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.Comment: 25 pages + 4 figures available upon request, SUNY-NTG-92/3

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.Comment: 18 pages, SUNY-NTG-92/4

Toward the Semiclassical Theory of the High Energy Heavy Ion Collisions

Sudden deposition of energy at the early stage of high energy heavy ion collisions makes virtual gluon fields real. The same is true for virtual vacuum fields $under$ the topological barrier, excited to real states $at$ or $above$ the barrier, gluomagnetic clusters of particular structure related to the $sphalerons$ of the electroweak theory. Semiclassically, these states play the role of the {\em ``turning points''}. After being produced they explode into a spherical shell of coherent field which then turn into several outgoing gluons. Furthermore, this explosions promptly produce quark pairs, as seen from explicit solution of the Dirac equation. The masses of such clusters depend on their size, and are expected to peak at $M\sim 3 GeV$. After we briefly review those consepts in a non-technical manner, we discuss what observable consequences the production of such clusters would make in the context of heavy ion collisions, especially at the RHIC energies. We discuss entropy and especially quark production, event-by-event fluctuations in collective effects like radial and elliptic flows and $J/\psi$ suppression. Coherent fields and their geometry increase the jet quenching, and we also point out the existene of ``explosive edge'' which jump-start collective effects and may affect unusual phenomena seen at RHIC at large $p_t$.Comment: Third version, substantially changed adding new sections and eliminating large part on jet quenching of the paper which brunched into a separate pape

Equation of State, Flow, Fluctuations and J/ψJ/\psi suppression

Radial flow observed at AGS/SPS energies is very strong, with collective velocities of matter reaching about 0.5c for central collisions of the heaviest ions. The lattice-based Equation of State (EOS) is however rather soft, due to the QCD phase transition. We show that both statements are consistent only if proper kinetic-based treatment of the freeze-out is made. In fact chemical and thermal freeze-out happen at quite different conditions, especially at SPS. Event-by-event fluctuations can shed new light on this problem. We also propose new model of "anomalous" $J/\psi$ suppression found for PbPb collisions, related it to prolonged lifetime of dense matter due the "softest point" of the EOS.Comment: Plenary Talk at Quark Matter 97, Tsukuba, Dec.199

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 accuracyComment: 43 pages + 9 figures available upon request, SUNY-NTG-92/4

Polymer Chains and Baryons in a Strongly Coupled Quark-Gluon Plasma

Recently there was a significant change of views on physical properties and underlying dynamics of Quark-Gluon Plasma at $T=170-350 MeV$, produced in heavy ion collisions at RHIC. Instead of being a gas of $q,g$ quasiparticles, a near-perfect liquid is observed. Also, precisely in this temperature interval, the interaction deduced from lattice studies is strong enough to support multiple binary bound states. This work is the first variational study of {\em multibody} bound states. We will consider: (i) ``polymer chains'' of the type $\bar q g g ..g q$; (ii) baryons $(qqq)$; (iii) closed (3-)chains of gluons $(ggg)$. We found that chains (i) form in exactly the same $T$ range as binary states, with the same binding {\em per bond}. The binding and $T$-range for diquarks, baryons and closed 3-chains are also established. We point out that the presence of chains, or possibly even a chain network, may drastically change the transport properties of matter, such as charm diffusion or jet energy loss. We further suggest that it seems to exist only for $T=(1-1.5)T_c$ and thus there may be a ``latent period'' for charm/jet quenching in RHIC collisions, while matter cools down to such $T$.Comment: New version submitted to Nuclear Physics A, with few changes in comments and figure

Toward the theory of strongly coupled Quark-Gluon Plasma

We review recent progress toward understanding of sQGP. The phenomenological part includes discussion of elliptic and conical flows at RHIC. Then we proceed to first quantum mechanical studies of manybody states at $T>Tc$, the ``polymeric chains'' $\bar q.g.g... q$ and baryons. A new model for sQGP is a classical dynamical system, in which color vector is changed via the Wong equation. First Molecular Dynamics (MD) results for its diffusion and viscosity are reported. Finally we speculate how strong correlations in matter may help solve puzzles related to jet quenching, both the magnitude and angular distribution.Comment: A plenary talk at Quark Matter 05, Budabest, Aug.200

What RHIC Experiments and Theory tell us about Properties of Quark-Gluon Plasma ?

This brief review summarizes the main experimental discoveries made at RHIC and then discusses their implications. The robust collective flow phenomena are well described by ideal hydrodynamics, with the Equation of State (EoS) predicted by lattice simulations. However the transport properties turned out to be unexpected, with rescattering cross section one-to-two orders of magnitude larger than expected from perturbative QCD. These and other theoretical developments indicate that Quark-Gluon Plasma (QGP) produced at RHIC, and probably in a wider temperature region $T_c<T<4T_c$, is not at all a weakly coupled quasiparticle gas, but is rather in a strongly coupled regime, sQGP for short. After reviewing two other ``strongly coupled systems'', (i) the strongly coupled supersymmetric theories studied via Maldacena duality; (ii) trapped ultra-cold atoms with very large scattering length, we return to sQGP and show that there should exist literally hundreds of bound states in it in the RHIC domain, most them colored. We then discuss recent ideas of their effect on the EoS, viscosity and jet quenching.Comment: Prepared for workshop on RHIC discoveries, BNL May 14,1

Two-loop Correction to the Instanton Density for the Double Well Potential

Feynman diagrams in the instanton background are used for the calculation of the tunneling amplitude, up to the two-loops order. Some mistakes made in the previous works are corrected. The same method is applied to the next-order corrections to the ground state wave function

Where the excess photons and dileptons in SPS nuclear collisions come from?

Recently the first single photon spectra from CERN energy heavy-ion collisions were reported by WA80, while NA34/3 and NA38 have obtained the spectra for dileptons with the mass up to 4-5 GeV. The production rates for photons and dileptons significantly increase when reactions involving the $A_1$ meson are included. However, with the conventional expansion scenario, the absolute yields are still significantly smaller than the observed ones. It may indicate that expansion in the ``mixed state" takes much more time