Dynamical symmetry breaking and particle mass generation in gauge field theories

Fomin, P. I.; Gusynin, V. P.; Miransky, V. A.; Sitenko, Yu. A.

doi:10.1007/bf02740014

Cited by 256 publications

(208 citation statements)

References 94 publications

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“…Provided that the (effective) quark-quark interaction reduces to the perturbative running coupling in the ultraviolet region, it is also straightforward to reproduce the asymptotic behavior of Eqs. (10) and (11) [12,13]. Both these phenomena are illustrated in Fig.…”

Section: Quark Propagatormentioning

confidence: 76%

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: Quark Propagatormentioning

confidence: 76%

QCD modeling of hadron physics

Maris

Tandy

2006

Nuclear Physics B - Proceedings Supplements

103

120

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“…Strong coupling QED in three space and one time dimension has been studied within the Dyson-Schwinger Equation (DSE) formalism for some time [1][2][3], in order to see whether there may be a phase transition to a nontrivial "local" theory at high momenta [2,[4][5][6], as a model for dynamical chiral symmetry breaking (DCSB) in walking technicolor theories [7,8], and also as an abelianized model for nonperturbative phenomena in QCD [9,10]. For a recent review of Dyson-Schwinger equations and their application see Ref.…”

Section: Introductionmentioning

confidence: 99%

Chiral symmetry breaking in quenched massive strong-coupling four-dimensional QED

Hawes

Williams

1995

Phys. Rev. D

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We present results from a study of subtractive renormalization of the fermion propagator Dyson-Schwinger equation (DSE) in massive strongcoupling quenched QED 4 . Results are compared for three different fermionphoton proper vertex Ansätze: bare γ µ , minimal Ball-Chiu, and CurtisPennington. The procedure is straightforward to implement and numerically stable. This is the first study in which this technique is used and it should prove useful in future DSE studies, whenever renormalization is required in numerical work.

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“…(21) [13,14]. The study of the BS equations in that model shows that there is indeed an infinite number of resonances in the channel with the quantum numbers of the NG bosons [24]. Their masses are nearly equal and are of the order of the fermion dynamical mass.…”

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confidence: 99%

“…It is well known (see, for example, Ref. [24]) that, because of the Ward identities for chiral currents, the SD equation for the dynamical fermion gap coincides with the Bethe-Salpeter (BS) equation for corresponding (gapless) NG bosons, which are quark-quark bound states in the present model. The infinite number of solutions ∆ (n) 0 (22) for the gap implies that there are massless states (which would become the NG bosons) in each of the vacua corresponding to different values of n. The genuine, stable, vacuum is that with n = 0.…”

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confidence: 99%

The effective potential of composite diquark fields and the spectrum of resonances in dense QCD

1999

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The effective potential of composite diquark fields responsible for color symmetry breaking in cold very dense QCD, in which long-range interactions dominate, is derived. The spectrum of excitations and the universality class of this dynamics are described.11.15. Ex, 12.38.Aw, 26.60.+c Recently, there has been considerable interest in the study of the color superconducting phase of cold dense QCD [1-10] (for recent reviews, see Ref.[11]). The color superconducting quark matter may exist in the interior of neutron stars, with baryon number densities exceeding a few times the normal nuclear density n 0 ≃ 0.17 fm −3 . Also, such matter could be created in accelerators by heavy ion collisions.The Ginzburg-Landau (GL) effective action method has been extremely successful in studying ordinary superconductivity of metals [12]. Recently, a similar approach has been utilized in the study of color superconductivity [3,4]. However, there the effective action was postulated based on symmetry and renormalization group arguments, and not derived from the microscopic theory, QCD.Following the original approach of Gorkov [12], it would be of a great interest to derive the effective action in color superconductivity directly from QCD. In this letter, we make a step in realizing this program and derive the effective potential for the order parameter of color superconductivity in cold dense QCD at such high baryon densities when the fermion pairing in the diquark channel dominates over that in the chiral one [1,2] and when long-range interactions dominate [4,5]. For this purpose, we will utilize the method of Ref. [13], which was originally used for the derivation of the effective action in quenched strong-coupling QED 4 (see also Ref. [14]) and then was successfully applied to QED 3 [15], quenched QED 4 in a magnetic field [16], and to some other models [17].The crucial feature in the dynamics of cold dense QCD, pointed recently in Refs. [4,5] (see also Ref.[6]), is the presence of the long-range interactions mediated by the unscreened gluon modes of the magnetic type. This point essentially distinguishes the dynamics of color superconductivity from that in the BCS theory of superconductivity in metals. In particular, this makes the derivation of the effective action in color superconductivity more complicated than the derivation of the GL effective action from the BCS theory.Our derivation of the effective potential in dense QCD will be based on the recent analysis of color superconductivity in the framework of the Schwinger-Dyson (SD) equations [7][8][9]. In this way, we will describe the universality class of the dynamics in cold dense QCD and, in particular, get insight into the character of the spectrum of excitations.As we shall see below, the universality class of the system at hand is that connected with long-range non-isotropic forces, producing a bifermion condensate. We will see that this class resembles (although does not quite coincide with) that of quenched QED 4 in a constant magnetic field [18,19]. The scaling ...

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Dynamical symmetry breaking and particle mass generation in gauge field theories

Cited by 256 publications

References 94 publications

QCD modeling of hadron physics

QCD modeling of hadron physics

Chiral symmetry breaking in quenched massive strong-coupling four-dimensional QED

The effective potential of composite diquark fields and the spectrum of resonances in dense QCD

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