The deconfinement phase transition, hadronization and the NJL model

One of the confident predictions of QCD is that at sufficiently high temperature and/or density, hadronic matter should undergo a thermodynamic phase transition to a colour deconfined state of matter - popularly called the Quark-Gluon Plasma (QGP). In low energy effective theories of Quantum Chromodynamics (QCD), one usually talks of the chiral transition for which a well defined order parameter exists. We investigate the dissociation of pions and kaons in a medium of hot quark matter decsribed by the Nambu - Jona Lasinio (NJL) model. The decay widths of pion and kaon are found to be large but finite at temperature much higher than the critical temperature for the chiral (or deconfinement) transition, the kaon decay width being much larger. Thus pions and even kaons (with a lower density compared to pions) may coexist with quarks and gluons at such high temperatures. On the basis of such premises, we investigate the process of hadronization in quark-gluon plasma with special emphasis on whether such processes shed any light on acceptable low energy effective theories of QCD.Comment: Invited talk at Hadrons'99, Coimbra, Portugal. To appear in the Proceedings "Hadron Physics : Effetive Theories of Low Energy QCD" (Ed. A. H. Blin), American Institute of Physics. 7 pages RevTeX, with 4 embedded postscript figure

Revisiting Synthesis for One-Counter Automata

We study the (parameter) synthesis problem for one-counter automata with parameters. One-counter automata are obtained by extending classical finite-state automata with a counter whose value can range over non-negative integers and be tested for zero. The updates and tests applicable to the counter can further be made parametric by introducing a set of integer-valued variables called parameters. The synthesis problem for such automata asks whether there exists a valuation of the parameters such that all infinite runs of the automaton satisfy some omega-regular property. Lechner showed that (the complement of) the problem can be encoded in a restricted one-alternation fragment of Presburger arithmetic with divisibility. In this work (i) we argue that said fragment, called AERPADPLUS, is unfortunately undecidable. Nevertheless, by a careful re-encoding of the problem into a decidable restriction of AERPADPLUS, (ii) we prove that the synthesis problem is decidable in general and in N2EXP for several fixed omega-regular properties. Finally, (iii) we give a polynomial-space algorithm for the special case of the problem where parameters can only be used in tests, and not updates, of the counter