arXiv subjects

J. J. M. Verbaarschot

Publications and source records attributed to J. J. M. Verbaarschot.

112 records · Page 7Linked to original sources

arXiv1993

Spectral Density of the QCD Dirac Operator near Zero Virtuality

We investigate the spectral properties of a random matrix model, which in the large $N$ limit, embodies the essentials of the QCD partition function at low energy. The exact spectral density and its pair correlation function are derived for an arbitrary number of flavors and zero topological charge. Their microscopic limit provide the master formulae for sum rules for the inverse powers of the eigenvalues of the QCD Dirac operator as recently discussed by Leutwyler and Smilga.

hep-th↗

arXiv1993

Quark Propagation in the Random Instanton Vacuum

This is the first of a series of papers devoted to a systematic study of QCD correlation functions in a framework of 'instanton vacuum' models. The topic of this paper is to work out approximate formulae for quark propagators in a multi-instanton environment. As an application, and also as a necessary step toward understanding the correlation functions, we study the propagators of scalar and spinor quarks, using the simplest possible model, the so called 'random instanton vacuum' (RIV). Results related to heavy-light mesons, are found to be very consistent with phenomenology.

hep-ph↗

arXiv1993

Mesonic Correlation Functions in the Random Instanton Vacuum

A general model-independent discussion of mesonic correlation functions is given. We derive new inequalities, including one stronger than Weingarten's inequality. Mesonic correlation functions are calculated in the random instanton vacuum and are compared with phenomenological expectations and lattice results. Both diagonal and non-diagonal correlators of all strange and light flavored currents, as well as the most important unflavored ones are considered. Our results are used to extract the masses and the coupling constants of the corresponding mesons. Not only the qualitative behaviour is reproduced in all channels, but in several channels the model works with amazing accuracy

hep-ph↗

arXiv1992

Random matrix theory and spectral sum rules for the Dirac operator in QCD

We construct a random matrix model that, in the large $N$ limit, reduces to the low energy limit of the QCD partition function put forward by Leutwyler and Smilga. This equivalence holds for an arbitrary number of flavors and any value of the QCD vacuum angle. In this model, moments of the inverse squares of the eigenvalues of the Dirac operator obey sum rules, which we conjecture to be universal. In other words, the validity of the sum rules depends only on the symmetries of the theory but not on its details. To illustrate this point we show that the sum rules hold for an interacting liquid of instantons. The physical interpretation is that the way the thermodynamic limit of the spectral density near zero is approached is universal. However, its value, $i.e.$ the chiral condensate, is not.

hep-th↗