Ultra-High Energy Cosmic Radiation

and what it teaches us about astro- and fundamental

physics

Günter SiglGReCO, Institut d’Astrophysique de Paris, CNRShttp://www.iap.fr/users/sigl/homepage.html

General facts and the experimental situation Acceleration (“bottom-up” scenario) Cosmic magnetic fields and their role in cosmic ray physics New physics (“top-down” scenario) New interactions and new particles

Further reading:short review: Science 291 (2001) 73long review: Physics Reports 327 (2000) 109review collection: Lecture Notes in Physics 576 (2001) (eds.: M.Lemoine, G.Sigl)

The cosmic ray spectrum stretches over some 12 orders of magnitude in energy and some 30 orders of magnitude in differential flux:

many Joules in one particle!

The structure of the spectrum and scenarios of its origin

supernova remnants pulsars, galactic wind AGN, top-down ??

knee ankle toe ?

electrons

-rays

muons

Ground array measures lateral distributionPrimary energy proportional to density 600m from shower core

Fly’s Eye technique measuresfluorescence emissionThe shower maximum is given by

Xmax ~ X0 + X1 log Ep

where X0 depends on primary typefor given energy Ep

Atmospheric Showers and their Detection

ground arrays

fluorescence detector

ground array

Current data at the highest energies

AGASA data in combination with Akeno, a 1 km2 high-density part to studycosmic rays down to the knee.

A Tension between the Newest Fluorescence Data (HiRes)and Ground Array Results?

Or: Is there a Cut-Off after all?

but consistent with Haverah ParkDiscontinuity with AGASA, but betteragreement with Akeno

Lowering the AGASA energy scale by about 20% brings it in accordancewith HiRes up to the GZK cut-off, but not beyond.

HiRes collaboration, astro-ph/0208301

May need an experiment combining ground array with fluorescence such asthe Auger project to resolve this issue.

But HiRes has also seen a >200 EeV event in stereo mode with only ~20% exposure of the mono-mode

Experiments starting date

acceptancein km2sr

angularresolution

energyresolution

High – ResFly’s Eye

since 1999 350-1000 few degrees in stereo mode

~40% mono~10% stereo

Telescope Array

maybe with Auger North

1700-5000 ~1o ? ~20% ?

Auger ground

full size in about 2004

>7000 < 2o ~15%

Auger hybrid

~2004 >700 ~0.25o ~8%

EUSO/OWLspace-based

>2010 ~105 ? ~1o ? <30% ?

radio detection

??? >1000 ? few degrees ? ???

Next-Generation Ultra-High Energy Cosmic Ray Experiments

compare to AGASA acceptance ~ 230 km2sr

The southern Auger site is underconstruction.

The Ultra-High Energy Cosmic Ray Mystery consists of(at least) Three Interrelated Challenges

1.) electromagnetically or strongly interacting particles above 1020 eV loose energy within less than about 50 Mpc.

2.) in most conventional scenarios exceptionally powerful acceleration sources within that distance are needed.

3.) The observed distribution seems to be very isotropic (except for a possible interesting small scale clustering)

The Greisen-Zatsepin-Kuzmin (GZK) effect

Nucleons can produce pions on the cosmic microwave background

nucleon

-resonance

multi-pion production

pair production energy loss

pion production energy loss

pion production rate

sources must be in cosmological backyardOnly Lorentz symmetry breaking at Г>1011

could avoid this conclusion.

eV1044

2 192

th

mmm

E N

M.Boratav

1st Order Fermi Shock Acceleration

This is the most widely acceptedscenario of cosmic ray acceleration

The fractional energy gain pershock crossing depends on thevelocity jump at the shock.Together with loss processes thisleads to a spectrum E-q withq > 2 typically.When the gyroradius becomescomparable to the shock size,the spectrum cuts off.

u1

u2

A possible acceleration site associated with shocks in hot spots of active galaxies

A possible acceleration site associated with shocks formed by colliding galaxies

eV G1010

104

sun8

bh20max

B

M

ME

Supermassive black holes as linear accelerators

Particles accelerated along the rotationaxis do not suffer from significantenergy losses and can achieve energiesup to

S.Colgate suggested that helicalmagnetic fields produced duringformation of galaxies around centralblack holes occasionally reconnect.Resulting electric fields can acceleratecosmic rays up to ~1023 eV.

