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Ultrahigh-Energy Cosmic Rays Particle Spectra from Crypton Decays

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Ultrahigh-Energy Cosmic Rays Particle Spectra from Crypton Decays PHYSICAL REVIEW D 74, 115003 (2006) Ultrahigh-energy cosmic rays particle spectra from crypton decays John Ellis,1 V.E. Mayes,2 and D. V. Nanopoulos2,3 1Theory Division, Physics Department, CERN, CH 1211 Geneva 23, Switzerland 2George P. and Cynthia W. Mitchell Institute for Fundamental Physics, Texas A&M University, College Station, Texas 77843, USA 3Astroparticle Physics Group, Houston Advanced Research Center (HARC), Mitchell Campus, Woodlands, Texas 77381, USA and Academy of Athens, Division of Natural Sciences, 28 Panepistimiou Avenue, Athens 10679, Greece (Received 13 February 2006; published 7 December 2006) We calculate the spectra of ultrahigh-energy cosmic rays (UHECRs) in an explicit top-down model based on the decays of metastable neutral ‘‘crypton’’ states in a flipped SU(5) string model. For each of the eight specific 10th-order superpotential operators that might dominate crypton decays, we calculate the spectra of both protons and photons, using a code incorporating supersymmetric evolution of the injected spectra. For all the decay operators, the total UHECR spectra are compatible with the available data. Also, the fractions of photons are compatible with all the published upper limits, but may be detectable in future experiments. DOI: 10.1103/PhysRevD.74.115003 PACS numbers: 12.60.Jv, 04.60.ÿm, 11.25.Wx, 96.50.Sÿ I. INTRODUCTION heterotic string-derived flipped SU(5) model may have exactly the right properties to play this role [11,12]. The existence of cosmic rays with energies above the These ‘‘flipped cryptons’’ are bound by SU(4) hidden- Greisen-Zatsepin-Kuzmin (GZK) cutoff [1,2] is one of the sector interactions, and include four-constituent metastable most important open problems in high-energy astrophysics bound states called tetrons that are analogues of the three- [3,4]. These ultrahigh-energy cosmic rays (UHECRs) may constituent baryons of QCD, as well as two-constituent be a tantalizing hint of novel and very powerful astrophys- mesonlike states. Indeed, it was within this flipped SU(5) ical accelerators, or they may be harbingers of new micro- model that the confinement solution to avoiding the strin- physics via the decays of metastable supermassive gent experimental limits placed on fractional charges was particles. It is remarkable that we still do not know whether first pointed out, and this model remains the only example the UHECRs originate from macrophysics or microphys- to have been worked through in any detail [11,12]. ics. If there is no GZK cutoff, as suggested by the AGASA In general, tetrons may decay through Nth-order non- data [5], the sources of the UHECRs would need to be renormalizable operators in the superpotential, which local. In this case, since local magnetic fields are unlikely would yield lifetimes that are expected to be of the order of to have deflected significantly their directions of propaga- tion, the UHECRs would ‘‘remember’’ the directions of ÿ 2 N 2 Nÿ3 their sources. Thus, one would expect some anisotropy in string Ms ; (1) the arrival directions of the UHECRs, associated either mX mX with discrete energetic astrophysical sources nearby, such 18 as BL Lac objects [4], or the distribution of (mainly where mX is the tetron mass and MS 10 GeV is the galactic) superheavy dark matter. No significant anisotropy string scale. The -dependent factor reflects the expected of the UHECRs has yet been seen, but the existing experi- dependence of high-order superpotential terms on the ef- ments have insufficient statistics to exclude one at the fective gauge coupling g. The mass scale associated with expected level [6]. On the other hand, the GZK cutoff these states is estimated using the renormalization group may be present in the HiRes data [7], in which case no for the SU(4) interactions to be 1012–1013 GeV, just exotic microphysics may be needed, and any astrophysical in the right range for their decays to produce the UHECRs. sources would be less restricted and more difficult to trace. The lifetimes of neutral tetrons without electric charge 11 17 The first batch of Auger [8] data are inconclusive on the has been estimated to lie in the range 0 10 –10 years, possible existence of the GZK cutoff. so that they may still be present in the Universe today, and Superheavy particles of the type required could have might produce the necessary flux of UHECRs if they are been produced gravitationally around the end of inflation sufficiently abundant. We have shown in our previous work [9]. Particularly interesting candidates for such superheavy [12] that the mesons and charged tetrons—whose present- particles are ‘‘cryptons,’’ bound states of the fractionally day abundances are subject to very stringent experimental charged constituents that arise generically [10] in the