arXiv subjects
Publications and source records attributed to Lei Chang.
We explain a form for the rainbow-ladder kernel whose momentum-dependence is consonant with modern DSE- and lattice-QCD results, and assess its capability as a tool in hadron physics. In every respect tested, this form produces results for observables that are at least equal to the best otherwise obtained in a comparable approach. Moreover, it enables the natural extraction of a monotonic running-coupling and -gluon-mass.
A Dyson-Schwinger equation calculation of the light hadron spectrum, which correlates the masses of meson and baryon ground- and excited-states within a single framework, produces a description of the Roper resonance that corresponds closely with conclusions drawn recently by EBAC. Namely, the Roper is a particular type of radial excitation of the nucleon's dressed-quark core augmented by a material meson cloud component. There are, in addition, some surprises.
A numerical study on interactions of two spherical drops in thermocapillary migration in microgravity is presented. Finite-difference methods were adopted and the interfaces of drops were captured by the front-tracking technique. It is found that the arrangement of drops directly influences their migrations and interaction, and that the motion of one drop is mainly determined by the disturbed temperature field because of the existence of the other drop.
We introduce a method based on the chiral susceptibility, which enables one to draw a phase diagram in the chemical-potential/temperature plane for strongly-interacting quarks whose interactions are described by any reasonable gap equation, even if the diagrammatic content of the quark-gluon vertex is unknown. We locate a critical endpoint (CEP) at (μ^E,T^E) ~ (1.0,0.9)T_c, where T_c is the critical temperature for chiral symmetry restoration at μ=0; and find that a domain of phase coexistence opens at the CEP whose area increases as a confinement length-scale grows.
The maximum entropy method is used to compute the dressed-quark spectral density from the self-consistent numerical solution of a rainbow truncation of QCD's gap equation at temperatures above that for which chiral symmetry is restored. In addition to the normal and plasmino modes, the spectral function also exhibits an essentially nonperturbative zero mode for temperatures extending to 1.4-1.8-times the critical temperature, T_c. In the neighbourhood of T_c, this long-wavelength mode contains the bulk of the spectral strength and so long as this mode persists, the system may fairly be described as a strongly-coupled state of matter.
Perturbation theory predicts that a massless fermion cannot possess a measurable magnetic moment. We explain, however, that the nonperturbative phenomenon of dynamical chiral symmetry breaking generates a momentum-dependent anomalous chromomagnetic moment for dressed light-quarks, which is large at infrared momenta; and demonstrate that consequently these same quarks also possess an anomalous electromagnetic moment with similar magnitude and opposite sign.
We provide a snapshot of recent progress in hadron physics made using QCD's Dyson-Schwinger equations, reviewing the generation of a quark anomalous chromomagnetic moment, which may explain the longstanding puzzle of the $a_1$-$ρ$ mass splitting, and the form of the pion and kaon valence-quark parton distribution functions.
Dynamical chiral symmetry breaking (DCSB) is a remarkably effective mass generating mechanism. It is also, amongst other things, the foundation for a successful application of chiral effective field theories, the origin of constituent-quark masses, and intimately connected with confinement in QCD. Using the Dyson-Schwinger equations (DSEs), we explain the origin and nature of DCSB, and elucidate some of its consequences, e.g.: a model-independent result for the pion susceptibility; the generation of a quark anomalous chromomagnetic moment, which may explain the longstanding puzzle of the a_1-rho mass splitting; its impact on the behaviour of the electromagnetic pion form factor -- thereby illustrating how data can be used to chart the momentum-dependence of the dressed-quark mass function; in the form of the pion and kaon valence-quark parton distribution functions, and the relation between them; and aspects of the neutron's electromagnetic form factors, in particular F_1^u/F_1^d and G_M^n. We argue that in solving QCD, a constructive feedback between theory and extant and forthcoming experiments will most rapidly enable constraints to be placed on the infrared behaviour of QCD's β-function, the nonperturbative quantity at the core of hadron physics; and emphasise throughout the role played by confrontation with data as a means of verifying our understanding of Nature.
We derive a novel model-independent result for the pion susceptibility in QCD via the isovector-pseudoscalar vacuum polarisation. In the neighbourhood of the chiral-limit, the pion susceptibility can be expressed as a sum of two independent terms. The first expresses the pion-pole contribution. The second is identical to the vacuum chiral susceptibility, which describes the response of QCD's ground-state to a fluctuation in the current-quark mass. In this result one finds a straightforward explanation of a mismatch between extant estimates of the pion susceptibility.
We derive a compact, semi-algebraic expression for the cold quark matter equation of state (EoS) in a covariant model that exhibits coincident deconfinement and chiral symmetry restoring transitions in-medium. Along the way we obtain algebraic expressions for: the number- and scalar-density distributions in both the confining Nambu and deconfined Wigner phases; and the vacuum-pressure difference between these phases, which defines a bag constant. The confining interaction materially alters the distribution functions from those of a Fermi gas and consequently has a significant impact on the model's thermodynamic properties, which is apparent in the EoS.
Two basic motivations for an upgraded JLab facility are the needs: to determine the essential nature of light-quark confinement and dynamical chiral symmetry breaking (DCSB); and to understand nucleon structure and spectroscopy in terms of QCD's elementary degrees of freedom. During the next ten years a programme of experiment and theory will be conducted that can address these questions. We present a Dyson-Schwinger equation perspective on this effort with numerous illustrations, amongst them: an interpretation of string-breaking; a symmetry-preserving truncation for mesons; the nucleon's strangeness sigma-term; and the neutron's charge distribution.
