Quark Propagator and Meson Correlators in the QCD Vacuum

Equal time, point to point correlation functions for spatially separated meson currents are calculated with respect to a variational construct for the ground state of QCD. Given such an ansatz we make no further approximations in the evaluation of the correlators. Our calculations for the vector, axial vector and scalar channels show qualitative agreement with the phenomenological predictions, whereas the pseudoscalar channel does not. However, the pseudoscalar correlator, when approximated by saturating with intermediate one-pion states agrees with results obtained from spectral density functions parameterised by pion decay constant and [Formula: see text] value obtained from chiral perturbation theory. We discuss this departure in the pseudoscalar channel, in the context of the quark propagation in the vacuum.

Download Full-text

VECTOR AND AXIAL-VECTOR CORRELATORS AND THE FOUR-QUARK CONDENSATE

Modern Physics Letters A ◽

10.1142/s0217732311036036 ◽

2011 ◽

Vol 26 (25) ◽

pp. 1887-1896

Author(s):

LI-AN CHEN ◽

LONG-QING HE

Keyword(s):

Decay Constant ◽

Approximation Scheme ◽

Sum Rules ◽

Axial Vector ◽

Quark Propagator ◽

Quark Condensate ◽

Ladder Approximation ◽

Pion Decay Constant ◽

The Difference ◽

Nonzero Contribution

In this paper we calculate the difference between vector and axial-vector correlators with two different vertices: the bare vertex and the Ball–Chiu vertex (BC vertex) ansatz. Through the difference we compare the results drawn from the chiral sum rules. The leading nonzero contribution of the difference of the correlators in the ultraviolet identifies the four-quark condensate, which is the leading nonperturbative phenomenon in QCD. Also the pion decay constant can be drawn. For the quark propagator, we employ two different models. One is calculated in the framework of the rainbow-ladder approximation scheme in the Dyson–Schwinger approach. The other is the analytic fit employed in Ref. 1. Results show that the dressing effects of the vector and axial-vector vertices are very important.

Download Full-text

VACUUM STRUCTURE IN QCD WITH QUARK AND GLUON CONDENSATES

International Journal of Modern Physics E ◽

10.1142/s0218301396000037 ◽

1996 ◽

Vol 05 (01) ◽

pp. 93-106 ◽

Cited By ~ 8

Author(s):

A. MISHRA ◽

H. MISHRA ◽

VARUN SHEEL ◽

S.P. MISRA ◽

P.K. PANDA

Keyword(s):

Ground State ◽

Energy Minimization ◽

Decay Constant ◽

Pion Decay ◽

Coupling Constant ◽

Pion Decay Constant ◽

Equal Time ◽

Vacuum Structure ◽

Qcd Vacuum ◽

Gluon Condensates

We consider here the vacuum structure in QCD with both quark and gluon condensates and a variational ansatz for the ground state. The method is nonperturbative, using only equal time algebra for the field operators. We then find that a constrained energy minimization of the Hamiltonian leads to a QCD vacuum with both quark and gluon condensates for αs>αc=0.62. The pion decay constant and the charge radius of the pion seem to fix the QCD coupling constant αs as 1.28, with the bag pressure given by [Formula: see text] This approach to QCD opens up possibilities of relating the mysterious vacuum structure with common place hadronic properties in a more direct manner.

Download Full-text

CHIRAL PERTURBATION THEORY AT THE QUARK LEVEL AND NEW NONPERTURBATIVE FORMULAE FOR THE PION DECAY CONSTANT IN QCD

International Journal of Modern Physics A ◽

10.1142/s0217751x94000303 ◽

1994 ◽

Vol 09 (04) ◽

pp. 605-634 ◽

Cited By ~ 4

Author(s):

V. SH. GOGOHIA

Keyword(s):

Perturbation Theory ◽

Momentum Transfer ◽

Chiral Perturbation Theory ◽

Decay Constant ◽

Axial Vector ◽

Bound State ◽

Pion Decay ◽

Pion Decay Constant ◽

Chiral Perturbation ◽

Quark Level

Introducing the most general expression for the corresponding axial-vector vertex, the flavor nonsinglet, chiral axial-vector Ward-Takahashi (WT) identity is investigated in the framework of dynamical chiral symmetry breaking (DCSB). A chiral perturbation theory at the quark level (CHPTq) is proposed in terms of a Taylor series expansions in powers of the external momenta q (momentum of a massless pion) for the direct solution of the above identity at small momentum transfer q (momentum of a massless pion). Correct treatment of initial dynamical singularities at q=0 within the CHPTq approach in accordance with the Ball and Chiu procedure makes it possible to decompose the axial-vector vertex into pole and regular parts in a self-consistent way. The Bethe-Salpeter (BS) bound-state amplitude of a massless pion restored from the identity is shown to coincide with the residue at pole q2=0, which is proportional to the pion decay constant. We find exact solution for the regular piece of the corresponding vertex at zero momentum transfer in terms of the quark propagator dynamical variables alone. This solution automatically satisfies asymptotic freedom (it approaches the point-like vertex at infinity). Applying the proposed CHPTq approach to the matrix element of the axial-vector current determining the pion decay constant, we find “exact” (within the BS bound-state amplitude, restored fom the axial WT identity), nonperturbative expression for the pion decay constant in the current algebra (CA) representation. We show explicitly that the well-known formula of Pagels-Stokar-Cornwall for the pion decay constant is a particular case of the CHPTq approach. We find also new, nonperturbative formulae for the pion decay constant in the Jackiw-Johnson (JJ) representation as well. They now have full physical sense within the CHPTq approach. Renormalization of these expressions as well as their application in technicolor theories with slowly running couplings are briefly discussed. We also propose to distinguish between the scales of DCSB at the quark and hadronic levels (the scale of effective field theory) as well as advocate a simple relation between them based on naive counting arguments.

