arXiv subjects

Reginald T. Cahill

Publications and source records attributed to Reginald T. Cahill.

43 records · Page 3Linked to original sources

arXiv1996

Pregeometric modelling of the spacetime phenomenology

At present we have only the very successful but phenomenological Einstein geometrical modelling of the spacetime phenomenon. This geometrical model provides a `container' for other theories, in particular the quantum field theories. Here we report progress in developing a {\em Heraclitean Quantum System}. This is a particular pregeometric theory for space and time in which no classical or geometric structures are assumed, but rather the emergence of such phenomena is sought.

gr-qc↗

arXiv1996

The global colour model of QCD and its relationship to the NJL model, chiral perturbation theory and other models

The Global Colour Model (GCM) of QCD is a very successful model. Not only is it formally derivable from QCD but under various conditions it reduces to the NJL model and also to Chiral Perturbation Theory, and to other models. Results presented include the effective gluon propagator, the difference between constituent and exact quark propagators, various meson and nucleon observables, a new mass formula for the Nambu-Goldstone mesons of QCD, and the change in the MIT bag constant in nuclei.

hep-ph↗

arXiv1996

The Pion Mass Formula

The often used Gell-Mann-Oakes-Renner mass formula for Nambu-Goldstone (NG) bosons in QCD, such as the pions, involves the condensate $<\overline{q}q>$, $f_π$ and the quark current masses. Within the context of the Global Colour Model (GCM) for QCD a manifestly different formula was recently found by Cahill and Gunner. Remarkably Langfeld and Kettner have shown the two formula to be equivalent. Here we note that the above recent analyses refer to the constituent pion and not the exact pion, even within the GCM. Further we generalise the Langfeld-Kettner identity to include the full response of the constituent quark propagators to the presence of a non-zero (and running) quark current mass.

hep-ph↗

arXiv1995

A New Mass Formula for NG Bosons in QCD

An often used mass formula for Nambu-Goldstone (NG) bosons in QCD, such as the pions, involves the condensate $<\overline{q}q>$, $f_π$ and the quark current masses. We argue, within the context of the Global Colour Model to QCD, that this expression is wrong. Analysis of the interplay between the Dyson-Schwinger equation for the constituent quark effect and the Bethe-Salpeter equation for the NG boson results in a new mass formula.

hep-ph↗

arXiv1995

Quark and Gluon Propagators from Meson Data

We report robust calculations of various low energy QCD hadronic properties. We use a multi-rank separable expansion for the gluon propagator which greatly facilitates the numerical computations within the Global Colour Model for QCD. The parameters for the propagators are determined by fitting experimental values for $f_π$ and the $π$ and $a_1$ meson masses.

hep-ph↗

arXiv1993

Quark-gluon vertex and structure of mesons and diquarks

*REVISED VERSION* Two quark propagators with different analytic structure are employed in on and off mass-shell Bethe-Salpeter type equations for the pion and scalar diquark form-factors. One of the quark propagators has been calculated with the inclusion of a trivial quark-gluon vertex and, as a consequence, contains a complex conjugate pair of logarithmic branch points. The other quark propagator includes a non-trivial vertex ansatz and is entire, with an essential singularity at infinity. The different quark propagators lead to qualitatively different diquark form-factors.

hep-ph↗

arXiv1993

pi-pi scattering in a QCD based model field theory

A model field theory, in which the interaction between quarks is mediated by dressed vector boson exchange, is used to analyse the pionic sector of QCD. It is shown that this model, which incorporates dynamical chiral symmetry breaking, asymptotic freedom and quark confinement, allows one to calculate $f_π$, $m_π$, $r_π$ and the partial wave amplitudes in $π$-$π$ scattering and obtain good agreement with the experimental data, with the latter being well described up to energies \mbox{$E\simeq 700$ MeV}.

hep-ph↗