Modelling the quark propagator

Bowman, Patrick O.; Heller, Urs M.; Leinweber, Derek B.; Williams, Anthony G.

doi:10.1016/s0920-5632(03)01533-0

Cited by 68 publications

(97 citation statements)

References 8 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…These predictions for the quark mass function have been confirmed in lattice simulations of QCD [14,15,16]. Pointwise agreement for a range of quark masses requires this interaction to be flavor-dependent [9], suggesting that dressing the quark-gluon vertex Γ i ν (q, p) is important.…”

Section: Quark Propagatormentioning

confidence: 72%

See 1 more Smart Citation

QCD modeling of hadron physics

Maris

Tandy

2006

Nuclear Physics B - Proceedings Supplements

102

120

View full text Add to dashboard Cite

We review recent developments in the understanding of meson properties as solutions of the Bethe-Salpeter equation in rainbow-ladder truncation. Included are recent results for the pseudoscalar and vector meson masses and leptonic decay constants, ranging from pions up to cc bound states; extrapolation to bb states is explored. We also present a new and improved calculation of Fπ(Q 2 ) and an analysis of the πγγ transition form factor for both π(140) and π(1330). Lattice-QCD results for propagators and the quark-gluon vertex are analyzed, and the effects of quark-gluon vertex dressing and the three-gluon coupling upon meson masses are considered. DYSON-SCHWINGER EQUATIONS OF QCDThe Dyson-Schwinger equations [DSEs] are the equations of motion of a quantum field theory. They form an infinite hierarchy of coupled integral equations for the Green's functions (n-point functions) of the theory. Bound states (mesons, baryons) appear as poles in the Green's functions. Thus, a study of the poles in n-point functions using the set of DSEs will tell us something about hadrons. For recent reviews on the DSEs and their use in hadron physics, see Refs. [1,2,3]. Quark propagatorThe exact DSE for the quark propagator is 1where D µν (q = k − p) is the renormalized dressed gluon propagator, and Γ i ν (k, p) is the renormalized dressed quark-gluon vertex. The notation k stands for Λ d 4 k/(2π) 4 . For divergent integrals a translationally invariant regularization is necessary; the regularization scale Λ is to be removed at the end of all calculations, after renormalization, and will be suppressed henceforth.1 We use Euclidean metric {γµ, γν } = 2δµν , γ † µ = γµ andThe solution of Eq. (1) can be written asrenormalized according to S(p) −1 = i / p + m(µ) at a sufficiently large spacelike µ 2 , with m(µ) the current quark mass at the scale µ. Both the propagator, S(p), and the vertex, Γ i µ depend on the quark flavor, although we have not indicated this explicitly. The renormalization constants Z 2 and Z 4 depend on the renormalization point and on the regularization mass-scale, but not on flavor: in our analysis we employ a flavor-independent renormalization scheme. MesonsBound states correspond to poles in n-point functions: for example a meson appears as a pole in the 2-quark, 2-antiquark Green's function G (4) = 0|q 1 q 2q1q2 |0 . In the vicinity of a meson, i.e. in the neighborhood of P 2 = −M 2 with M being the meson mass, such a Green's function behaves likewhere P is the total 4-momentum of the meson, p o and p i are the momenta of the outgoing quark and incoming quark respectively, and similarly for k i and k o . Momentum conservation relates these momenta:

show abstract

Section: Quark Propagatormentioning

confidence: 72%

“…Dynamical quark mass functions obtained with the DSE-Lat model together with the quenched lattice data [15]. Adapted from [9].…”

Section: Lattice-inspired Rainbow Modelmentioning

confidence: 99%

QCD modeling of hadron physics

Maris

Tandy

2006

Nuclear Physics B - Proceedings Supplements

102

120

View full text Add to dashboard Cite

show abstract

“…The model parameter C for the vertex is determined by a fit to selected global features of quenched lattice-QCD data for the quark propagator [29] and the quark-gluon vertex [22]. Thess data are available for both quantities at current quark mass m =m = 60 MeV.…”

Section: B Algebraic Vertex and Quark Propagatormentioning

confidence: 99%

Quark-gluon vertex dressing and meson masses beyond ladder-rainbow truncation

2007

View full text Add to dashboard Cite

We include a generalized infinite class of quark-gluon vertex dressing diagrams in a study of how dynamics beyond the ladder-rainbow truncation influences the Bethe-Salpeter description of light quark pseudoscalar and vector mesons.The diagrammatic specification of the vertex is mapped into a corresponding specification of the Bethe-Salpeter kernel, which preserves chiral symmetry. This study adopts the algebraic format afforded by the simple interaction kernel used in previous work on this topic. The new feature of the present work is that in every diagram summed for the vertex and the corresponding Bethe-Salpeter kernel, each quark-gluon vertex is required to be the self-consistent vertex solution. We also adopt from previous work the effective accounting for the role of the explicitly non-Abelian three gluon coupling in a global manner through one parameter determined from recent lattice-QCD data for the vertex.With the more consistent vertex used here, the error in ladder-rainbow truncation for vector mesons is never more than 10% as the current quark mass is varied from the u/d region to the b region.

show abstract

“…For example, DCSB is responsible for the generation of large constituent-like masses for dressedquarks in QCD, an outcome that could have been anticipated from Refs. [1,2]; it is a longstanding prediction of Dyson-Schwinger equation (DSE) studies [3] and has recently been observed in numerical simulations of latticeregularised QCD [4,5]. DCSB is also the keystone in the realisation of Goldstone's theorem through pseudoscalar mesons in QCD [6], and thereby the remarkably small value of the ratio of π-and ρ-meson masses, and the weak ππ interaction at low energies [7].…”

Section: Introductionmentioning

confidence: 99%

Dynamical chiral symmetry breaking and a critical mass

et al. 2007

View full text Add to dashboard Cite

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 − ∼ 0.45 GeV. In our discussion we employ properties of the two DCSB solutions of the gap equation that enable a valid definition of qq 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.

show abstract

Modelling the quark propagator

Cited by 68 publications

References 8 publications

QCD modeling of hadron physics

QCD modeling of hadron physics

Quark-gluon vertex dressing and meson masses beyond ladder-rainbow truncation

Dynamical chiral symmetry breaking and a critical mass

Contact Info

Product

Resources

About