arXiv subjects

P. Maris

Publications and source records attributed to P. Maris.

At least 109 records · Page 6Linked to original sources

arXiv2000

Continuum QCD and light mesons

The ladder-rainbow truncation of the set of Dyson-Schwinger equations is used to study light mesons. The parameters in the effective interaction are constrained by the chiral condensate and f_π; the current quark masses are fitted to m_πand m_K. The dressed quark propagators are in qualitative agreement with recent lattice-QCD results at low q^2 while having the correct perturbative behavior at large q^2. The resulting vector meson masses are within 5% of the experimental values. The obtained electromagnetic form factors and strong and electroweak coupling constants are also in good agreement with the data. At finite temperature, this truncation leads to a mean-field chiral phase transition. The spatial pion mass is almost constant below this transition, but rises with T close to and above T_c. The mass of its chiral partner, an idealized sigma meson, decreases with T until T_c, where it becomes degenerate with the pion.

nucl-th↗

arXiv2000

Dyson-Schwinger calculations of meson form factors

The ladder-rainbow truncation of the set of Dyson-Schwinger equations is used to study the pion and kaon electromagnetic form factors and the $γ^\star π^0 γ$ transition form factor in impulse approximation. With model parameters previously fixed by the pseudoscalar meson masses and decay constants, the obtained form factors are in good agreement with the data.

nucl-th↗

arXiv2000

The $π$, $K^+$, and $K^0$ electromagnetic form factors

The rainbow truncation of the quark Dyson-Schwinger equation is combined with the ladder Bethe-Salpeter equation for the meson amplitudes and the dressed quark-photon vertex in a self-consistent Poincaré-invariant study of the pion and kaon electromagnetic form factors in impulse approximation. We demonstrate explicitly that the current is conserved in this approach and that the obtained results are independent of the momentum partitioning in the Bethe-Salpeter amplitudes. With model gluon parameters previously fixed by the condensate, the pion mass and decay constant, and the kaon mass, the charge radii and spacelike form factors are found to be in good agreement with the experimental data.

nucl-th↗

arXiv2000

T-dependence of pseudoscalar and scalar correlations

Inhomogeneous pseudoscalar and scalar Bethe-Salpeter equations solved using a renormalisation-group-improved rainbow-ladder truncation exhibit bound state poles below and above T_c, the critical temperature for chiral symmetry restoration. Above T_c the bound state amplitudes are identical, as are the positions and residues of the pseudoscalar and scalar poles in the vertices. In the chiral limit the pi^0 -> gamma gamma coupling vanishes at T_c, as do f_pi, m_sigma, g_{sigma pi pi}. For light current-quark masses the 2-pi decay channel of the isoscalar-scalar meson remains open until very near T_c, and the widths of the dominant pion decay modes remain significant in the vicinity of the crossover.

nucl-th↗

arXiv1999

The Quark-Photon Vertex and the Pion Charge Radius

The rainbow truncation of the quark Dyson-Schwinger equation is combined with the ladder Bethe-Salpeter equation for the dressed quark-photon vertex to study the low-momentum behavior of the pion electromagnetic form factor. With model gluon parameters previously fixed by the pion mass and decay constant, the pion charge radius $r_π$ is found to be in excellent agreement with the data. When the often-used Ball-Chiu Ansatz is used to construct the quark-photon vertex directly from the quark propagator, less than half of $r_π^2$ is generated. The remainder of $r^2_π$ is seen to be attributable to the presence of the $ρ$-pole in the solution of the ladder Bethe-Salpeter equation.

nucl-th↗

arXiv1999

Calculating the critical exponents of the chiral phase transition

We calculate the critical exponents of the chiral phase transition at nonzero temperature using the thermal and chiral susceptibilities. We show that within a class of confining Dyson-Schwinger equation (DSE) models the transition is mean field, and that an accurate determination of the critical exponents requires extremely small values of the current-quark mass, several order of magnitude smaller than realistic up- and down-quark masses. In general, rainbow truncation models of QCD exhibit mean field exponents as a result of the gap equation's fermion substructure.

