Semiclassical theory of high energy collisions and RHIC puzzles

The semiclassical theory of tunneling through the topological barrier in gauge theories was until recently focused only on virtual processes in the vacuum, described by the zero-energy Euclidean solutions - the instantons. Its applications for high energy collisions in a QCD context are relatively recent. Like in quantum mechanics, the semiclassical path naturally splits into a sub-barrier Euclidean part, followed by a non-trivial over-the-barrier Minkowski evolution. These two are separated by the familiar turning states, in a form of purely magnetic clusters. Recent technical developments included simple analytic solution of the Yang-Mills equations for the turning states, analytic and numerical solutions for their explosions (in Minkowski time), and recently an analytic solution of the Dirac equation in the field of exploding cluster, describing production of 2N_f light quarks. There is also progress in calculation of the cross section itself. The phenomenological part of the talk includes brief discussion of possible cluster formation in hadronic (pp, γ^∗p) reactions, as a part of "soft Pomeron". We also briefly review puzzling results of the first RHIC runs, and speculate to which extent high rate of quark pair production and other features of topological clusters may help to explain those puzzles. Especially important is recently pointed out observation that coherence of classical glue and the specific geometry of the exploding clusters may significantly enhance the so called jet quenching.