Bethe-Salpeter Meson Masses Beyond Ladder Approximation

Watson, Peter; Cassing, W.; Tandy, P. C.

doi:10.1007/s00601-004-0067-x

Cited by 85 publications

(141 citation statements)

References 31 publications

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“…Calculations of the a 1 and b 1 mesons using a similar model give results for these masses that are several hundred MeV too low [35,36] when compared to experiments. Also the mass of the first radially excited pion is, within this model, significantly smaller than the experimental value [18].…”

Section: Heavier U and D Quark Mesonsmentioning

confidence: 89%

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QCD modeling of hadron physics

Maris

Tandy

2006

Nuclear Physics B - Proceedings Supplements

103

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: Heavier U and D Quark Mesonsmentioning

confidence: 89%

“…With a nonzero current quark mass, this form factor indeed behaves like Eq. (36), and it approaches zero from below as Q 2 1 = Q 2 2 → ∞, since its decay constant is negative. In the chiral limit however, the decay constantf π1 is zero, as dictated by Eq.…”

Section: π γ γ Transition Form Factormentioning

confidence: 99%

QCD modeling of hadron physics

Maris

Tandy

2006

Nuclear Physics B - Proceedings Supplements

103

120

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“…Hence, functional derivatives act explicitly upon this object and "cut" quark lines, thus promoting the two-point function to a four-point function that is identified with the Bethe-Salpeter kernel. Now, for convenience we may define a quark-gluon vertex as an auxiliary function that represents the resummation of these higher order corrections [248][249][250][374][375][376][377][378]. Then, being a functional of the quark propagator Γ µ = Γ µ [S], it must be cut implicitly, see [379,380] for a discussion, where an integral representation of the vertex is necessary so as to avoid an ambiguity in defining the momenta.…”

Section: Approximations and Truncationsmentioning

confidence: 99%

Baryons as relativistic three-quark bound states

Eichmann

Sanchis-Alepuz

Williams

et al. 2016

Progress in Particle and Nuclear Physics

436

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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“…In addition, Eq. (19) means that a 7 is not an independent parameter. Our initial goal is to locate the bifurcation point, α c .…”

Section: Critical Coupling For Dcsbmentioning

confidence: 99%

“…[13][14][15][16], insights from which have subsequently been exploited; e.g., Refs. [17][18][19][20][21][22][23][24][25][26][27][28].…”

mentioning

confidence: 99%

Dynamical chiral symmetry breaking and the fermion–gauge-boson vertex

et al. 2012

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We present a workable model for the fermion-photon vertex, which is expressed solely in terms of functions that appear in the fermion propagator and independent of the angle between the relative momenta, and does not explicitly depend on the covariant-gauge parameter. It nevertheless produces a critical coupling for dynamical chiral symmetry breaking that is practically independent of the covariant-gauge parameter and an anomalous magnetic moment distribution for the dressed fermion that agrees in important respects with realistic numerical solutions of the inhomogeneous vector Bethe-Salpeter equation.

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Bethe-Salpeter Meson Masses Beyond Ladder Approximation

Cited by 85 publications

References 31 publications

QCD modeling of hadron physics

QCD modeling of hadron physics

Baryons as relativistic three-quark bound states

Dynamical chiral symmetry breaking and the fermion–gauge-boson vertex

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