Quark condensate contributions to the gluon self-energy and the ? meson sum rule

1989 ◽  
Vol 42 (3) ◽  
pp. 499-503 ◽  
Author(s):  
T. G. Steele
Keyword(s):  
Quark Condensate ◽  
Sum Rule ◽  
Self Energy

scholarly journals GENERAL FORMULA FOR THE FOUR-QUARK CONDENSATE AND VACUUM FACTORIZATION ASSUMPTION

2008 ◽  
Vol 23 (10) ◽  
pp. 1507-1520 ◽  
Author(s):  
HONG-SHI ZONG ◽  
DENG-KE HE ◽  
FENG-YAO HOU ◽  
WEI-MIN SUN
Keyword(s):  
General Formula ◽  
Linear Response ◽  
Chemical Potential ◽  
Background Field ◽  
Quark Propagator ◽  
Quark Condensate ◽  
Sum Rule ◽  
Factorization Problem ◽  
Field Approach ◽  
General Method

By differentiating the dressed quark propagator with respect to a variable background field, the linear response of the dressed quark propagator in the presence of the background field can be obtained. From this general method, using the vector background field as an illustration, we derive a general formula for the four-quark condensate [Formula: see text]. This formula contains the corresponding fully dressed vector vertex and it is shown that factorization for [Formula: see text] holds only when the dressed vertex is taken to be the bare one. This property also holds for all other types of four-quark condensate. By comparing this formula with the general expression for the corresponding vacuum susceptibility, it is found that there exists some intrinsic relation between these two quantities, which are usually treated as independent phenomenological inputs in the QCD sum rule external field approach. The above results are also generalized to the case of finite chemical potential and the factorization problem of the four-quark condensate at finite chemical potential is discussed.

STRONG SU(2) BREAKING AND MASS SPLITTINGS IN PSEUDOSCALAR MESONS

1996 ◽  
Vol 11 (29) ◽  
pp. 5245-5259 ◽  
Author(s):  
A. N. MITRA
Keyword(s):  
Mass Difference ◽  
Dynamical Symmetry ◽  
Quark Condensate ◽  
Low Energy ◽  
The Self ◽  
Quark Loop ◽  
Self Energy ◽  
A Value ◽  
Pseudoscalar Mesons ◽  
Vector Exchange

The mass splittings within the SU(2) multiplets of pseudoscalar mesons (π, K, D, B) are used as a laboratory to determine the mass difference between d and u quarks (current), through the simplest (two-point) quark-loop diagrams for the self-energies of the corresponding hadrons, together with the associated quark-condensate diagrams within the loops. The second-order e.m. correction is also calculated with a photon line joining the two opposite quark lines in the self-energy loop. The basic ingredient is a hadron–quark-vertex function generated from a vector-exchange-like (chirally invariant) four-fermion Lagrangian (with current quarks) under dynamical symmetry breaking (DχSB), precalibrated to spectroscopy and other important low-energy amplitudes. The results which are expressed as proportional to the u−d mass difference δc, but are otherwise free from any adjustable parameters, reproduce in a rather accurate way all the SU(2) mass differences (from kaon to bottom) with δc = 4.0 MeV, when all the three self-energy diagrams are included. The pion receives only e.m. contributions with a value 5.24 MeV.

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.

Self-energy Models for Scattering in Semiconductor Nanoscale Devices: Causality Considerations and the Spectral Sum Rule

2013 ◽  
Vol 1551 ◽  
pp. 17-22 ◽  
Author(s):  
John R. Barker ◽  
Antonio Martinez
Keyword(s):  
Green Function ◽  
Spectral Density ◽  
Density Of States ◽  
Inelastic Electron ◽  
Causality Condition ◽  
Nanoscale Devices ◽  
Sum Rule ◽  
Nanowire Transistors ◽  
Self Energy ◽  
Energy Models

ABSTRACTThe modelling of of silicon gate-all-around nanowire transistors by non-equilibrium Green function methods requires the computation of self-energies for inelastic electron-phonon interactions. It is shown that many approximations designed to reduce numerical complexityto these self-energies in fact fail because they do not satisfy appropriate causality conditions. Four familiar approximations are discussed and their failures resolved. It is also shown that a condition for the spectral density sum rule to hold (and hence accurate density of states in energy) depends on a simple causality condition.

