Suzhou Huang

Evidence for the role of instantons in hadron structure from lattice QCD.

Cooling is used as a filter on a set of gluon fields sampling the Wilson action to selectively remove essentially all fluctuations of the gluon field except for the instantons. The close agreement between quenched lattice QCD results with cooled and uncooled configurations for vacuum correlation functions of hadronic currents and for density-density correlation functions in hadronic bound states provides strong evidence for the dominant role of instantons in determining light hadron structure and quark propagation in the QCD vacuum.

The Relevant Scale Parameter in the High Temperature Phase of QCD

Abstract We introduce the running coupling constant of QCD in the high temperature phase, g 2 (T) , through a renormalization scheme where the dimensional reduction is optimal at the one-loop level. We then calculate the relevant scale parameter, ΛT, which characterizes the running of g 2 (T) with T, using the background field method in the static sector. It is found that Λ T /Λ=e( γE+ 1 22 )/(4π) ≈ 0.148 . We further verify that the coupling g 2 (T) is also optimal for lattice perturbative calculations. Our result naturally explains why the high temperature limit of QCD sets in at temperatures as low as a few times the critical temperature. In addition, our Λt agrees remarkably well with the scale parameter determined from the lattice measurement of the spatial string tension of the SU(2) gauge theory at high T.

Correlation functions of hadron currents in the QCD vacuum calculated in lattice QCD

Point-to-point vacuum correlation functions for spatially separated hadron currents are calculated in quenched lattice QCD on a 16[sup 3][times]24 lattice with 6/[ital g][sup 2]=5.7. The lattice data are analyzed in terms of dispersion relations, which enable us to extract physical information from small distances where asymptotic freedom is apparent to large distances where the hadronic resonances dominate. In the pseudoscalar, vector, and axial vector channels where experimental data or phenomenological information are available, semiquantitative agreement is obtained. In the nucleon and [Delta] channels, where no experimental data exist, our lattice data complement experiments. Comparison with approximations based on sum rules and interacting instantons are made, and technical details of the lattice calculation are described.

The Dimensionally Reduced Effective Theory for Quarks in High Temperature QCD

We show that QCD undergoes a partial dimensional reduction at high temperatures also in the quark sector. In the kinematic region relevant to screening physics, where the lowest Matsubara modes are close to their “mass shells”, all static Green functions involving both quarks and gluons are reproducible in the high-T limit by a renormalizable three-dimensional Lagrangian up to order g2(T) ∼ 1/1nT. This three-dimensional theory only contains explicitly the lightest bosonic and fermionic Matsubara modes, while the heavier modes correct the tree-level couplings and generate extra local vertices. We also find that the quark degrees of freedom that have been retained in the reduced theory are non-relativistic in the high-T limit. We then improve our result to order g4(T) through an explicit non-relativistic expansion, in the spirit of the heavy-quark effective theory. This effective theory is relevant for studying QCD screening phenomena with observables made from quarks, e.g. mesonic and baryonic currents, already at temperatures not much higher than the chiral transition temperature Tc.

Statistical mechanics of relativistic anyon-like systems☆

Abstract To study the manifestation of the Aharonov-Bohm effect in many-body systems we consider the statistical mechanics of the Gross-Neveu model on a ring (1+1 dimensions) and on a cylinder (2+1 dimensions) with a thin solenoid coinciding with the axis. For such systems with a non-trivial magnetic flux (θ) many thermodynamical observables, such as the order parameter, induced current and virial coefficients, display a periodic but non-analytic dependence on θ. In the (2+1)-dimensional case we further find that there is an interval of θ ϵ ( 1 3 , 2 3 ) (modulo integers) where parity is always spontaneously broken, independent of the circumference of the cylinder. We show that the mean-field character of the phase transitions is preserved to the leading order in 1/N, by veryfying the θ-independence of all the critical exponents. The precise nature of the quasi-particle, locally fermion-like and globally anyon-like, is illuminated through the calculation of the equal-time commutator and the decomposition of the propagator into a sum over paths classified by winding numbers.

Calculation of moments of nucleon structure functions

Abstract Preliminary results are presented in our program to calculate low moments of structure functions for the proton and neutron on a 243 × 32 lattice at β = 6.2. A comparison is made for a variety of smeared nucleon sources and preliminary results for the calculation of the nucleon tensor charge are presented.

Constraining Spectral Functions at Finite Temperature and Chemical Potential with Exact Sum Rules in Asymptotically Free Theories

Within the framework of the operator product expansion (OPE) and the renormalization group equation (RGE), we show that the temperature and chemical potential dependence of the zeroth moment of a spectral function (SF) is completely determined by the one-loop structure in an asymptotically free theory, and in particular in QCD. Logarithmic corrections are found to play an essential role in the derivation. This exact result constrains the shape of SF’s, and implies striking effects near phase transitions. Phenomenological parameterizations of the SF, often used in applications such as the analysis of lattice QCD data or QCD sum rule calculations at finite temperature and baryon density must satisfy these constraints. We also explicitly illustrate in detail the exact sum rule in the Gross-Neveu model.

Lattice analysis of two-point hadronic correlators in the QCD vacuum

Results from the first lattice QCD analysis of vacuum correlators of local hadronic currents using dispersion relations are presented. We have explored the vector, pseudoscalar, axial, and scalar meson channels, and the proton-like and delta-like baryon channels. The lattice results are shown to agree qualitatively with experimental results in channels where experimental data exist, and shed insight into interacting instanton approximations and sum rule calculations in the other channels.

Contrasting real-time dynamics with screening phenomena at finite temperature.

We discuss the interpretation of Euclidean correlation functions at finite temperature (T) and their relationship with the corresponding real-time Green’s functions. The soluble 2+1 dimensional Gross-Neveu model in the large-N limit is used throughout as a working example. First, the real-time bound state, identified as an elementary excitation at finite T, is solved. The bound state mass, the dispersion relation at low momenta, the coupling constant and decay constant are calculated. To characterize the structure of the bound state the on-shell form factor is carefully introduced and calculated. Then we examine the corresponding screening state and contrast the screening mass, coupling constant, decay constant and the screening Bethe-Salpeter amplitude with the real-time quantities. We find that, although they can be used as qualitative indicators in the low-T regime, the screening states at finite T in general do not reflect the properties of the corresponding real-time bound states. Besides, other relevant issues, such as the subtlety of the real-time manifestation of conservation laws due to some internal symmetries at T 6 0, the temperature dependence of the pseudoscalar spectral function and its sum rule, and the high-T limit of the screening state and its implications to the dimensional reduction, are also discussed in detail.

Evidence for the role of instantons in hadron structure from lattice QCD

Abstract Cooling is used as a filter on a set of gluon fields sampling the Wilson action to selectively remove essentially all fluctuations of the gluon field except for the instantons. The close agreement between quenched lattice QCD results with cooled and uncooled configurations for vacuum correlation functions of hadronic currents and for density-density correlation functions in hadronic sound states provides strong evidence for the dominant role of instantons in determining light hadron structure and quark propagation in the QCD vacuum.