In high-energy collisions, the soft $p_T$ spectra for produced mesons contain information on the motion of the quarks and antiquarks which form these mesons. We extract this information in the context of the flux-tube model with Schwinger's mechanism for particle production. We solve the Dirac equation for quarks (and antiquarks) inside a flux tube, described as an infinitely long cylinder of radius $r_0$, with a uniform electric field $\kappa$ inside it. We calculate the production rate of quarks, antiquarks, and pions as a function of $p_T$. We study first a sharp transverse boundary, and find that the result deviates from the experimental soft $p_T$ spectra, with its characteristic exponential fall. We therefore introduce a scalar potential which varies smoothly in the radial direction. With simplifying assumptions we show how the experimental $p_T$ spectra of pions, created in $p-p$ collisions, determine the transverse wave function and the scalar potential that would produce it. The classical turning point for this potential is of the order of 0.6 fm. However, the potential flattens out considerably beyond that point. The wave function decays as $r^{\frac{-3\mathrm{}}{2}}$ and there appears to be a considerable excursion of the quark into regions far beyond the classical turning point.

• Received 6 March 1992

DOI:https://doi.org/10.1103/PhysRevD.46.997