Download Full-text

THE SPECTRAL DENSITY FUNCTIONS OF THE ADSORPTION SYSTEM K-/112/W AN ATTEMPT OF SURFACE DIFFUSION INVESTIGATION

Le Journal de Physique Colloques ◽

10.1051/jphyscol:1984903 ◽

1984 ◽

Vol 45 (C9) ◽

pp. C9-13-C9-16 ◽

Cited By ~ 3

Author(s):

J. Beben ◽

Ch. Kleint ◽

R. Meclewski

Keyword(s):

Spectral Density ◽

Surface Diffusion ◽

Density Functions ◽

Adsorption System ◽

Spectral Density Functions

Download Full-text

A New Spectral Method for Modeling Dynamic Ice Actions

23rd International Conference on Offshore Mechanics and Arctic Engineering, Volume 3 ◽

10.1115/omae2004-51360 ◽

2004 ◽

Author(s):

Tuomo Ka¨rna¨ ◽

Yan Qu ◽

Walter L. Ku¨hnlein

Keyword(s):

Dynamic Response ◽

Spectral Density ◽

Time Correlation ◽

General Purpose ◽

Density Functions ◽

Offshore Structure ◽

Spectral Density Functions ◽

Ice Force ◽

Ice Forces ◽

Scale Data

This paper presents a method of evaluating the response of a vertical offshore structure that is subjected to dynamic ice actions. The model concerns a loading scenario where a uniform ice sheet is drifting and crushing against the structure. Full scale data obtained at the lighthouse Norstro¨msgrund is used in the derivation of a method that applies both to narrow and wide structures. A large amount of events with directly measured local forces was used to derive formulas for spectral density functions of the ice force. A non-dimensional formula that was derived for the autospectrum applies for all ice thicknesses. Coherence functions are used to define the cross-spectra of the local ice forces. The two kind of spectral density functions for local forces can be used to evaluate the spectral density of the total ice force. The method takes account of both the spatial and time correlation between the local forces. Accordingly, the model provides a tool to consider the non-simultaneous characteristics of the local ice pressures while assessing the total ice force. The model can be used in conjunction with general purpose FE programs to evaluate the dynamic response of an offshore structure.

Download Full-text

Influence of Red Blood Cell Concentrations on the Measurement of Turbulence Using Hot-Film Anemometer

Journal of Biomechanical Engineering ◽

10.1115/1.3138442 ◽

1983 ◽

Vol 105 (4) ◽

pp. 406-410 ◽

Cited By ~ 3

Author(s):

A. M. Sallam ◽

N. H. C. Hwang

Keyword(s):

Phosphate Buffer Solution ◽

Experimental Information ◽

Characteristic Change ◽

Density Functions ◽

Buffer Solution ◽

Number Range ◽

Flow Phenomenon ◽

Human Red Blood Cells ◽

Spectral Density Functions ◽

Hot Film

Measurement of local velocity fluctuations was made with an L-shaped conical hot-film probe in a submerged circular jet. The experiment was carried out in solutions of washed human red blood cells (RBC) in a phosphate buffer solution (PBS), at hematocrit concentrations (Ht percent) of 10, 19, 29, and 38 percent. The viscosity of the testing solutions was kept at 3.2 c.p. by adding proper amount of dextran. The experiment was conducted at Reynolds numbers (NR) 674, 963, 1255 and 1410, based on the jet exit velocity and exit diameter. Statistical analyses were performed on the recorded instantaneous velocity signals to obtain the root-mean-square (rms) values, the probability density functions (PDF) and the power spectral density functions (PSDF) of the signals. Within the range tested, we noticed an incidental rise in rms values at 19 to 29 Ht percent for NR = 963 similar to those reported earlier in the literature. Further analyses using PDF and PSDF, however, showed neither a trend nor any physical significance of this rise. Based on the analyses of both the PDF and the PSDF, we believe that the incidental rise in rms value can be partially attributed to the high spikes registered by the probe in a high RBC concentrations fluid flow. The bombardment of RBC on the probe thermal boundary layer may cause a characteristic change in the probe response to certain flow phenomenon, at least within the Reynolds number range used in this study. Additional theoretical and experimental information is needed to pin point the nature of this response. We thus suggest that the second and higher moments of the HFA signals obtained in a fluctuating flow field involving a liquid with relatively high contaminant concentrations cannot be interpreted as a simple flow phenomenon.

Download Full-text