EFFECTIVE MESON MASS IN NUCLEAR MATTER BASED ON DISPERSION EQUATION INCLUDING ${\rm N} \bar{\rm N},\ \Delta \bar{\rm N},\ \bar\Delta {\rm N}$ EXCITATIONS

2004 ◽  
Vol 13 (05) ◽  
pp. 973-986
Author(s):  
MASAHIRO NAKANO ◽  
LIANG-GANG LIU ◽  
HIROYUKI MATSUURA ◽  
TAISUKE NAGASAWA ◽  
KEN-ICHI MAKINO ◽  
...  
Keyword(s):  
Nuclear Matter ◽  
Dispersion Equation ◽  
Baryon Density ◽  
Usual Sense ◽  
Meson Mass ◽  
Chiral Symmetry Restoration ◽  
Subtraction Method ◽  
Sum Rule ◽  
Self Energy ◽  
Rule Method

Effective meson masses of σ, ω, ρ and π in nuclear matter are calculated from the meson self-energy of the particle–antiparticle excitations. Instead of the traditional renormalization, the dispersion relation method is used to calculate the real part from the finite imaginary part, since the tensor coupling of the pion and ρ meson is not renormalized in the usual sense. In this paper, we show the effects from antidelta-nucleon and delta-antinucleon excitations in π meson mass beside nucleon–antinucleon excitation. It is also shown that agreement is obtained on the ω meson mass predicted by the subtraction method and ρ meson mass by the QCD sum rule method. It is concluded that the dispersion equation method leads to the fact that all the meson mass decreases as the baryon density increases, and it supports the chiral symmetry restoration.

scholarly journals Inverse moment of the Bs-meson distribution amplitude from QCD sum rule

2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
Alexander Khodjamirian ◽  
Rusa Mandal ◽  
Thomas Mannel
Keyword(s):  
Light Cone ◽  
Quark Mass ◽  
Strange Quark ◽  
Quark Condensate ◽  
Distribution Amplitude ◽  
Symmetry Violation ◽  
Sum Rule ◽  
Strange Quark Mass ◽  
The Difference ◽  
Inverse Moment

Abstract We derive a QCD sum rule for the inverse moment of the Bs-meson light-cone distribution amplitude in HQET. Within this method, the SU(3)f l symmetry violation is traced to the strange quark mass and to the difference between strange and nonstrange quark condensate densities. We predict the ratio of inverse moments λBs/λB = 1.19 ± 0.14 which can be used in various applications of these distribution amplitudes to the analyses of Bs-meson decays, provided an accurate value of λB is available from other sources, such as the B → ℓνℓγ decay.

NEW INSIGHTS ON VECTOR MESONS: A DIALOG BETWEEN $f^{T}_{V}$ AND fV

2008 ◽  
Vol 23 (21) ◽  
pp. 3209-3212
Author(s):  
OSCAR CATÀ
Keyword(s):  
Magnetic Susceptibility ◽  
Excellent Agreement ◽  
High Energy ◽  
Quark Condensate ◽  
Vector Mesons ◽  
Meson Resonance ◽  
Sum Rule ◽  
High Energy Behavior ◽  
Energy Behavior ◽  
Hadronic Model

We examine the high energy behavior of the two-point correlators 〈VV〉, 〈TT〉, 〈VT〉 and its implications on the spectrum of spin-1 vector mesons. This leads to an estimate of [Formula: see text] in excellent agreement with the recent sum rule and lattice determinations. This information is later implemented in a hadronic model and used to estimate the value of the magnetic susceptibility of the quark condensate χ0. Our analysis shows that lowest meson resonance may turn out to be a bad approximation for this quantity.

COVARIANT MODEL OF CHIRAL SYMMETRY BREAKING IN QCD

1990 ◽  
Vol 05 (06) ◽  
pp. 399-406 ◽  
Author(s):  
G. KREIN ◽  
A.G. WILLIAMS
Keyword(s):  
Symmetry Breaking ◽  
Chiral Symmetry ◽  
Chiral Symmetry Breaking ◽  
Dyson Equation ◽  
Quark Condensate ◽  
Asymptotic Freedom ◽  
Gluon Vertex ◽  
Self Energy ◽  
Covariant Model ◽  
Ansatz Approach

With the aim of developing covariant QCD-based models of hadrons we study dynamical chiral symmetry breaking in an ansatz approach to QCD. The quark self-energy is calculated from the Schwinger-Dyson equation using an ansatz for the proper quark-gluon vertex consistent with QCD symmetries. Both asymptotic freedom and behavior consistent with confinement are included in the dressed gluon propagator. With essentially one free parameter we find that we can obtain good results for physically relevant quantities including the pion decay constant fπ, the quark condensate [Formula: see text], the scale parameter ΛQCD, and the constituent quark mass.

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