On The Injection Spectrum of Ultrahigh Energy Cosmic Rays in the Top-Down Scenario

Abstract

We analyze the uncertainties involved in obtaining the injection spectra of UHECR particles in the top-down scenario of their origin. We show that the DGLAP $Q^2$ evolution of fragmentation functions (FF) to $Q=M_X$ (mass of the X particle) from their initial values at low $Q$ is subject to considerable uncertainties. We therefore argue that, for $x\lsim 0.1$ (the $x$ region of interest for most large $M_X$ values of interest, $x\equiv 2E/M_X$ being the scaled energy variable), the FF obtained from DGLAP evolution is no more reliable than that provided, for example, by a simple Gaussian form (in the variable $\ln (1/x)$) obtained under the Modified Leading Log Approximation (MLLA). Additionally, we find that for $x\gsim0.1$, the evolution in $Q^2$ of the singlet FF, which determines the injection spectrum, is ``minimal'' -- the singlet FF changes by barely a factor of 2 after evolving it over $\sim$ 14 orders of magnitude in $Q\sim M_X$. We, therefore, argue that as long as the measurement of the UHECR spectrum above $\sim10^{20}\ev$ is going to remain uncertain by a factor of 2 or larger, it is good enough for most practical purposes to directly use any one of the available initial parametrisations of the FFs in the $x$ region $x\gsim0.1$ based on low energy data even without evolving them to the requisite $Q^2$ value.

arXiv commentMinor changes, added a reference, version to appear in Phys. Rev. D

References in corpus (15)

• Origin and Propagation of Extremely High Energy Cosmic Rays
• Fragmentation Functions for Pions, Kaons, and Protons at Next-to-Leading Order
• Energy determination in the Akeno Giant Air Shower Array experiment
• Fragmentation Functions from Flavour-inclusive and Flavour-tagged e^+e^- Annihilations
• Measurement of the Flux of Ultrahigh Energy Cosmic Rays from Monocular Observations by the High Resolution Fly's Eye Experiment
• Extremely high energy cosmic rays from relic particle decays
• Perturbative QCD Approach to Multiparticle Production
• Pion and Kaon Production in $e^{+}{e}^{-}$ and $ep$ Collisions at Next-to-Leading Order
• Astrophysical Origins of Ultrahigh Energy Cosmic Rays
• Production of pi+, K+, K0, K*0, phi, p and Lambda-0 in Hadronic Z0 Decays
• Fragmentation functions in SUSY QCD and UHECR spectra produced in top-down models
• Monte Carlo simulation for jet fragmentation in SUSY-QCD
• Detailed analysis of the decay spectrum of a super-heavy X particle
• Grand Unification Signal from Ultra High Energy Cosmic Rays?
• Super-heavy X particle decay and Ultra-High Energy Cosmic Rays

Cited by in corpus (1)

• Ultra High Energy Cosmic Rays & Super-heavy Dark Matter