Prompt quark production by exploding sphalerons

Following recent works on the production and subsequent explosive decay of QCD sphaleronlike clusters, we discuss the mechanism of quark pair production in this process. We first show how the gauge field explosive solution of Luscher and Schechter can be achieved by noncentral conformal mapping from the O(4)-symmetric solution. Our main result is a new solution to the Dirac equation in real time in this configuration, obtained by the same inversion of the fermion O(4) zero mode. It explicitly shows how the quark acceleration occurs, starting from the spherically O(3)-symmetric zero energy chiral quark state to the final spectrum of nonzero energies. The sphaleronlike clusters with any Chern-Simons number always produce (Formula presented) quarks, and the antisphaleron-like clusters the opposite chirality. The result are relevant for hadron-hadron and nucleus-nucleus collisions at large (Formula presented) wherein such clusters can be produced.