes adding to the continuum ? regime formulae, in the spirit of the Symanzik expansion, the relevant operators parametrising the leading cutoff effects. We compute the partition function, the chiral condensate, scalar and pseudo-scalar correlation functions. The final formulae can be used to fit lattice data to extract physical low energy constants, and to estimate systematic uncertainties coming from discretization errors. Moreover they suggest ways on how to remove these cutoff effects, the core of which are captured by the continuum zero modes.     

Spontaneous chiral-symmetry breaking of lattice QCD with massless dynamical quarks

One of the most challenging issues in QCD is the investigation of spontaneous chiral-symmetry breaking, which is characterized by the non-vanishing chiral condensate when the bare fermion mass is zero. In standard methods of the lattice gauge theory, one has to perform expensive simulations at multiple bare quark masses, and employ some modeled functions to extrapolate the data to the chiral limit. This paper applies the probability distribution function method to computing the chiral condensate in lattice QCD with massless dynamical quarks, without any ambiguous mass extrapolation. The results for staggered quarks indicate that this might be a promising and efficient method for investigating the spontaneous chiral-symmetry breaking in lattice QCD, which deserves further investigation.     

Instanton liquid at a finite density of quark matter

For the case of finite quark and baryon densities, the interaction of light quarks with an instanton liquid is considered in a phase that involves a nonvanishing chiral condensate. The generating functional is considered in the tadpole approximation, and the behavior of the dynamical quark mass and the behavior of the chiral condensate, as well as the behavior of the instanton-liquid (gluon-condensate) density, which grows slightly with the quark chemical potential, are explored. Arguments are presented in favor of the statement that the quark-density threshold for the emergence of a diquark condensate grows sizably owing to interaction with the instanton liquid.     

Discussion of thermodynamic features within the PNJL model

We discuss some thermodynamical features of a QCD system within the two-flavor Polyakov loop extended Nambu–Jona-Lasinio(PNJL) model. Several thermodynamical quantities of interest(pressure, energy density,specific heat, speed of sound, etc.) are investigated and discussed in detail with two different forms of Polyakov loop potential. The effective coupling strength G incorporating a quark feedback(quark condensate) through operator product expansion is also discussed, as well as the relationship between color deconfinement and chiral phase crossover.We find that some thermodynamical quantities have quite different behavior for different Polyakov loop potentials.By changing the characteristic temperature T_0 of the pure Yang-Mills field, we find that when T_0 becomes small,color deconfinement might happen earlier than chiral phase crossover, while their relationship can be determined via some thermodynamical quantities. Furthermore, the behavior of the thermodynamical quantities is quite different in the two different forms of Polyakov loop potential studied. Especially, one of the potentials, specific heat, has two peaks, which correspond to color deconfinement and chiral phase crossover respectively. This interesting phenomenon may shed some light on whether the inflection points of the chiral condensate and deconfinement transitions happen at the same temperature or not for lattice QCD and experimental studies.     

Possible pseudogap phase in QCD

Thermal pion fluctuations, in principle, can completely disorder the phase of quark condensate and thus restore chiral symmetry. If this happens before the quark condensate melts, strongly interacting matter will be in the pseudogap state just above the chiral phase transition. The quark condensate does not vanish locally, and quarks acquire constituent masses in the pseudogap phase, despite the fact that chiral symmetry is restored.     

Meson Effects on the Chiral Condensate at Finite Density

Meson corrections on the chiral condensate up to next-to-leading order in a 1/N_c expansion at finite density are investigated in the NJL model with explicit chiral symmetry breaking. Compared with mean-field results, the chiral phase transition is still of the first order while the properties near the critical density for chiral phase transition are found to change significantly.     

Moments of isovector quark distributions in lattice QCD

We investigate the connection of lattice calculations of moments of isovector parton distributions to the physical regime through extrapolations in the quark mass. We consider the one-pion loop renormalisation of the nucleon matrix elements of the corresponding operators and thereby develop formulae with which to extrapolate the moments of the unpolarised, helicity and transversity distributions. These formulae are consistent with chiral perturbation theory in chiral limit and incorporate the correct heavy-quark limits. In the polarised cases, the inclusion of intermediate states involving the -isobar is found to be very important. The results of our extrapolations are in general agreement with the phenomenological values of these moments where they are known, and for the first time we make reliable predictions for the low moments of the isovector transversity distribution.Received: 30 September 2002, Published online: 22 October 2003PACS: 12.38.Gc Lattice QCD calculations - 11.30.Rd Chiral symmetries     

N_f dependence of the quark condensate from a chiral sum rule

How fast does the quark condensate in QCD-like theories vary as a function of is inferred from real QCD using chiral perturbation theory at order one loop. A sum rule is derived for the single relevant chiral coupling constant, . A model independent lower bound is obtained. The spectral function satisfies a Weinberg-type superconvergence relation. It is discussed how this, together with chiral constraints, allows a solid evaluation of , based on experimental – S-wave T-matrix input. The resulting value of is compatible with a strong dependence possibly suggestive of the proximity of a chiral phase transition. Received: 3 September / Published online: 6 April 2000     

