Duality and Single-Particle Production

Following Mueller, we relate the single-particle production cross section for the process $a+b\to x+$ anything to a discontinuity of the six-line amplitude $a+b+\overline{x}\to a+b+\overline{x}$. Using the dual-resonance model for the six-line amplitude, we obtain an explicit form for the production cross section at high energies. The formula exhibits the expected features of limiting fragmentation, an invariant central region, and triple-Regge asymptotic behavior. In addition, it has a universal cutoff in transverse momentum of the form $e^{-4b{p_{\perp }}^2}$ in the central region, where $b$ is the universal trajectory slope. We discuss for particle production some general consequences of duality in the missing mass. For example, we relate the behavior of two-body scattering amplitudes at wide angles to the transverse-momentum dependence of production cross sections. Finally, we discuss the possible experimental relevance of our results.