Emission Spectrum of Fundamental Strings: An Algebraic Approach

TL;DR

This paper develops an algebraic method to calculate decay rates of fundamental strings across all mass ranges, revealing mass independence in certain decay processes and providing exact interaction rates that could enhance understanding of hot string gases.

Contribution

Introduces a linear difference equation approach to compute exact string decay rates for arbitrary masses, extending beyond the long string approximation.

Findings

Decay rates for heavy open strings are mass-independent.

Closed string decay rates depend on reduced mass and scale with M and m_R.

Method provides microscopic basis for string interactions in thermal models.

Abstract

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 $M \to m+\M'$ 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 $M m_{R}^{(1-D)/2}$, where $m_{R}$ is the reduced mass of the decy 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.