An exact form is presented for the axial-vector Bethe-Salpeter equation, which is valid when the quark-gluon vertex is fully dressed. A Ward-Takahashi identity for the Bethe-Salpeter kernel is derived therefrom and solved for a class of dressed quark-gluon vertex models. The solution provides a symmetry-preserving closed system of gap and vertex equations. The analysis can be extended to the vector equation. This enables a comparison between the responses of pseudoscalar- and scalar meson masses to nonperturbatively dressing the quark-gluon vertex. The result indicates that dynamical chiral symmetry breaking enhances spin-orbit splitting in the meson spectrum.
The chiral susceptibility is given by the scalar vacuum polarisation at zero total momentum. This follows directly from the expression for the vacuum quark condensate so long as a nonperturbative symmetry preserving truncation scheme is employed. For QCD in-vacuum the susceptibility can rigorously be defined via a Pauli-Villars regularisation procedure. Owing to the scalar Ward identity, irrespective of the form or Ansatz for the kernel of the gap equation, the consistent scalar vertex at zero total momentum can automatically be obtained and hence the consistent susceptibility. This enables calculation of the chiral susceptibility for markedly different vertex Ansaetze. For the two cases considered, the results were consistent and the minor quantitative differences easily understood. The susceptibility can be used to demarcate the domain of coupling strength within a theory upon which chiral symmetry is dynamically broken. Degenerate massless scalar and pseudoscalar bound-states appear at the critical coupling for dynamical chiral symmetry breaking.
We re-investigate the vector and axial-vector vacuum susceptibilities by taking advantage of the vector and axial-vector Ward-Takahashi identities. We show analytically that, in the chiral limit, the vector vacuum susceptibility is zero and the axial-vector vacuum susceptibility equals three fourths of the square of the pion decay constant. Besides, our analysis reproduces the Weinberg sum rule.
In general the kernel of QCD's gap equation possesses a domain of analyticity upon which the equation's solution at nonzero chemical potential is simply obtained from the in-vacuum result through analytic continuation. On this domain the single-quark number- and scalar-density distribution functions are mu-independent. This is illustrated via two models for the gap equation's kernel. The models are alike in concentrating support in the infrared. They differ in the form of the vertex but qualitatively the results are largely insensitive to the Ansatz. In vacuum both models realise chiral symmetry in the Nambu-Goldstone mode and in the chiral limit, with increasing chemical potential, exhibit a first-order chiral symmetry restoring transition at mu~M(0), where M(p^2) is the dressed-quark mass function. There is evidence to suggest that any associated deconfinement transition is coincident and also of first-order.
The axial-vector Ward-Takahashi identity is used to derive mass formulae for neutral pseudoscalar mesons. Flavour symmetry breaking entails non-ideal flavour content for these states. Adding that the η^\prime is not a Goldstone mode, exact chiral-limit relations are developed from the identity. They connect the dressed-quark propagator to the topological susceptibility. It is confirmed that in the chiral limit the η^\prime mass is proportional to the matrix element which connects this state to the vacuum via the topological susceptibility. The implications of the mass formulae are illustrated using an elementary dynamical model, which includes an Ansatz for that part of the Bethe-Salpeter kernel related to the non-Abelian anomaly. In addition to the current-quark masses, the model involves two parameters, one of which is a mass-scale. It is employed in an analysis of pseudoscalar- and vector-meson bound-states. While the effects of SU(N_f=2) and SU(N_f=3) flavour symmetry breaking are emphasised, the five-flavour spectra are described. Despite its simplicity, the model is elucidative and phenomenologically efficacious; e.g., it predicts η-η^\prime mixing angles of ~ (-15 degrees) and π^0-ηangles of ~ 1 degree.
On a bounded, measurable domain of non-negative current-quark mass, realistic models of QCD's gap equation can simultaneously admit two inequivalent dynamical chiral symmetry breaking (DCSB) solutions and a solution that is unambiguously connected with the realisation of chiral symmetry in the Wigner mode. The Wigner solution and one of the DCSB solutions are destabilised by a current-quark mass and both disappear when that mass exceeds a critical value. This critical value also bounds the domain on which the surviving DCSB solution possesses a chiral expansion. This value can therefore be viewed as an upper bound on the domain within which a perturbative expansion in the current-quark mass around the chiral limit is uniformly valid for physical quantities. For a pseudoscalar meson constituted of equal mass current-quarks, it corresponds to a mass m_{0^-}~0.45GeV. In our discussion we employ properties of the two DCSB solutions of the gap equation that enable a valid definition of in the presence of a nonzero current-mass. The behaviour of this condensate indicates that the essentially dynamical component of chiral symmetry breaking decreases with increasing current-quark mass.
We propose a chemical potential dependent effective gluon propagator and study the chiral quark condensate in strongly interacting matter in the framework of Dyson-Schwinger equation approach. The obtained results manifest that, as the effect of the chemical potential on the effective gluon propagator is taken into account, the chiral quark condensate decreases gradually with the increasing of the chemical potential if it is less than the critical value, and the condensate vanishes suddenly at the critical chemical potential. The inclusion of the chemical potential in the effective gluon propagator enhances the decreasing rate and decreases the critical chemical potential. It indicates that the chiral symmetry can be restored completely at a critical chemical potential and restored partially as the chemical potential is less than the critical value. If the effective gluon propagator is independent of the chemical potential, the chiral symmetry can only be restored suddenly but no gradual restoration.