Top-Down Models and UHECRs - rencontres de blois

Top-Down Models and UHECRs 

Michael Kachelrieß 

NTNU, Trondheim

Bottom-up versus top-down models 

Bottom-up models 

acceleration in electromagnetic fields 

⇒ charged particles: protons, nuclei, electrons 

photons and neutrinos as secondaries 

Rencontres de Blois 2008 Michael Kachelrieß Top-Down Models

Bottom-up versus top-down models 

Bottom-up models 

acceleration in electromagnetic fields 

⇒ charged particles: protons, nuclei, electrons 

photons and neutrinos as secondaries 

Top-down models 

relics from early universe 

non-thermal or thermal 

point particle or non-perturbative solutions 

stable or decaying 

fragmentation products: mainly photons, neutrinos 

↔ DM 


Dark matter candidates 

0 

−5 

SM neutrinos 

−10 

WIMP 

log(σ/pbarn) 

−15 

−20 

−25 

−30 

−35 

axion 

axino 

gravitino 

SHDM 

−40 

−18−15−12−9 −6 −3 0 3 6 9 12 15 18 

log(m/GeV) 


The standard candidate: WIMP 

inflation suggested Ω = 1, CMB shows that Ω ≈ 1 

BBN constrains baryon content, Ω b h 2 = 0.019 ±0.001 

LSS requires that DM is dissipation-less and “cold” 

thermal production of CDM, 

Ω X h 2 ∼ 3 ×10−27 cm 3 /s 

〈σv〉 

suggests weakly interacting DM particle with mass m ∼ m Z 


The standard candidate: WIMP 

inflation suggested Ω = 1, CMB shows that Ω ≈ 1 

BBN constrains baryon content, Ω b h 2 = 0.019 ±0.001 

LSS requires that DM is dissipation-less and “cold” 

thermal production of CDM, 

Ω X h 2 ∼ 3 ×10−27 cm 3 /s 

〈σv〉 

suggests weakly interacting DM particle with mass m ∼ m Z 

unitarity limit: m < ∼ 

100 TeV 


Status of neutralino DM after LEPII: 

800 

tan β = 10 , µ > 0 

700 

m h = 114 GeV 

m 0 (GeV) 

600 

500 

400 

m χ ± = 103.5 GeV 

300 

200 

100 

0 

100 200 300 400 500 600 700 800 900 1000 

m 1/2 (GeV) 


Status of neutralino DM after LEPII: 

3500 

m t = 171 GeV , tan β = 10 , µ > 0 

3000 

m 0 (GeV) 

2000 

m h = 114 GeV 

1000 

0 

100 1000 1500 

m 1/2 (GeV) 


Indirect detection claims: 

Signal from 

χχ annihilations in the diffuse extragalactic photon background: 


Indirect detection claims: [Elsässer, Mannheim ’04 ] 

Signal from χχ annihilations in the diffuse extragalactic 

photon background: 

E 2 x Gamma Ray Intensity / (GeV cm -2 s -1 sr -1 ) 

10 -6 

10 -7 

EGRET 

µ = 978GeV 

m 2 = -1035GeV 

m A = 1036GeV 

tan β = 6.6 

m S = 1814GeV 

A t = 0.88 

A b = -2.10 

Ωh 2 = 0.1 

Salamon & Stecker 

Blazar Model 

Straw Person's 

Blazar Model: 

χ 2 /ν =1.05 

Dark Matter 

α = -2.33 

m χ = 520 GeV 

χ 

= 3.1 x 10 -25 cm 3 s -1 

Scenario (Total) 

χ 2 /ν =0.74 

0,1 1 10 100 1000 

Observed Gamma Ray Energy / GeV 


Indirect detection claims: 

Signal from χχ annihilations in the diffuse extragalactic 

photon background: 

E 2 x Gamma Ray Intensity / (GeV cm -2 s -1 sr -1 ) 

10 -6 

10 -7 

EGRET 

µ = 978GeV 

m 2 = -1035GeV 

m A = 1036GeV 

tan β = 6.6 

m S = 1814GeV 

A t = 0.88 

A b = -2.10 

Ωh 2 = 0.1 

Salamon & Stecker 

Blazar Model 

Straw Person's 

Blazar Model: 

