All DDF/lightcone two-particle decay widths up to level $8$ in open bosonic string in critical dimension

TL;DR

This paper systematically computes decay widths of open bosonic string states up to level 8, revealing dominant decay channels, stability patterns, and the role of photons in decay processes.

Contribution

It provides the first comprehensive analysis of two-particle decay channels for states up to level 8, highlighting decay patterns and stability features.

Findings

Decay width ratios between slowest and fastest states are of order one.

Dominant decay channels involve at least one photon, often carrying significant energy.

States on the leading Regge trajectory are among the most stable.

Abstract

We carry out an ``experimental analysis'' in which we explicitly compute all possible Abelian two-particle decay channels (excluding the tachyon) of open bosonic massive states up to level (8), amounting to approximately 2,000,000 cases. The aim is to develop intuition about which states are the most stable and to identify the dominant decay channels. Our results show that, for all levels considered, the ratio of decay widths between the slowest- and fastest-decaying states is of order one. In most cases, the dominant polarized decay channel accounts for at least $10\%$ of the total decay width, while the first five channels together contribute roughly 60%. Even when we sum about $10000$ polarized channels. Dominant polarized channels always involve at least one photon and all strings ultimately decay into a photon carrying energy at the string scale. The most stable states are made using the DDF/lightcone oscillators $A_{-1}$ and some $A_{-2}$ and are close relatives of the states on the leading Regge trajectory. Finally, we discuss how the computation on the lightcone differs from the equal-time computation due to ``surges'', i.e., decays into a tachyon and a higher-mass state, and we hypothesize that, in bosonic string theory, decays into tachyons constitute the dominant decay channels.