The absorptive line shape of hadronic atoms

Abstract

The exact line shape for all energies is derived analytically in the limit of negligible nuclear dimensions. The shape deviates from the Breit-Wigner form. The high-energy tail of the line has a universal shape, independent of the absorptive strength. The tails are different for different initial states, however. The integrated line strength diverges logarithmically. Renormalization of the hadron wavefunction by strong interactions leads to the usual shape near resonance and restores convergence for very large energies. The results resolve a logical inconsistency in the normal analysis of hadronic atoms and are of practical importance. It is shown that bound hadronic states (e.g., Y 0 ∗ ) give natural contributions in the high energy region. Numerical illustrations are given.