Universality near zero virtuality

In this paper we study a random matrix model with the chiral and flavor structure of the QCD Dirac operator and a temperature dependence given by the lowest Matsubara frequency. Using the supersymmetric method for random matrix theory, we obtain an exact, analytic expression for the average spectral density. In the large-n limit, the spectral density can be obtained from the solution to a cubic equation. This spectral density is nonzero in the vicinity of eigenvalue zero only for temperatures below the critical temperature of this model. Our main result is the demonstration that the microscopic limit of the spectral density is independent of temperature (apart from a temperature dependent scale factor expressed in terms of the chiral condensate) up to the critical temperature. This is due to a number of remarkable cancellations. This result provides strong support for the conjecture that the microscopic spectral density is universal. In our derivation, we emphasize the symmetries of the partition function and show that this universal behavior is closely related to the existence of an invariant saddle-point manifold.     

Do we need to use regularization for the thermal part in the NJL model?

The Nambu–Jona-Lasinio(NJL)model is one of the most useful tools for studying non-perturbative strong interactions in matter.Because it is a nonrenormalizable model,the choice of regularization is a subtle issue.In this paper,we discuss one of the general issues regarding regularization in the NJL model,which is whether we need to use regularization for the thermal part by evaluating the quark chiral condensate and thermal properties in the two-flavor NJL model.The calculations in this work include three regularization schemes that contain both gauge covariant and invariant schemes.We found that,regardless of the regularization scheme we choose,it is necessary to use regularization for the thermal part when calculating physical quantities related to the chiral condensate and to not use regularization for the thermal part when calculating physical quantities related to the grand potential.     

Evading the sign problem in random matrix simulations

We show how the sign problem occurring in dynamical simulations of random matrices at a nonzero chemical potential can be avoided by judiciously combining matrices into subsets. For each subset the sum of fermionic determinants is real and positive such that importance sampling can be used in Monte Carlo simulations. The number of matrices per subset is proportional to the matrix dimension. We measure the chiral condensate and observe that the statistical error is independent of the chemical potential and grows linearly with the matrix dimension, which contrasts strongly with its exponential growth in reweighting methods.     

带有2+1味道Wilson费米子的格点量子色动力学在有限温度、有限密度下的相变

利用格点规范理论研究了带有2＋1味道费米子的量子色动力学在有限密度及温度下的相变问题,研究了去禁闭相变与化学势和裸质量参数之间的依赖关系,并利用有限体积效应分析以及Monte Carlo模拟的演化序列所反映出的特点对相变的类型做了确认,给出了相结构图. 关键词： 格点量子色动力学 相变     

Thermodynamical and Chiral Limit in Computer Simulations of Lattice Quant um Field Theories

The finite-size effects which appear in computer simulations of chiral-symmetry breaking in lattice gauge theory are analyzed. To reduce these systematic errors, a better method for extrapolating the chiral condensate to the infinite volume and chiral limit is proposed.     

有限温下三维QED中费米速度对费米子手征凝聚的影响（英文）

三维QED 具有两个和QCD类似的性质:动力学手征对称破缺和禁闭。为了研究动力学手征对称破缺,基于彩虹近似,在Dyson-Schwinger 方程框架下,通过迭代求解有限温下的费米子自能方程,讨论了不同的费米速度下费米子手征凝聚与费米子味数之间的关系。发现在有限温下,对于固定的费米子味数,费米手征凝聚随费米速度的变大而单调减小。Analogous to Quantum QCD, QED₃ has two interesting features: dynamical chiral symmetry breaking (DCSB) and confinement. By adopting the rainbow approximation, we numerically solve the fermion self-energy equation at finite temperature in the framework of Dyson-Schwinger equations and discuss the relation between chiral condensate and fermion flavor for several fermion velocities in the finite temperature QED₃. It is found that the fermion chiral condensate decreases monotonically with the fermion velocity increasing for a fixed N at finite temperature.     

Chiral symmetry breaking and condensates in the rishon model

The rishon model is studied in the limit g_c → 0, α → 0 when its global flavour symmetry is SU(6) × SU(6) × U(1) analogous to six massless flavour QCD. Recently it was shown that the ad hoc breaking SU(6) × SU(6) → SU(3) × SU(3) allows the anomaly constraint to be satisfied. In this paper this is shown to be but one of several successful patterns of chiral symmetry breaking. The condensates required to perform these breakings are fully discussed. A plausibility argument based on single gauge boson exchange is presented which determines the condensate uniquely to be 〈(v_LV_L)³〉 corresponding to the original breaking above. The same argument applies to QCD, which is argued to differ in its chiral behaviour due to the large intrinsic masses of the quarks. The implications of the above condensate and pattern of chiral symmetry breaking for the rishon model include the prediction of integer charged colour octet fermions, a naive mass formula m_e = 2m_u ? m_d, new insight into the parity-violating condensate 〈(v_Lv_L)²(v_Rv_R)〉 and the prediction of 52 new pseudos whose masses are estimated.