χ 2 /ν =1.05 

Dark Matter 

α = -2.33 

Scenario (Total) 

χ 2 /ν =0.74 

m χ = 520 GeV 

χ 

= 3.1 x 10 -25 cm 3 s -1 

0,1 1 10 100 1000 

Observed Gamma Ray Energy / GeV 

problem: 

search for small excess on top of “astrophysical background” 


Reminder: GZK puzzle as motivation for top-down models 

no obvious counter-parts for 10 20 eV events 




acceleration beyond 10 20 eV difficult 





AGASA excess 





AGASA excess 

misinterpretation of GZK suppression as GZK cutoff 


Modification factor: [Berezinsky, Gazizov, Grigorieva ’03 ] 

10 0 η total 

2 

modification factor 

10 -1 

10 -2 

1: γ g 

=2.7 

2: γ g 

=2.0 

η ee 

2 

1 

1 

10 17 10 18 10 19 10 20 10 21 


Modification factor: AGASA excess 

10 0 Akeno-AGASA 


10 -1 

η ee 

10 -2 

γ g 

=2.7 

η total 

10 17 10 18 10 19 10 20 10 21 


Modification factor: 

Nuclei 

red shift 

10 0 η total 

η ee 


10 -1 

p 

He 

Al 

Fe 

γ g 

=2.7 

10 -2 

10 17 10 18 10 19 10 20 10 21 

Rencontres de Blois 2008 Michael Kachelrieß 

E, eV 

Top-Down Models

GZK suppression – dependence on n s 

j(E) E 2 [eV cm -2 s -1 sr -1 ] 

10 -2 1 

AGASA 

z=0.1 

10 2 10 18 10 19 10 20 10 21 

50 Mpc 

z=0 

z=0.03 

E [eV] 

[MK, Semikoz and Tortola ’03 ] 


GZK suppression – dependence on n s 

j(E) E 2 [eV cm -2 s -1 sr -1 ] 

10 -2 1 

HiRes 

z=0.1 

10 2 10 17 10 18 10 19 10 20 10 21 

50 Mpc 

z=0 

z=0.03 

E [eV] 

[MK, Semikoz and Tortola ’03 ] 


Top-Down Models 

UHECR primaries are produced by decays of supermassive particle 

X with M X > ∼ 

10 12 GeV. 

topological defects: monopoles, strings, ... 

superheavy metastable particles 

[Hill ’83; Ostriker, Thompson, Witten ’86 ] 

[Berezinsky, MK, Vilenkin ’97; Kuzmin, Rubakov ’97 ] 

Advantages: 

no acceleration problem 

no visible sources 

if X ∈ CDM, no GZK-cutoff 

theoretically motivated; testable predictions 


Gravitational creation of superheavy matter 

Small fluctuations of field Φ obey 

¨φ k + [ k 2 +m 2 eff(τ) ] φ k = 0 




¨φ k + [ k 2 +m 2 eff(τ) ] φ k = 0 

If m eff is time dependent, vacuum fluctuations will be 

transformed into real particles. 




¨φ k + [ k 2 +m 2 eff(τ) ] φ k = 0 



⇒ expansion of Universe, 

m 2 eff = M 2 a 2 +(6ξ −1) a′′ 

a 

leads to particle production 




¨φ k + [ k 2 +m 2 eff(τ) ] φ k = 0 



⇒ expansion of Universe, 

meff 2 = M 2 a 2 +(6ξ −1) a′′ 

a 

leads to particle production 

In inflationary cosmology 

Ω X h 2 ∼ 

( 

MX 

10 12 GeV 

) 2 

T RH 

10 9 GeV 

dependent only on cosmology, for M X < ∼ 

H I 

Rencontres de Blois 2008 Michael Kachelrieß Top-Down Models 

[Kuzmin, Tkachev ’98; Chung, Kolb, Riotto ’98 ]

Gravitational creation of superheavy matter: 


Properties of superheavy matter: 

was never in thermal equlibrium: 

