Dressed perturbation theory: a perturbative approach to Dyson-Schwinger and Bethe-Salpeter equations in QCD

Krein, G.

doi:10.22323/1.193.0021

Cited by 3 publications

(4 citation statements)

References 20 publications

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“…(3). For systems with nonzero isospin, I = 0, quark propagators appearing in gluon vacuum-polarisation diagrams may be neglected and the kernel can be expressed as a sum of just two terms [3,17,18,33,52,53]:…”

Section: Insufficiency Of Vertex-dressed Ladder Kernelsmentioning

confidence: 99%

“…For systems with nonzero isospin, I = 0, quark propagators appearing in gluon vacuum-polarisation diagrams may be neglected and the kernel can be expressed as a sum of just two terms [3,17,18,33,52,53]: K I =0 (k, q; P ) = K S (k, q; P ) + K Γ (k, q; P ) , (4) as depicted in the lower panel of Fig. 2, where the content of the vertex Λ µ is completely determined by the functional derivative of the dressed gluon-quark vertex:…”

Section: Insufficiency Of Vertex-dressed Ladder Kernelsmentioning

confidence: 99%

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Symmetry preserving truncations of the gap and Bethe-Salpeter equations

et al. 2016

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Ward-Green-Takahashi (WGT) identities play a crucial role in hadron physics, e.g. imposing stringent relationships between the kernels of the one-and two-body problems, which must be preserved in any veracious treatment of mesons as bound-states. In this connection, one may view the dressed gluon-quark vertex, Γ a µ , as fundamental. We use a novel representation of Γ a µ , in terms of the gluon-quark scattering matrix, to develop a method capable of elucidating the unique quarkantiquark Bethe-Salpeter kernel, K , that is symmetry-consistent with a given quark gap equation.A strength of the scheme is its ability to expose and capitalise on graphic symmetries within the kernels. This is displayed in an analysis that reveals the origin of H-diagrams in K , which are twoparticle-irreducible contributions, generated as two-loop diagrams involving the three-gluon vertex, that cannot be absorbed as a dressing of Γ a µ in a Bethe-Salpeter kernel nor expressed as a member of the class of crossed-box diagrams. Thus, there are no general circumstances under which the WGT identities essential for a valid description of mesons can be preserved by a Bethe-Salpeter kernel obtained simply by dressing both gluon-quark vertices in a ladder-like truncation; and, moreover, adding any number of similarly-dressed crossed-box diagrams cannot improve the situation.

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Section: Insufficiency Of Vertex-dressed Ladder Kernelsmentioning

confidence: 99%

Section: Insufficiency Of Vertex-dressed Ladder Kernelsmentioning

confidence: 99%

Symmetry preserving truncations of the gap and Bethe-Salpeter equations

et al. 2016

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“…One envisages progress with methods based on systematic improvements on a zeroth-order approximation that captures essential features of QCD, examples of which are those of Refs. [43,44,17,45].…”

Section: Discussionmentioning

confidence: 99%

“…Complex-mass poles are found in this model, but for parameters very different from those in (50). Moreover, positivity violation is also obtained when using the on-shell renomalization scheme, specified by the equations ( 41)- (43). In this scheme, the pole mass is set as a renormalization condition.…”

Section: Model Calculationmentioning

confidence: 99%

Quark Propagator in Minkowski Space

Solis

Luiz

et al. 2019

Few-Body Syst

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The analytic structure of the quark propagator in Minkowski space is more complex than in Euclidean space due to the possible existence of poles and branch cuts at timelike momenta. These singularities impose enormous complications on the numerical treatment of the nonperturbative Dyson-Schwinger equation for the quark propagator. Here we discuss a computational method that avoids most of these complications. The method makes use of the spectral representation of the propagator and of its inverse. The use of spectral functions allows one to handle in exact manner poles and branch cuts in momentum integrals. We obtain model-independent integral equations for the spectral functions and perform their renormalization by employing a momentum-subtraction scheme. We discuss an algorithm for solving numerically the integral equations and present explicit calculations in a schematic model for the quark-gluon scattering kernel.

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Excited Hadrons and the Analytical Structure of Bound-State Interaction Kernels

et al. 2016

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We highlight Hermiticity issues in bound-state equations whose kernels are subject to a highly asymmetric mass and momentum distribution and whose eigenvalue spectrum becomes complex for radially excited states. We trace back the presence of imaginary parts in the eigenvalues and wave functions to truncation artifacts and suggest how they can be eliminated in the case of charmed mesons. The solutions of the gap equation in the complex plane, which play a crucial role in the analytic structure of the Bethe-Salpeter kernel, are discussed for several interaction models and qualitatively and quantitatively compared to analytic continuations by means of complex-conjugate pole models fitted to real solutions.

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Dressed perturbation theory: a perturbative approach to Dyson-Schwinger and Bethe-Salpeter equations in QCD

Cited by 3 publications

References 20 publications

Symmetry preserving truncations of the gap and Bethe-Salpeter equations

Symmetry preserving truncations of the gap and Bethe-Salpeter equations

Quark Propagator in Minkowski Space

Excited Hadrons and the Analytical Structure of Bound-State Interaction Kernels

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