Or Can Plasma Wakefields excite by Alfven Shocks in -Ray Bursts accelerate cosmic rays up to 1024 eV?

Chen, Tajima, Takahashi,astro-ph/0205287

Arrival Directions of Cosmic Rays above 4x1019 eV

Akeno 20 km2, 17/02/1990 – 31/07/2001, zenith angle < 45o

Red squares : events above 1020 eV, green circles : events of (4 – 10)x1019 eV

Shaded circles = clustering within 2.5o.

Chance probability of clustering from isotropic distribution is < 1%.

galactic plane

supergalactic plane

Arrival Directions of Cosmic Rays above 1019 eV

Spectrum of the clustered component in the AGASA data

Possible explanations: * point-like sources of charged particles in case of insignificant magnetic deflection * point-like sources of neutral primaries * magnetic lensing of charged primaries

HiRes sees no significant anisotropy above 1018 eV

Cosmic Magnetic Fields and their Role in Cosmic Ray Physics

2.) Cosmic rays up to ~1018 eV are partially confined in the Galaxy.

Energy densities in cosmic rays, in the galactic magnetic field, in the turbulent flow, and gravitational energy are of comparable magnitude.

The galactic cosmic ray luminosity LCR required to maintain its observed density uCR~1eVcm-3 in the galactic volume Vgal for a confinement time tCR~107 yr, LCR ~ uCR Vgal / tCR ~ 1041 erg/sec, is ~10% of the kinetic energy rate of galactic supernovae.

1.) Magnetic fields are main players in cosmic ray acceleration.

However, there are still problems with this standard interpretation: Upper limits on -ray fluxes from supernova remnants are below predictions from interactions of accelerated cosmic rays with ambient medium!

3.) The knee is probably a deconfinement effect as suggested by rigidity dependence measured by KASCADE:

4.) Cosmic rays above ~1019 eV are probably extragalactic and may be deflected mostly by extragalactic fields BXG rather than by galactic fields.

However, very little is known about about BXG: It could be as small as 10-20 G (primordial seeds, Biermann battery) or up to fractions of micro Gauss if concentrated in the local Supercluster (equipartition with plasma).

strength of BXG

small deflection=> many sources

strong deflection=> few sources possible

Monoenergetic or« high before low »

no time-energy correlation

burst sources continuous sources

clusters due to magnetic lensing or due to a neutral component

Example:Magnetic field of 10-10 Gauss, coherence scale 1 Mpcburst source at 50 Mpc distance

tim

e d

ela

ydiff

ere

nti

al sp

ect

rum

Lemoine, Sigl

cuts through the energy-time distribution:

To get an impression on the numbers involved:

Transition rectilinear-diffusive regime

Neglect energy losses for simplicity.

Time delay over distance d in a field Brms of coherence length λc for smalldeflection:

yr Mpc 1G 10Mpc 10eV10

105.14

),(),( c

2

9rms

22

2023

2

BdEZ

dEddE

This becomes comparable to distance d at energy Ec:

eV Mpc 1G 10Mpc 10

107.42/1

c6rms

2/1

20c

BdE

In the rectilinear regime for total differential power Q(E) injected insided, the differential flux reads

2)4(

)()(

d

EQEj

In the diffusive regime characterized by a diffusion constant D(E),particles are confined during a time scale

)(),(

2

ED

ddE

which leads to the flux

)()4(

)()(

2 EdD

EQEj

For a given power spectrum B(k) of the magnetic field an often used(very approximate) estimate of the diffusion coefficient is

,

)(3

)()(

)(1/r

22

rmsg

g

E

kBdkk

BErED

where Brms2=∫0

∞dkk2<B2(k)>, and the gyroradius is

kpc G 10eV 10

110)(1

6-rms

201

rmsg

BEZ

ZeB

EEr

IF E<<Ec and IF energy losses can be approximated as continuous,dE/dt=-b(E) (this is not the case for pion production), the local cosmic raydensity n(E,r) obeys the diffusion equation

),(),(),(),()(),( rEqrEnrEDrEnEbrEn Et

Where now q(E,r) is the differential injection rate per volume,Q(E)=∫d3rq(E,r). Analytical solutions exist (Syrovatskii), but the necessaryassumptions are in general too restrictive for ultra-high energy cosmic rays.

