Spectrum of Physical States in a Dual-Resonance Model

Abstract

The dual-resonance model entails an exponentially growing resonance spectrum for the hadrons. It is well known that not all the states which achieve the factorization are physical ones; there are spurious and ghost states among them. We give a general formula for counting the ghost states at any given mass value and also an asymptotic expression for the ghost spectrum. The Virasoro model, in which the leading trajectory intercept is unity, is not considered here. A method for constructing the subspace of real states, which is orthogonal to the space of spurious states, is also given. After removing the ghost states from the real states, the remaining ones are taken as physical states, which then constitute the resonance spectrum. Implications of this resonance spectrum in the statistical approach are briefly discussed.