On reaction thresholds in doubly special relativity

TL;DR

This paper investigates reaction thresholds in doubly special relativity theories, finding that both frameworks do not permit forbidden processes and that their thresholds are affected differently at first order.

Contribution

It provides a detailed analysis of particle process thresholds in two DSR frameworks using modified conservation laws, clarifying their physical implications.

Findings

Both DSR frameworks do not allow forbidden particle processes.

Thresholds are altered at first order: lowered in Amelino-Camelia, variable in Maguejo-Smolin.

No additional processes are permitted in either framework.

Abstract

Two theories of special relativity with an additional invariant scale, "doubly special relativity" (DSR), are tested with calculations of particle process kinematics. Using the Judes-Visser modified conservation laws, thresholds are studied in both theories. In contrast to some linear approximations, which allow for particle processes forbidden in special relativity, both the Amelino-Camelia and Maguejo-Smolin frameworks allow no additional processes. To first order, the Amelino-Camelia framework thresholds are lowered and the Maguejo-Smolin framework thresholds may be raised or lowered.