⇒ unitarity limit M < ∼ 30 TeV does not apply 





can be strongly interacting and dissipation-less: 

small relative energy transfer dE/(Edt) per time requires: 

either small σ or 

small energy transfer y 

⇒ any DM particle with m X > ∼ 10 TeV is dissipation-less 





can be strongly interacting and dissipation-less: 

small relative energy transfer dE/(Edt) per time requires: 

either small σ or 

small energy transfer y 

⇒ any DM particle with m X > ∼ 10 TeV is dissipation-less 

lifetime: 

metastable or stable due to some (gauged) R symmetry 


Detection of superheavy matter: 

direct detection: density 1/M X , recoil energy is constant 

⇒ large σ XN required 

log σ (cm 2 ) 

-20 

-22 

-24 

-26 

-28 

-30 

-32 

4 6 8 10 12 14 16 

log M χ 

(GeV) 



indirect detection via neutrinos from the Sun: 

signal should compete with usual fluxes 

⇒ 〈σv〉 ∼ 10 −26 cm 2 needed 



UHECR above the GZK cutoff via nucleon, photon secondaries 

1e+26 

E 3 J(E)/m −2 s −1 eV 2 

1e+25 

1e+24 

1e+23 

1e+18 1e+19 1e+20 1e+21 

E/eV 


Lifetime: 

stable: annihilation gives too small flux 

decay: too fast 

For M X > ∼ 

10 10 GeV even gravitational interactions result in 

cosmological short lifetimes, τ X ≪ t 0 . 

global symmetry broken by wormhole effects, τ X ∝ exp(S) 

symmetry broken by instanton effects, 

τ X ∝ exp(−4π 2 /g 2 ) 

discrete symmetries forbid operators with d < 9 

crypton or fractionally charged and confined particle of 

superstring theories 


Fragmentation of heavy particles 

consider Bremsstrahlung, X → ¯f fV: 

soft and collinear singularities generate terms ln 2 (m 2 V /m2 X ) for 

m 2 X ≫ m2 V ⇒ compensate the small couplings g2 , 

g 2 ln 2 (m 2 X /m2 V ) ≈ 1 






g 2 ln 2 (m 2 X /m2 V ) ≈ 1 

M X > ∼ 

10 6 GeV, ⇒ naive perturbation theory breaks down: 

electroweak and SUSY sector have a QCD-like behavior 

(“jets”) 

[Berezinsky, MK ’98, Berezinsky, MK, Ostapchenko ’02 ] 






g 2 ln 2 (m 2 X /m2 V ) ≈ 1 

M X > ∼ 

10 6 GeV, ⇒ naive perturbation theory breaks down: 

electroweak and SUSY sector have a QCD-like behavior 

(“jets”) 

(modified) DGLAP description possible 

[Berezinsky, MK ’98, Berezinsky, MK, Ostapchenko ’02 ] 



˜g 

˜q L ˜q 

X 

L 

q L 

q 

˜q L 

˜g 

g 

q L 

˜q R 

B 

˜q R 

W 

q 

q 

q 

g 

1 TeV 

˜χ 0 2 

q 

g 

q p 

q n 

q 

e − 

L γ 

ν e 

˜χ 

q 

0 1 π 0 γ 

a − ρ − 

1 

π − ν µ 

µ − ν µ 

τ 

π 0 γ ν e 

ν τ 

e − 

γ 

g 

g 

q 

q 

q 

q 

π 0 

γ 

γ 

ν τ 

(SUSY 

+ SU(2) ⊗ U(1) 

breaking) 

1 GeV 

(hadronization) 


Signatures of SHDM decays 

flat spectra dE/E 1.9 up to m X /2 

1e+26 

E 3 J(E)/m −2 s −1 eV 2 

1e+25 

1e+24 

1e+23 

1e+18 1e+19 1e+20 1e+21 

E/eV 

[Aloisio, Berezinsky, MK, ’03 ] 

⇒ SHDM dominates UHECR flux only above ∼ 8 ×10 19 eV 




composition: 

γ/p ≫ 1, large neutrino fluxes, no nuclei 

LSPs, if R parity conserved 

0.01 

x 3 Di(x,MX) 

0.001 

0.0001 

1e-05 

1e-06 

1e-07 

1e-08 

1e-09 

10 16 GeV 

10 14 GeV 

1e-10 

1e-05 0.0001 0.001 0.01 0.1 1 



F 

at a 

from 

Z-bu 

(dot 

Fig. 2.—The r m(1000) 

vs. E0 

relation for observed events (circles and 

Rencontres squares). de Blois 2008 The solid line is Michael a fit Kachelrieß to data between Top-Down 10 19 Models and 10 20 eV. The expected 

