Scattering, Absorption and Emission of Highly Excited Strings

TL;DR

This paper derives exact formulas for scattering, absorption, and emission of highly excited string states, revealing frequency-independent and frequency-dependent cross-sections and thermal emission characteristics.

Contribution

It provides new compact formulas for scattering amplitudes and explicit expressions for absorption and emission rates of highly excited strings, independent of their microscopic structure.

Findings

Constant, frequency-independent absorption cross-section for massless modes in open strings.

Frequency-dependent absorption cross-section for closed strings, indicating a grey-body factor.

Emission rates exhibit a Boltzmann factor at Hagedorn temperature at energies below the string mass scale.

Abstract

We study tree-level scattering processes of arbitrary string states using the DDF formalism and suitable coherent vertex operators. We obtain new exact compact formulae for heavy-heavy-light-light scattering amplitudes in open or closed bosonic string theories, and derive explicit exact expressions for the absorption cross-sections, and corresponding emission rates, of highly excited string states using the optical theorem and time reversal symmetry. We show that these expressions are independent of the microscopic structure of the excited string states without averaging. For the absorption of massless modes in open string theory, in particular, we find a constant, frequency-independent cross-section. In contrast, the corresponding cross-section for the absorption of massless modes by excited closed strings depends linearly on the frequency, implying a non-trivial grey-body factor. In both cases, at energies below the scale set by the mass of the highly excited strings, we find emission rates with a Boltzmann factor at Hagedorn temperature.