Emission Spectrum of Fundamental Strings: An Algebraic Approach

We formulate a linear difference equation which yields averaged semi-inclusive decay rates for arbitrary, not necessarily large, values of the masses. We show that the rates for decays M → m+M ′ of typical heavy open strings are independent of the masses M and m, and compute the “mass deffect” M−m−M ′. For closed strings we find decay rates proportional to Mm(1−D)/2 R , wheremR is the reduced mass of the decay products. Our method yields exact interaction rates valid for all mass ranges and may provide a fully microscopic basis, not limited to the long string approximation, for the interactions in the Boltzmann equation approach to hot string gases.