On Semi-classical Pion Production in Heavy Ion Collisions

In high energy heavy ion collisions the pion multiplicity is large, and one might expect that pions are radiated semi-classically. The axial symmetry of the collision and approximately zero isotopic spin of the colliding nuclei result then in peculiar isotopic spin – azimuth correlations of the produced pions. These correlations are easy to test – and should be tested Alexander von Humboldt Forschungspreisträger Central collisions of heavy ions at high energies are expected to produce many pions (see for instance [1]), so many that the typical number of pion quanta per unit cell of phase space may substantially exceed unity. Under such circumstances, one may speculate about the possibility that, in the early stages of the collisions, a classical pion field develops, before subsequently decaying into pions [2, 3, 4]. One interesting possibility showing how this could happen following chiral symmetry restoration has been investigated recently [5]. Independently of the detailed dynamics, the formation of an intermediate classical pion field could result in certain correlations in the production of pions with definite isospin components. The main point of this letter is to show that, indeed, rather peculiar correlations can be indicated from symmetry considerations only – the role of dynamics is to guarantee that the pion radiation is so strong that it can be treated semi-classically; testing the correlations is a way to check that hypothesis. These correlations, quite distinct from the much studied Bose Einstein correlations, find their origin in the special correlations which develop between spatial and isospin coordinates in the solution of the non linear field equations obeyed by classical pion fields. Mathematically, one can write the amplitude of N pions’ production with the help of the Lehmann–Symanzik–Zimmermann formula, where the N -point pion Green function is presented through the functional integral over the pion fields: A1N (k1 . . . kN ) = lim k2 n→m 2 π ∫