hid- limits—would have decayed with short lifetimes early in den sectors of models of particle physics derived from the the Universe. In the course of studying the possible tetron 1 heterotic string. Cryptons arising in the hidden sector of a lifetimes, we identified various 10th-order superpotential operators that might govern neutral tetron decays. Thus, in 1Such states may also be a generic feature of models con- this specific model of flipped cryptons we are able to go structed from intersecting D-branes. beyond generic statements regarding the injected UHECR 1550-7998=2006=74(11)=115003(11) 115003-1 © 2006 The American Physical Society JOHN ELLIS, V.E. MAYES, AND D. V. NANOPOULOS PHYSICAL REVIEW D 74, 115003 (2006) particle spectra that may result from their decays, and right range to produce the UHECR. However, as pointed make a number of specific predictions. out in the introduction, flipped SU(5) cryptons satisfy both This enables us to address an important experimental of these criteria, which makes them very attractive as a top- constraint on such crypton models of the UHECRs. down explanation of the UHECR. Indeed the flipped cryp- Although ‘‘top-down’’ models such as crypton decays ton is probably the most natural and most physically mo- may appear to be natural explanations for the UHECRs tivated of any top-down candidate. (if they exist), they generically share a potential drawback. There are three generic statements that can be presently The spectra of UHECRs that they produce might be ex- made about a decaying superheavy X particle explanation pected to have large photon fractions, in possible conflict for the UHECR: with the observation that most of the UHECR primaries (1) Since the superheavy relics may accumulate locally appear to be protons or nuclei. The Auger collaboration has in the galactic halo with an overdensity 104–5 over recently set an upper limit of 26% on the photon fraction the cosmological average, they may avoid the GZK above 1019 eV [13], and the limit may even be as low as cutoff. 7%–14% [14]), while an upper limit of 50% at energies (2) Because of the displacement of our solar system above 1020 GeV has been set by the AGASA collaboration with respect to the galactic plane, there should be [15]. some anisotropy in the arrival directions of the In this paper, we first give a review of relevant aspects of UHECR with respect to the galactic center. the flipped SU(5) heterotic string model. We then analyze (3) Photons tend to be the dominant component of the the specific primary multibody decay modes governed by UHECR flux produced by the superheavy X decay. the various different 10th-order superpotential operators However, the photons may scatter off the galactic found in our previous paper. We then calculate the radio background, which is poorly measured, and UHECR particle spectra that would be injected by these thus may be somewhat attenuated. decays using one of the most detailed and complete codes The injection spectrum produced by such a decaying currently available [16], paying particular attention to the superheavy relic X particles with number density nX and photon fraction. The total UHECR spectra obtained from lifetime X is proportional to the inclusive decay width: the various superpotential terms do not differ greatly. On halo nX 1 dÿ X ! g1 the other hand, we find that different decay operators may E : (2) give rather different photon fractions, particularly at the X ÿX dE highest energies. However, in every case, we find that the If a spherical halo of radius Rhalo and uniform number calculated spectra after supersymmetric evolution and density nX is assumed, then the galactic halo contribution fragmentation are compatible with the published upper to the UHECR will be given by limits on the photon fractions in various energy ranges, when we include the UHECR background resulting from a halo 1 halo J Rhalo E: (3) homogenous extragalactic distribution of sources and in- 4 corporate the pileup expected from the GZK effect. There In general, the X particles will decay into one or more is no need to appeal to the cosmic radio background to partons which hadronize into other particles g of the mini- absorb a significant fraction of the photons in order to bring mal supersymmetric standard model (MSSM), which carry them below the AGASA and other limits. a fraction x of the maximum available momentum MX=2 and a fraction z of the parton momentum. For such a decay, II. GENERIC SUPERHEAVY RELIC DECAY the inclusive decay width can be factored as Z ! X x 2 2 The basic idea in generic top-down explanations (see 1 dÿ X g1 1 dÿa y; ;MX [17,18]) is that the UHECR are produced via the decay of ÿX dE a 0 ÿa dy yx=z some relic particles or topological defects left over from g 2 Da z; ; (4) the inflationary epoch and which are locally clustered in g 2 the galactic halo as cold, dark matter with an overdensity where Da z; is the fragmentation function (FF) for cos 4–5 nX=nX 10 .
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