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

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.

scholarly journals Quark Propagator and Meson Correlators in the QCD Vacuum

1997 ◽  
Vol 06 (02) ◽  
pp. 275-286 ◽  
Author(s):  
Varun Sheel ◽  
Hiranmaya Mishra ◽  
Jitendra C. Parikh
Keyword(s):  
Decay Constant ◽  
Axial Vector ◽  
Quark Propagator ◽  
Density Functions ◽  
Pion Decay Constant ◽  
Qcd Vacuum ◽  
Spectral Density Functions ◽  
Point Correlation ◽  
Point To Point ◽  
Time Point

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.

π0 DECAY AT CRITICAL TEMPERATURE

1992 ◽  
Vol 07 (27) ◽  
pp. 2493-2503 ◽  
Author(s):  
PIN-ZHEN BI ◽  
JOHANN RAFELSKI
Keyword(s):  
Decay Width ◽  
Decay Constant ◽  
Pion Mass ◽  
Quark Condensate ◽  
Chiral Symmetry Restoration ◽  
Pion Decay Constant ◽  
Two Photon ◽  
Photon Decay ◽  
Hot Matter ◽  
Influence Of Temperature On

The influence of temperature on the pion decay constant and the two-photon decay of π0 is considered near the chiral symmetry restoration point. We analyze how the mass and decay width relate to each other and find that the π0 decay width in hot matter is suppressed, provided that the pion mass vanishes at the critical point; it diverges if pion mass remains finite while quark condensate is dissolved at T c .

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

1994 ◽  
Vol 09 (04) ◽  
pp. 605-634 ◽  
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.

PION DECAY CONSTANT AND THE GELL-MANN-OAKES-RENNER RELATION IN NUCLEI

1994 ◽  
Vol 09 (04) ◽  
pp. 279-287 ◽  
Author(s):  
G. CHANFRAY ◽  
M. ERICSON ◽  
M. KIRCHBACH
Keyword(s):  
Decay Constant ◽  
Pion Mass ◽  
Axial Current ◽  
Quark Condensate ◽  
Nuclear Medium ◽  
Pion Decay ◽  
Pion Decay Constant ◽  
S Wave ◽  
Self Energy ◽  
Time Component

We study the pion decay constant, associated with the time component of the axial current, in the nuclear medium in terms of the pion self-energy. The theoretical scheme exploits chiral properties of the s-wave πN amplitude as previously applied to the study of the medium renormalized pion mass. We show that the Gell-Mann-Oakes-Renner relation holds to a good approximation in the medium. The renormalizations of the pion decay constant and the pion mass are consistent with that predicted for the quark condensate in the medium.

scholarly journals THE QUARK CONDENSATE IN THE GELL-MANN-OAKES-RENNER RELATION

1996 ◽  
Vol 11 (16) ◽  
pp. 1331-1337 ◽  
Author(s):  
K. LANGFELD ◽  
C. KETTNER
Keyword(s):  
Quark Propagator ◽  
Quark Condensate ◽  
Usual Definition ◽  
Gluon Exchange ◽  
Current Mass ◽  
Definition Of

The quark condensate which enters the Gell-Mann-Oakes-Renner (GMOR) relation, is investigated in the framework of one-gluon-exchange models. The usual definition of the quark condensate via the trace of the quark propagator produces a logarithmic divergent condensate. In the product of current mass and condensate, this divergence is precisely compensated by the bare current mass. The finite value of the product in fact does not contradict the relation recently obtained by Cahill and Gunner. Therefore the GMOR relation is still satisfied.

scholarly journals An asymptotic formula for the pion decay constant in a large volume

2004 ◽  
Vol 590 (3-4) ◽  
pp. 258-264 ◽  
Author(s):  
Gilberto Colangelo ◽  
Christoph Haefeli
Keyword(s):  
Asymptotic Formula ◽  
Large Volume ◽  
Decay Constant ◽  
Pion Decay ◽  
Pion Decay Constant

scholarly journals Finite Temperature QCD Sum Rules: A Review

2017 ◽  
Vol 2017 ◽  
pp. 1-24 ◽  
Author(s):  
Alejandro Ayala ◽  
C. A. Dominguez ◽  
M. Loewe
Keyword(s):  
Finite Temperature ◽  
Chemical Potential ◽  
Sum Rules ◽  
Light Quark ◽  
Axial Vector ◽  
Heavy Ion ◽  
Qcd Sum Rules ◽  
Rho Meson ◽  
Ion Collisions ◽  
Rule Method

The method of QCD sum rules at finite temperature is reviewed, with emphasis on recent results. These include predictions for the survival of charmonium and bottonium states, at and beyond the critical temperature for deconfinement, as later confirmed by lattice QCD simulations. Also included are determinations in the light-quark vector and axial-vector channels, allowing analysing the Weinberg sum rules and predicting the dimuon spectrum in heavy-ion collisions in the region of the rho-meson. Also, in this sector, the determination of the temperature behaviour of the up-down quark mass, together with the pion decay constant, will be described. Finally, an extension of the QCD sum rule method to incorporate finite baryon chemical potential is reviewed.

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