arXiv subjects

Peter C. Tandy

Publications and source records attributed to Peter C. Tandy.

24 records · Page 2Linked to original sources

arXiv2007

Consequences Of Fully Dressing Quark-Gluon Vertex Function With Two-Point Gluon Lines

We extend recent studies of the effects of quark-gluon vertex dressing upon the solutions of the Dyson-Schwinger equation for the quark propagator. A momentum delta function is used to represent the dominant infrared strength of the effective gluon propagator so that the resulting integral equations become algebraic. The quark-gluon vertex is constructed from the complete set of diagrams involving only 2-point gluon lines. The additional diagrams, including those with crossed gluon lines, are shown to make an important contribution to the DSE solutions for the quark propagator, because of their large color factors and the rapid growth in their number.

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arXiv2007

Flavour symmetry breaking and meson masses

The axial-vector Ward-Takahashi identity is used to derive mass formulae for neutral pseudoscalar mesons. Flavour symmetry breaking entails non-ideal flavour content for these states. Adding that the η^\prime is not a Goldstone mode, exact chiral-limit relations are developed from the identity. They connect the dressed-quark propagator to the topological susceptibility. It is confirmed that in the chiral limit the η^\prime mass is proportional to the matrix element which connects this state to the vacuum via the topological susceptibility. The implications of the mass formulae are illustrated using an elementary dynamical model, which includes an Ansatz for that part of the Bethe-Salpeter kernel related to the non-Abelian anomaly. In addition to the current-quark masses, the model involves two parameters, one of which is a mass-scale. It is employed in an analysis of pseudoscalar- and vector-meson bound-states. While the effects of SU(N_f=2) and SU(N_f=3) flavour symmetry breaking are emphasised, the five-flavour spectra are described. Despite its simplicity, the model is elucidative and phenomenologically efficacious; e.g., it predicts η-η^\prime mixing angles of ~ (-15 degrees) and π^0-ηangles of ~ 1 degree.

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arXiv2006

Quark-gluon vertex dressing and meson masses beyond ladder-rainbow truncation

We include a generalized infinite class of quark-gluon vertex dressing diagrams in a study of how dynamics beyond the ladder-rainbow truncation influences the Bethe-Salpeter description of light quark pseudoscalar and vector mesons. The diagrammatic specification of the vertex is mapped into a corresponding specification of the Bethe-Salpeter kernel, which preserves chiral symmetry. This study adopts the algebraic format afforded by the simple interaction kernel used in previous work on this topic. The new feature of the present work is that in every diagram summed for the vertex and the corresponding Bethe-Salpeter kernel, each quark-gluon vertex is required to be the self-consistent vertex solution. We also adopt from previous work the effective accounting for the role of the explicitly non-Abelian three gluon coupling in a global manner through one parameter determined from recent lattice-QCD data for the vertex. With the more consistent vertex used here, the error in ladder-rainbow truncation for vector mesons is never more than 10% as the current quark mass is varied from the u/d region to the b region.

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arXiv2003

Covariant QCD Modeling of Light Meson Physics

We summarize recent progress in soft QCD modeling based on the set of Dyson--Schwinger equations truncated to ladder-rainbow level. This covariant approach to hadron physics accommodates quark confinement and implements the QCD one-loop renormalization group behavior. We compare the dressed quark propagator, pseudoscalar and vector meson masses as a function of quark mass, and the rho -> pi pi coupling to recent lattice-QCD data. The error in the Gell-Mann--Oakes--Renner relation with increasing quark mass is quantified by comparison to the exact pseudoscalar mass relation as evaluated within the ladder-rainbow Dyson-Schwinger model.

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arXiv2001

Mesons as Bound States of Confined Quarks: Zero and Finite Temperature

We survey recent work on the properties and decays of mesons as bound states of confined quarks at both zero and finite temperature. The framework for these investigations is the set of QCD Dyson--Schwinger equations truncated to ladder-rainbow level. The infrared structure of the ladder-rainbow kernel is described by two parameters; the ultraviolet behavior is fixed by the one-loop renormalizaton group behavior of QCD. The work is restricted to the $u$, $d$ and $s$ quark sector and allows a Poincaré-covariant study of the masses and electroweak decay constants of the ground state pseudoscalars and vectors: $π$, $K$, $ρ/ω$, $K^\star$ and $ϕ$. Within the impulse approximation, we summarize results for the $π$ and $K$ charge form factors. Their timelike behavior exhibits the vector meson production resonances and from this the associated vector meson strong decay constants are extracted. The confining property of the quark self-energy dynamically produced in this work prevents the appearance of spurious $\bar{q}q$ production effects. The finite temperature behavior of this model, and closely related ones, is summarized for: the chiral restoration transition, the deconfinement transition, the $T$-dependence of the spatial meson mode masses, and the $T$-dependence of selected electroweak and strong decay widths. The $T$-dependence obtained for meson masses is compared to results from lattice QCD.

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arXiv2001

Soft QCD Modeling of Meson Electromagnetic Form Factors

We summarize recent progress in soft QCD modeling based on the set of Dyson--Schwinger equations truncated to ladder-rainbow level. We pay particular attention to electromagnetic elastic and transition form factors of the pion. This covariant approach accommodates quark confinement and implements the QCD one-loop renormalization group behavior. The dressed quark propagators are compared to the most recent lattice-QCD data.

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