Pion susceptibility of the QCD vacuum from an effective quark–quark interaction

Zong, Hong-Shi; Qi, Shi; Chen, Wei; Sun, Weimin; Zhao, En-Guang

doi:10.1016/j.physletb.2003.09.099

Cited by 27 publications

(18 citation statements)

References 56 publications

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“…(-4) In the calculation presented below, we will need the normal-ordered chiral condensate vac| :ψ(0)ψ(0) : |vac = vac|ψ(0)ψ(0)|vac − Ω|ψ(0)ψ(0)|Ω . Quite different from the non-perturbative symmetry-broken vacuum state |vac , |Ω is the perturbative vacuum state that is chiral symmetric [40]. As a function of α, the value of vac| :ψ(0)ψ(0) : |vac will be specified in Sec.III.…”

Section: Dyson-schwinger Equation and Dynamical Mass Generationmentioning

confidence: 99%

Dynamical fermion mass generation and exciton spectra in graphene

2011

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The Coulomb interaction between massless Dirac fermions may induce dynamical chiral symmetry breaking by forming excitonic pairs in clean graphene, leading to semimetal-insulator transition. If the Dirac fermions have zero bare mass, an exact continuous chiral symmetry is dynamically broken and thus there are massless Goldstone excitons. If the Dirac fermions have a small bare mass, an approximate continuous chiral symmetry is dynamically broken and the resultant Goldstone type excitons become massive, which is analogous to what happens in QCD. In this paper, after solving Dyson-Schwinger gap equation in the presence of a small bare fermion mass, we found a remarkable reduction of the critical Coulomb interaction strength for excitonic pair formation and a strong enhancement of dynamical fermion mass. We then calculate the masses of Goldstone type excitons using the SVZ sum rule method and operator product expansion technique developed in QCD and find that the exciton masses are much larger than bare fermion mass but smaller than the width of dynamical fermion mass gap. We also study the spin susceptibilities and estimate the masses of non-Goldstone type excitons using the same tools.

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Section: Dyson-schwinger Equation and Dynamical Mass Generationmentioning

confidence: 99%

Dynamical fermion mass generation and exciton spectra in graphene

2011

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“…Here we follow the notations in Refs. [15,16]. |0 denotes the exact QCD vacuum and |0 is the perturbative QCD vacuum, while G ,PT (x) ≡ 0|T [q(x)q(0)] 0 J and G ,N P (x) ≡ 0 | : T [q(x)q(0)] : |0 J is the linear response of the dressed quark propagator coupled perturbatively and nonperturbatively to the external current, respectively.…”

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confidence: 99%

“…In addition, the bracketting colons "::" are only a notation which means that we subtract the contribution of the perturbative term G ,PT (x) from G (x). The vacuum susceptibility χ in the QCD sum rule external field treatment can be defined as [14,16,17] G cc ,N P…”

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confidence: 99%

“…(11) and (12), it is not difficult to get the following expression: (16) where the notation Tr includes trace over the Dirac, color, and coordinate space indices. To be more specific, Tr [γ ν γ 5 G · VG] can be rewritten as…”

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confidence: 99%

“…However, if we follow the previous approach proposed by Refs. [12,16], we have the axial vector vacuum susceptibility…”

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Modified approach for calculating axial vector vacuum susceptibility

et al. 2006

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We generalize our previous work [Phys. Rev. C 72, 035202 (2005)] on the linear response theory of the dressed quark propagator in the presence of a constant external field to the case of a variable external field in order to make it applicable to a wider class of problems. Using the axial vector vacuum susceptibility as an illustration, we apply this general formalism to extract a new expression for the axial vector vacuum susceptibility in the quantum chromodynamical (QCD) sum rule two-point external field formula. The numerical values of the axial vector vacuum susceptibility are calculated within the framework of the rainbow-ladder approximation of the Dyson-Schwinger approach. A comparison with the results of the previous approaches is given.

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Progress in vacuum susceptibilities and their applications to the chiral phase transition of QCD

et al. 2015

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The QCD vacuum condensates and various vacuum susceptibilities are all important parameters which characterize the nonperturbative properties of the QCD vacuum. In the QCD sum rules external field formula, various QCD vacuum susceptibilities play important roles in determining the properties of hadrons. In this paper, we review the recent progress in studies of vacuum susceptibilities together with their applications to the chiral phase transition of QCD. The results of the tensor, the vector, the axial-vector, the scalar, and the pseudo-scalar vacuum susceptibilities are shown in detail in the framework of Dyson-Schwinger equations.

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Pion susceptibility of the QCD vacuum from an effective quark–quark interaction

Abstract: A modified method for calculating the pion vacuum susceptibility from an effective quark-quark interaction model is derived. Within this approach it is shown that the pion vacuum susceptibility is free of ultraviolet divergence and is much smaller than the previous estimations.

Cited by 27 publications

References 56 publications

Dynamical fermion mass generation and exciton spectra in graphene

Dynamical fermion mass generation and exciton spectra in graphene

Modified approach for calculating axial vector vacuum susceptibility

Progress in vacuum susceptibilities and their applications to the chiral phase transition of QCD

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