nucl-th↗

arXiv1999

The quark-photon vertex and meson electromagnetic form factors

The ladder Bethe-Salpeter solution for the dressed photon-quark vertex is used to study the low-momentum behavior of the pion electromagnetic and the $γ^\star π^0 γ$ transition form factors. With model parameters previously fixed by light meson masses and decay constants, the low-momentum slope of both form factors is in excellent agreement with the data. In comparison, the often-used Ball-Chiu Ansatz for the vertex is found to be deficient; less than half of the obtained $r_π^2$ is generated by that Ansatz while the remainder of the charge radius could be attributed to the tail of the $ρ$ resonance.

nucl-th↗

arXiv1999

Dyson-Schwinger studies of meson masses and decay constants

The masses and decay constants of the light mesons are studied within a ladder-rainbow truncation of the set of Dyson-Schwinger equations using a model 2-point gluon function. The one phenomenological parameter and two current quark masses are fitted to reproduce $f_π$, $m_π$ and $m_K$. Our results for $f_K$, and for the vector mesons $ρ$, $ϕ$, and $K^\star$ are in good agreement with the experimental values.

nucl-th↗

arXiv1998

Heavy Meson Observables and Dyson-Schwinger Equations

Dyson-Schwinger equation (DSE) studies show that the b-quark mass-function is approximately constant, and that this is true to a lesser extent for the c-quark. These observations provide the basis for a study of the leptonic and semileptonic decays of heavy pseudoscalar mesons using a ``heavy-quark'' limit of the DSEs. When exact, this limit reduces the number of independent form factors. Semileptonic decays with light mesons in the final state are also accessible because the DSEs provide a description of light-quark propagation characteristics and light-meson structure. A description of B-meson decays is straightforward, however, the study of decays involving the D-meson indicates that c-quark mass-corrections are quantitatively important.

nucl-th↗

arXiv1998

Chemical potential dependence of pi and rho properties

Using a confining, Dyson-Schwinger equation model of QCD at finite temperature (T) and chemical potential (mu) we study the behaviour of , m_pi, f_pi and the masses of the rho- and phi-mesons. For each of these quantities there is a necessary anticorrelation between its response to T and its response to mu. (- ) and f_pi decrease with T and increase with mu; m_pi is almost insensitive to T and mu until very near the border of the confinement domain; and the mass of the longitudinal component of the vector mesons increases with T and decreases with mu. At T=0, the rho-meson mass is reduced by approximately 15% at nuclear matter density. These results are a consequence of the necessary momentum-dependence of the dressed-quark self-energy.

nucl-th↗

arXiv1997

Heavy- to light-meson transition form factors

Semileptonic heavy -> heavy and heavy -> light meson transitions are studied as a phenomenological application of a heavy-quark limit of Dyson-Schwinger equations. Employing two parameters: E, the difference between the mass of the heavy meson and the effective-mass of the heavy quark; and Lambda, the width of the heavy-meson Bethe-Salpeter amplitude, we calculate f_+(t) for all decays on their entire kinematically accessible t-domain. Our study favours f_B in the range 0.135-0.17 GeV and with E=0.44 GeV and 1/Lambda = 0.14 fm we obtain f_+^{B pi}(0) = 0.46. As a result of neglecting 1/m_c-corrections, we estimate that our calculated values of ρ^2 = 0.87 and f_+^{DK}(0)=0.62 are too low by approximately 15%. However, the bulk of these corrections should cancel in our calculated values of Br(D -> πl nu)/Br(D -> K l nu)=0.13 and f_+^{D pi}(0)/f_+^{DK}(0) = 1.16.

nucl-th↗

arXiv1997

Differences between heavy and light quarks

The quark Dyson-Schwinger equation shows that there are distinct differences between light and heavy quarks. The dynamical mass function of the light quarks is characterised by a sharp increase below 1 GeV, whereas the mass function of the heavy quarks is approximately constant in this infrared region. As a consequence, the heavy-meson masses increase linearly with the current-quark masses, whereas the light pseudoscalar meson masses are proportional to the square root of the current-quark masses.

nucl-th↗

arXiv1997

Leptonic and semileptonic decays of heavy mesons

A heavy-quark limit of the Dyson-Schwinger equations is introduced and used in an exploratory study of leptonic and semileptonic decays of heavy mesons. The application of this framework to heavy-to-light semileptonic decays, which require a good knowledge of light-quark propagation characteristics and light-meson bound state amplitudes, is illustrated.

