Pion mass and decay constant

Maris, Pieter; Roberts, Craig D.; Tandy, P. C.

doi:10.1016/s0370-2693(97)01535-9

Cited by 511 publications

(692 citation statements)

References 19 publications

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“…12. In the ultraviolet, theqq scattering kernel appearing in Γ A σ coincides with 5 Note that the color factor of the color-singlet Γ A σ contribution to the strong dressing of the quark-photon vertex…”

Section: Modeling the Quark-gluon Vertexmentioning

confidence: 86%

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QCD modeling of hadron physics

Maris

Tandy

2006

Nuclear Physics B - Proceedings Supplements

101

120

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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:

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Section: Modeling the Quark-gluon Vertexmentioning

confidence: 86%

“…Among other things, this guarantees the Goldstone boson nature of the flavor non-singlet pseudoscalars independently of model details [5].…”

Section: Effect On Meson Observablesmentioning

confidence: 93%

QCD modeling of hadron physics

Maris

Tandy

2006

Nuclear Physics B - Proceedings Supplements

101

120

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“…Its essence is to show that the pion decay constant does not vanish in the chiral limit as a consequence of dynamical chiral symmetry breaking. The precise relation is [311] f…”

Section: Tetraquark Nomentioning

confidence: 99%

Baryons as relativistic three-quark bound states

Eichmann

Sanchis-Alepuz

Williams

et al. 2016

Progress in Particle and Nuclear Physics

416

530

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We review the spectrum and electromagnetic properties of baryons described as relativistic three-quark bound states within QCD. The composite nature of baryons results in a rich excitation spectrum, whilst leading to highly non-trivial structural properties explored by the coupling to external (electromagnetic and other) currents. Both present many unsolved problems despite decades of experimental and theoretical research. We discuss the progress in these fields from a theoretical perspective, focusing on nonperturbative QCD as encoded in the functional approach via Dyson-Schwinger and Bethe-Salpeter equations. We give a systematic overview as to how results are obtained in this framework and explain technical connections to lattice QCD. We also discuss the mutual relations to the quark model, which still serves as a reference to distinguish 'expected' from 'unexpected' physics. We confront recent results on the spectrum of non-strange and strange baryons, their form factors and the issues of two-photon processes and Compton scattering determined in the DysonSchwinger framework with those of lattice QCD and the available experimental data. The general aim is to identify the underlying physical mechanisms behind the plethora of observable phenomena in terms of the underlying quark and gluon degrees of freedom.

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“…Moreover, in considering the U A (1)-problem one need only focus on the case A 0 = 0 because if that is false, then following Ref. [32] it is clear that the η ′ is certainly a Goldstone mode. A 0 is a pseudoscalar vertex and can therefore be expressed…”

Section: Neutral Pseudoscalars and The η ′mentioning

confidence: 99%

Hadron properties and Dyson–Schwinger equations

Roberts

2008

Progress in Particle and Nuclear Physics

179

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An overview of the theory and phenomenology of hadrons and QCD is provided from a DysonSchwinger equation viewpoint. Following a discussion of the definition and realisation of light-quark confinement, the nonperturbative nature of the running mass in QCD and inferences from the gap equation relating to the radius of convergence for expansions of observables in the current-quark mass are described. Some exact results for pseudoscalar mesons are also highlighted, with details relating to the U A (1) problem, and calculated masses of the lightest J = 0, 1 states are discussed. Studies of nucleon properties are recapitulated upon and illustrated: through a comparison of the ln-weighted ratios of Pauli and Dirac form factors for the neutron and proton; and a perspective on the contribution of quark orbital angular momentum to the spin of a nucleon at rest. Comments on prospects for the future of the study of quarks in hadrons and nuclei round out the contribution.

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Pion mass and decay constant

Cited by 511 publications

References 19 publications

QCD modeling of hadron physics

QCD modeling of hadron physics

Baryons as relativistic three-quark bound states

Hadron properties and Dyson–Schwinger equations

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