Monte Carlo codes are therfore in general indispensable.

Strong, highly structured fields in our Supergalactic Neighbourhood ?

Medina Tanco, Lect.Not.Phys 542, p.155

Principle of deflection code

A particle is registered every time a trajectory crosses the spherearound the observer. This version to be applied for individualsource/magnetic field realizations and inhomogeneous structures.

sourcesphere aroundobserver

source

sphere around source

A particle is registered every time a trajectorycrosses the sphere around the source. Thisversion to be applied for homogeneousstructures and if only interested in averagedistributions.

Effects of a single source: Numerical simulations

A source at 3.4 Mpc distance injecting protons with spectrum E-2.4 up to 1022 eVA uniform Kolmogorov magnetic field, <B2(k)>~k-11/3, of rms strength 0.3 μG,and largest turbulent eddy size of 1 Mpc.

Isola, Lemoine, Sigl

Conclusions: 1.) Isotropy is inconsistent with only one source. 2.) Strong fields produce interesting lensing (clustering) effects.

105 trajectories,251 images between20 and 300 EeV,2.5o angular resolution

Same scenario, averaged over many magnetic field realisations

That the flux produced by CenA is too anisotropic can also be seen fromthe realization averaged spectra visible by detectors in different locations

AGASA, northernhemisphere solid angle

averaged

southern hemisphere

Isola, Lemoine, Sigl, Phys.Rev.D 65 (2002) 023004

Summary of spectral effects

Continuous source distributionFollowing the Gaussian profile.B=3x10-7 G, d=10 Mpc

)()( EQEj

)(

)()(

ED

EQEj

in rectilinear regime

in diffusive regime

)()(

2

ED

dE in diffusive regime

2)( EE in rectilinear regime

How many sources for a given large-scale magnetic field strength?

Current (AGASA) data can be fit with ~0.3 micro Gauss maximal field strengthand ~10 sources:

Local Supercluster as Gaussian sheet of radius 20 Mpc and thickness 3 Mpccentered at 20 Mpc distance from Earth.Assume source density follows that profile, field is stochastic and uniformwith a Kolmogorov spectrum up to largest eddy scale of 1 Mpc.

Isola, Sigl, astro-ph/0203273

Diamonds=simulations; statistical and total (including cosmic variance) error barsHistogram=AGASA data.

power spectrum auto-correlation function

CL=46%

CL=92%

Observable spectrum is dominated by sources in the local neighborhoodif fields are fractions of a micro Gauss

Realization averaged contributionfrom 10 sources in the localsupercluster injecting an E-2 protonspectrum up to 1022 eV.Note the steepening due toconfinement at low energies.

Contribution from isotropic protonflux impinging at 40 Mpc fromobserver with an E-2.4 spectrum(mimicking steepening due toconfinement in source region).

The observation of a GZK cutoffdoes not necessarily implycosmological sources.

Isola, Sigl, astro-ph/0203273

baryon density-cutthrough 50Mpc3 box

Supergalactic Neighbourhood and Magnetic Fields from large scale structureSimulations are strongly structured

How many sources in a strongly structured and magnitezed environment?

Assume source density follows baryon density; 100 identical sources.Normalized magnetic fields from large scale structure simulations.

Current (AGASA) data can be fit with 10-100 sources if observer is surroundedby fields ≥ 0.1 micro Gauss:

CL=17%

power spectrum

Isola, Sigl, astro-ph/0203273, Miniati, Ensslin, Sigl, in preparation

Diamonds=simulations; statistical and total (including cosmic variance) error barsHistogram=AGASA data.

auto-correlation function

CL=63%

The spectrum in this scenario lies between AGASA and HiResobservations

Generalization to heavy nuclei

Example:If source injects heavy nuclei,diffusion can enhance the heavycomponent relative to theweak-field case.

All secondary nuclei are followedand registered upon crossing asphere around the source.

B=10-12 G, E>1019 eV

B=2x10-8 G, E>1019 eV

Bertone, Isola, Lemoine, Sigl, astro-ph/0209192

Here we assume E-2 iron injectionup to 1022 eV.

However, the injection spectrumnecessary to reproduce observedspectrum is ~E-1.6 and thus ratherhard.