nucl-th↗

arXiv1997

pi- and K-meson Bethe-Salpeter Amplitudes

Independent of assumptions about the form of the quark-quark scattering kernel, K, we derive the explicit relation between the flavour-nonsinglet pseudoscalar meson Bethe-Salpeter amplitude, Gamma_H, and the dressed-quark propagator in the chiral limit. In addition to a term proportional to gamma_5, Gamma_H necessarily contains qualitatively and quantitatively important terms proportional to gamma_5 gamma.P and gamma_5 gamma.k k.P, where P is the total momentum of the bound state. The axial-vector vertex contains a bound state pole described by Gamma_H, whose residue is the leptonic decay constant for the bound state. The pseudoscalar vertex also contains such a bound state pole and, in the chiral limit, the residue of this pole is related to the vacuum quark condensate. The axial-vector Ward-Takahashi identity relates these pole residues; with the Gell-Mann--Oakes-Renner relation a corollary of this identity. The dominant ultraviolet asymptotic behaviour of the scalar functions in the meson Bethe-Salpeter amplitude is fully determined by the behaviour of the chiral limit quark mass function, and is characteristic of the QCD renormalisation group. The rainbow-ladder Ansatz for K, with a simple model for the dressed-quark-quark interaction, is used to illustrate and elucidate these general results. The model preserves the one-loop renormalisation group structure of QCD. The numerical studies also provide a means of exploring procedures for solving the Bethe-Salpeter equation without a three-dimensional reduction.

nucl-th↗

arXiv1997

Pion mass and decay constant

Independent of assumptions about the form of the quark-antiquark scattering kernel we derive the explicit relation between the pion Bethe-Salpeter amplitude, Gamma_pi, and the quark propagator in the chiral limit; Gamma_pi necessarily involves a non-negligible gamma_5 gamma.P term (P is the pion four-momentum). We also obtain exact expressions for the pion decay constant, f_pi, and mass, both of which depend on Gamma_pi; and demonstrate the equivalence between f_pi and the pion Bethe-Salpeter normalisation constant in the chiral limit. We stress the importance of preserving the axial-vector Ward-Takahashi identity in any study of the pion itself, and in any study whose goal is a unified understanding of the properties of the pion and other hadronic bound states.

nucl-th↗

arXiv1997

Semileptonic decays of heavy mesons

The semileptonic and leptonic decays of heavy mesons are studied as a phenomenological application and exploration of a heavy-quark limit of Dyson-Schwinger equations. The single form factor, $ξ(w)$, which characterises the semileptonic decay in this limit, is calculated and compares well with recent experimental extractions. We obtain a lower bound of 1/3 on the slope-parameter $ρ^2 \equiv -ξ^\prime(1)$, which, in calculations with realistic input, is exceeded by a great deal: agreement with experimental data requiring $ρ^2 \sim 1.2 - 1.6$. The flavour and momentum dependence of the light-quark propagators has observable consequences.

nucl-th↗

arXiv1996

The Influence of the Full Vertex and Vacuum Polarization on the Fermion Propagator in QED3

We investigate the influence of the full vacuum polarization and vertex function on the fermion propagator, using the coupled Dyson--Schwinger equations for the photon and fermion propagator. We show that, within a range of vertex functions, the general behavior of the fermion propagator does not depend on the exact details of the vertex, both in the massless and in the massive phase. Independent of the precise vertex function, there is a critical number of fermion flavors for dynamical mass generation in $(2+1)$-dimensional QED. A consistent treatment of the vacuum polarization is essential for these results.

hep-ph↗

arXiv1995

Dynamical Mass Generation in QED3 with Chern--Simons Term

In (2+1)-dimensional QED with a Chern-Simons term, we study dynamical breaking of chiral symmetry, using the Dyson--Schwinger equation for the fermions. There is a region in parameter space were dynamical chiral symmetry breaking occurs, just as in pure QED3 (without Chern--Simons term); outside this region, this chiral symmetry breaking solution does not exists. Our results, both numerically and analytically, show that the chiral phase transition is a discontinuous first-order transition.

hep-ph↗