Constraints from cosmic rays on non-systematic Lorentz violation

Abstract

Abstract.In this article we analyze the radiation loss from a high energy cosmic ray proton propagating in a spacetime with non-systematic Lorentz violation. From an effective field theory perspective we illuminate flaws in previous attempts that use threshold approaches to analyze this problem. We argue that in general such approaches are of rather limited use when dealing with non-systematic Lorentz violating scenarios. The main issues we raise are a) the limited applicability of threshold energy conservation rules when translation invariance is broken and b) the large amounts of proton particle production due to the time dependence of the fluctuations. Ignoring particle production, we derive a constraint on the magnitude of velocity fluctuation |v f | < 10 −6.5 , much weaker than has been previously argued. However, we show that in fact particle production makes any such constraint completely unreliable.

Quantum-Spacetime Phenomenology

“…In this respect I should bring to the attention of my readers the studies of non-systematic effects for ultra-high-energy cosmic rays reported in Refs. [37, 310, 106]. …”

The small-scale structure of spacetime

“…Note, though, that the symmetry violations in this scenario vary rapidly and essentially stochastically in both space and time. Such "nonsystematic" Lorentz violations are harder to study, but there is evidence that they lead to much weaker observational constraints [59].…”

Spontaneous dimensional reduction?

“…One must worry about experimental implications of the resulting violation of Lorentz invariance. But this violation is "nonsystematic"-its parameters vary rapidly in space and timeand such phenomena seem much harder to detect than "systematic" violations [43].…”