Dominguez - Quantum Chromodynamics Sum Rules

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This book is intended for readers with a good knowledge of quantum field theory, in general, and quantum chromodynamics (QCD), in particular. It is addressed to readers planning to start research in QCD in the framework of sum rules. Currently, there are two major approaches to obtain information in QCD, i.e. lattice QCD (LQCD) and QCD sum rules (QCDSR). The latter is the subject matter of this book. It deals with the current state-of-the-art formulation of QCDSR in the complex squared energy plane, called finite energy sum rules (FESR). This allows for a relation between QCD and hadronic physics following from Cauchys residue theorem in that plane. As a result, current FESR determinations of a plethora of QCD and hadronic parameters rival in precision with those from LQCD. This healthy competition is extremely beneficial for our understanding of the strong interactions at the most elementary level.

This book is not a review of past work on QCDSR. The pioneering formulation of QCDSR in the framework of integral transforms, e.g. Laplace and Hilbert, while having played a fundamental role in the development of the subject, is currently no match for the precision achieved from FESR. In addition, and most importantly, the FESR parameter related to quark-gluon deconfinement (at finite temperature) has recently been shown to be related to the Polyakov loop of LQCD. This brings these two approaches into a beneficial partnership.

The topics discussed in this book concern mostly QCD at zero temperature. A last chapter on finite temperature QCDSR has been kept short, as there is a recent comprehensive review on this subject. The extension of QCDSR to include hadronic/QCD matter in the presence of very strong magnetic fields is not covered here. This new research direction is currently in a state of flux, so the reader is advised to consult the literature.

The author wishes to thank his QCD sum rule collaborators: Alejandro Ayala, Jose Bordes, Pietro Colangelo, Marcelo Loewe, Giuseppe Nardulli , Nasrallah Nasrallah, Nello Paver, Jose Pearrocha, Eduardo de Rafael, J. Cristobal Rojas, Karl Schilcher, Joan Sola, Hubert Spiesberger, and Cristian Villavicencio.

Special thanks are due to Marcelo Loewe for reading the manuscript, and to Alexes Mes and Jed Stephens for providing Eq. ( ).

This work was supported in part by the University of Cape Town, (South Africa), and by the Alexander von Humboldt Foundation (Germany).