arXiv subjects

Pieter Maris

Publications and source records attributed to Pieter Maris.

84 records · Page 5Linked to original sources

arXiv2002

Meson elastic and transition form factors

The Dyson-Schwinger equations of QCD, truncated to ladder-rainbow level, are used to calculate meson form factors in impulse approximation. The infrared strength of the ladder-rainbow kernel is described by two parameters fitted to the chiral condensate and f_pi; the ultraviolet behavior is fixed by the QCD running coupling. This obtained elastic form factors F_pi(Q^2) and F_K(Q^2) agree well with the available data. We also calculate the rho to pi gamma and K* to K gamma transition form factors, which are useful for meson-exchange models.

nucl-th↗

arXiv2002

Chiral symmetry breaking in (2+1) dimensional QED

We study dynamical mass generation in QED in (2+1) dimensions using Hamiltonian lattice methods. We use staggered fermions, and perform simulations with explicit dynamical fermions in the chiral limit. We demonstrate that a recently developed method to reduce the fermion sign problem can successfully be applied to this problem. Our results are in agreement with both the strong coupling expansion and with Euclidean lattice simulations.

hep-lat↗

arXiv2001

Chirally symmetric quark description of low energy π-πscattering

Weinberg's theorem for π-πscattering, including the Adler zero at threshold in the chiral limit, is analytically proved for microscopic quark models that preserve chiral symmetry. Implementing Ward-Takahashi identities, the isospin 0 and 2 scattering lengths are derived in exact agreement with Weinberg's low energy results. Our proof applies to alternative quark formulations including the Hamiltonian and Euclidean space Dyson-Schwinger approaches. Finally, the threshold π-πscattering amplitudes are calculated using the Dyson-Schwinger equations in the rainbow-ladder truncation, confirming the formal derivation.

hep-ph↗

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

K_{l3} transition form factors

The rainbow truncation of the quark Dyson-Schwinger equation is combined with the ladder Bethe-Salpeter equation for the meson bound state amplitudes and the dressed quark-W vertex in a manifestly covariant calculation of the K_{l3} transition form factors and decay width in impulse approximation. With model gluon parameters previously fixed by the chiral condensate, the pion mass and decay constant, and the kaon mass, our results for the K_{l3} form factors and the kaon semileptonic decay width are in good agreement with the experimental data.

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arXiv1999

Bethe-Salpeter Study of Vector Meson Masses and Decay Constants

The masses and decay constants of the light vector mesons $ρ/ω$, $ϕ$ and $K^\star$ are studied within a ladder-rainbow truncation of the coupled Dyson-Schwinger and Bethe-Salpeter equations of QCD with a model 2-point gluon function. The approach is consistent with quark and gluon confinement, reproduces the correct one-loop renormalization group behavior of QCD, generates dynamical chiral symmetry breaking, and preserves the relevant Ward identities. The one phenomenological parameter and two current quark masses are fixed by requiring that the calculated $f_π, m_π$ and $m_K$ are correct. The resulting $f_K$ is within 3% of the experimental value. For the vector mesons, all eight transverse covariants are included and the dominant ones are identified; the complete angle dependence of the amplitudes is also retained. The calculated values for the masses $m_ρ, m_ϕ$ and $m_{K^\star}$ are within 5%, while the decay constants $f_ρ, f_ϕ$ and $f_{K^\star}$ for electromagnetic and leptonic decays are within 10% of the experimental values.

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arXiv1998

Mean field exponents and small quark masses

We demonstrate that the restoration of chiral symmetry at finite-T in a class of confining Dyson-Schwinger equation (DSE) models of QCD is a mean field transition, and that an accurate determination of the critical exponents using the chiral and thermal susceptibilities requires very small values of the current-quark mass: log_{10}(m/m_u) < -5. Other classes of DSE models characterised by qualitatively different interactions also exhibit a mean field transition. Incipient in this observation is the suggestion that mean field exponents are a result of the gap equation's fermion substructure and not of the interaction.

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arXiv1998

Infrared Behaviour of Propagators and Vertices

We elucidate constraints imposed by confinement and dynamical chiral symmetry breaking on the infrared behaviour of the dressed-quark and -gluon propagators, and dressed-quark-gluon vertex. In covariant gauges the dressing of the gluon propagator is completely specified by P(k^2):= 1/[1+Pi(k^2)], where Pi(k^2) is the vacuum polarisation. In the absence of particle-like singularities in the dressed-quark-gluon vertex, extant proposals for the dressed-gluon propagator that manifest P(k^2=0)=0 and Max[P(k^2)]~10 neither confine quarks nor break chiral symmetry dynamically. This class includes all existing estimates of P(k^2) via numerical simulations.

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arXiv1998

QCD bound states and their response to extremes of temperature and density

We describe the application of Dyson-Schwinger equations to the calculation of hadron observables. The studies at zero temperature (T) and quark chemical potential (mu) provide a springboard for the extension to finite-(T,mu). Our exemplars highlight that much of hadronic physics can be understood as simply a manifestation of the nonperturbative, momentum-dependent dressing of the elementary Schwinger functions in QCD.

nucl-th↗

arXiv1998

Pseudovector components of the pion, pi^0 -> gamma gamma, and F_pi(q^2)

As a consequence of dynamical chiral symmetry breaking the pion Bethe-Salpeter amplitude necessarily contains terms proportional to gamma_5 gamma.P and gamma_5 gamma.k, where k is the relative and P the total momentum of the constituents. These terms are essential for the preservation of low energy theorems, such as the Gell-Mann--Oakes-Renner relation and those describing anomalous decays of the pion, and to obtaining an electromagnetic pion form factor that falls as 1/q^2 for large q^2, up to calculable ln(q^2)-corrections. In a simple model, which correlates low- and high-energy pion observables, we find q^2 F_pi(q^2) ~ 0.12 - 0.19 GeV^2 for q^2 >~10 GeV^2.

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arXiv1995

Four-Body Chiral Order Parameters in the Massless Fermion Phase

The fermion four-point functions and condensates as the chiral symmetry order parameters are calculated analytically in U(1) gauge theory in the massless phase. It is shown that in leading order of the loop expansion of the effective action, there is a critical coupling for the nonperturbative parity-invariant chirality-changing four-fermion functions; this critical coupling however is the same as that for dynamical mass generation. Therefore there is no breaking of chiral symmetry through the condensation of four-fermion functions below the critical coupling for dynamical mass generation for the fermions.

hep-ph↗

arXiv1995

First-order Phase Transition in Three-dimensional QED with Chern--Simons Term

We have studied the chiral phase transition in three-dimensional QED in the presence of a Chern--Simons term for the gauge field. There exists a phase where the chiral symmetry is broken dynamically and we have determined the critical line for this symmetry breaking as a function of the effective coupling and the strength of the additional Chern--Simons term. In the presence of a Chern--Simons term, the chiral phase transition turns out to be first order, in sharp contrast to the phase transition in pure three-dimensional QED.

hep-ph↗