Grand unified theories, topological defects, and ultrahigh-energy cosmic rays

Abstract

The ultrahigh-energy (UHE) proton and neutrino spectra resulting from collapse or annihilations of topological defects surviving from the GUT era are calculated. Irrespective of the specific process under consideration (which determines the overall normalization of the spectrum), the UHE proton spectrum always 'recovers' at ~ 1.8 x 10 11 GeV after a partial Greisen-Zatsepin-Kuz'min 'cutoff' at ~ 5 x 10 10 GeV and continues to a GUT-scale energy with a universal shape determined by the physics of hadronic jet fragmentation. Implications of our results are discussed. Topological defects [l], e.g., monopoles, cosmic strings, domain walls, superconducting cosmic strings, etc., and various possible hybrid objects made of these, are likely to have i been formed in symmetry-breaking phase transitions in the early universe. Because of their topological stability the defects can survive indefinitely, until and unless physically destroyed due to collapse, annihilations or other reasons[2-5). When topological defects are destroyed the energy trapped in them is released in the form of massive quanta (hereafter generically referred to as X particles) of the various fields (gauge bosons, biggs bosons, superheavy fermions) that 'constitute' the defects. The X-particles can then decay into known quarks, gluons, leptons, etc, which ultimately materialize into, among other particles, nucleons, gamma rays and neutrinos with energies up to ~ m x , the mass of the X-particles released from the defects. If the defects were originally formed in a phase transition at the GUT-scale ~ 10 16 GeV, then we have here a possible natural mechanism of production of ultrahigh-energy (UHE) cosmic ray (CR) particles up to an energy of this order, without any acceleration mechanism. Below we give a general calculation of the expected evolved proton as well as neutrino spectra resulting from this kind of processes.We assume a fio = 1 "flat" universe and a Hubble constant HQ = 100.h Km.s~1.Mpc~l, with h = 0.75 throughout.The rate of release of X-particles due to destruction of topological defects can, in general, be effectively expressed in terms of two fundamental parameters entering in the problem, namely, the mass scale m x and the Hubble time ~ t, in the form (with ft = c = 'XV^t j( 1) where K and p are dimensionless constants whose values depend on the specific process involving specific kind of topological defect, (the 'amplitude' K may, in general, depend on p), and n x (t,-) denotes the number density of the X-particles released at the time t{. For example, p = 1 for a system of collapsing cosmic string loops [4,5] as well as for a system of collapsing monopolonia [2,7], while p = 0 for a system of saturated superconducting cosmic 2 string loops [3]. We shall see below that the observed UHE CR flux gives an upper limit to the possible value of « for any given value of p.We assume that each X decays into a quark and a lepton each carrying an energy m x J2.The quarks fragment and produce jets of hadrons. We use the following hadronic fr...

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