UH 

acc



composition: 

0.8 

0.7 

0.6 

0.5 

0.4 

0.3 

0.2 

0.1 

[33] 

[32] 

0.0 

10 19 10 20 10 21 

E (eV) 




composition: 

galactic anisotropy: [Dubovsky, Tinyakov ’98 ] 

10 

NFW 

10 20 eV 

6x10 19 eV 

3x10 19 eV 

10 19 ev 

1 

0 20 40 


Topological defect models 

+ “generic” in SUSY-GUTs 

+ produced during reheating 

- typical density: one per horizon/correlation length 

- main energy loss low-energy radiation 


Topological defect models [Allen, Shellard ’06 ] 

box 2ct 

matter 

epoch 

scaling 

regime 







favourable models for UHECRs: 

monopole-antimonopole pairs 

hybrid defects: cosmic necklaces 







favourable models for UHECRs: 

monopole-antimonopole pairs 

hybrid defects: cosmic necklaces 

G → H ⊗U(1) → H ⊗Z 2 

monopoles M ∼ η m /e connected by strings µ s ∼ η 2 s 

parameter r = M/(µd): 

r ≪ 1 normal string dynamics 

r ≫ 1 non-rel. string network 


Status of topological defect models – necklaces: 

1e+27 

E 3 J(E)/m −2 s −1 eV 2 

1e+26 

1e+25 

1e+24 

1e+23 

ν 

p 

γ 

p+γ 

1e+22 

1e+18 1e+19 1e+20 1e+21 1e+22 

E/eV 

[Aloisio, Berezinsky, MK, ’03 ] 


Status of topological defect models – necklaces: 

1e+27 

E 3 J(E)/m −2 s −1 eV 2 

1e+26 

1e+25 

1e+24 

1e+23 

ν 

p 

γ 

p+γ 

1e+22 

1e+18 1e+19 1e+20 1e+21 1e+22 

E/eV 

⇒ shape of spectrum allows only sub-dominant contribution 

• UHE photon fraction reduced 


Cosmic necklaces: [Blanco-Pillado, Olum ’07 ] 


Idea of EGRET limit 

all energy in γ and e ± cascades down to GeV–TeV range, bounded 

by observations: 

ω cas 

Z t0 

= f em m X dt (1+z) −4 ṅ X (t) 

∼ 

< 2 ·10−6 eV/cm 3 

0 


Elmag. cascades and EGRET limit: 

EGRET 

j(E) E 2 [eV cm -2 s -1 sr -1 ] 

10 2 

0.2 

1.8 

γ 

ν i 

p 

10 4 1.8 

0.2 

1.8 

10 8 10 10 10 12 10 14 10 16 10 18 10 20 10 22 

1 

0.2 

E [eV] 

[Semikoz, Sigl ’03 ] 


Summary 

AGASA excess as main motivation for top-down models is 

gone 

no positive evidence for superheavy dark matter from its two 

key signatures: 

photons 

galactic anisotropy 

SHDM remains an interesting DM candidate 

topological defects are generic prediction of (SUSY-) GUTs 

should be searched for as subdominant sources of UHECR 


Sensitivity of neutrino detectors 

NUTEL 

BAIKAL 

γ-ray bound 

j(E) E 2 [eV cm -2 s -1 sr -1 ] 

10 2 

10 

atm ν 

10 3 

10 12 10 14 10 16 10 18 10 20 10 22 

AMANDA-II, ANTARES 

WB bound 

ICECUBE 

RICE 

TA 

AUGER 

MPR bound 

EUSO 

ANITA 30 days 

1 

E [eV] 


Sensitivity of neutrino detectors 

NUTEL 

BAIKAL 

γ-ray bound 

j(E) E 2 [eV cm -2 s -1 sr -1 ] 

10 2 

10 

atm ν 

10 3 

10 12 10 14 10 16 10 18 10 20 10 22 

AMANDA-II, ANTARES 

WB bound 

ICECUBE 

RICE 

TA 

AUGER 

MPR bound 

EUSO 

ANITA 30 days 

1 

E [eV]

Top-Down Models and UHECRs - rencontres de blois

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