B=2x10-8 G, d=7.1 Mpc

B=2x10-8 G, d=3.2 Mpc

Composition as function of energy.

2nd example: Helium primaries do not survive beyond ~20 Mpc at the highest energies

B=10-12 G, E>1020 eV

Bertone, Isola, Lemoine, Sigl, astro-ph/0209192

Ultra-High Energy Cosmic Rays and the Connection to-ray and Neutrino Astrophysics

rays

neutrinoso

XN

p

accelerated protons interact:

=> energy fluences in -rays and neutrinos are comparable due to isospin symmetry.

The neutrino spectrum is unmodified,whereas -rays pile up below the pairproduction threshold on the CMB at afew 1014 eV.

The Universe acts as a calorimeter forthe total injected electromagneticenergy above the pair threshold. Thisconstrains the neutrino fluxes.

The total injected electromagnetic energy is constrained by the diffuse -rayflux measured by EGRET in the MeV – 100 GeV regime

Neutrino flux upper limit for opaque sourcesdetermined by EGRETbound

Neutrino flux upper limitfor transparent sourcesmore strongly constrainedby primary cosmic rayflux at 1018 – 1019 eV(Waxman-Bahcall;Mannheim-Protheroe-Rachen)

i

Example: diffuse sources injecting E-1 proton spectrum extending up to2x1022 eV with (1+z)3 up to redshift z=2. Shown are primary proton fluxtogether with secondary -ray and neutrino fluxes.

The cosmogenic neutrino flux produced by pion production by cosmic raysduring propagation can violate the Waxman-Bahcall bound for injection

spectra harder than ~E-1.5 and source luminosities increasing with redshift

Example: dependence on injectionspectral index

WB bound

-ray and cosmic ray fluxes must beconsistent with observations.

WB bound

Kalashev, Kuzmin, Semikoz, Sigl, PRD 66 (2002) 063004

Cline, Stecker, astro-ph/0003459

A compilation of neutrino flux predictions

EGRET bound

MPR bound

WB bound

Alternative: Top-Down Scenario

Decay of early Universe relics of masses ≥1012 GeV

Benchmark estimate of required decay rate:

mass. particle- the with

GeV10GeV10)(

Mpc10

srseVcm

)(yrAU13

1 assume now ; )(

4

1)(

1

16

5.1

161-1-2-

21-3-

spectrumdecayrate

decaypath

freemean flux measured

Xm

mE

El

EjEn

m

E

mdE

dN

dE

dNnElEj

X

XX

XXX

This is not a big number!

1.) long-lived massive free particles (“WIMPZILLA” dark matter)

yr1010 1012XX t

Fine tuning problem of normalizing ΩX/tX to observed flux. predicted -ray domination probably inconsistent with data.

But for cosmic strings (or necklaces) the Higgs-Kibble mechanism yields

2.) particles released from topological defects2

criticaldefect scaling t Fine tuning problem of normalizing to observed flux.3

defect tfX

GeV1010ion normalizat

scale breakingsymmetry with ,

1413

22string

vf

vtv

Fine tuning problem only by few orders of magnitude if Absorption in radio background can lead to nucleon domination.

)1(Of

Two types of Top-Down scenarios

Topological defects are unavoidable products of phase transitionsassociated with symmetry change

1.) Iron: Bloch wall

)3(:Curie SOGTT )2(:Curie SOHTT

Examples:

2.) breaking of gauge symmetries in the early Universe ~1 defect per causal horizon (Higgs-Kibble mechanism) in Grand Unified Theories (GUTs) this implies magnetic monopole production which would overclose the Universe. This was one of the motivations that INFLATION was invented.

=> particle and/or defect creation must occur during reheating after inflation. Microwave background anisotropies implies scale Hinflation~1013 GeV.

=> natural scale for relics to explain ultra-high energy cosmic rays!

Flux calculations in Top-Down scenarios

a) Assume mode of X-particle decay in GUTs

jets hadronic

:Example qqlX

c) fold in injection history and solve the transport equations for propagation

b) Determine hadronic quark fragmentation spectrum extrapolated from accelerator data within QCD: modified leading log approximation (Dokshitzer et al.) with and without supersymmetry versus older approximations (Hill). More detailed calculations by Kachelriess, Berezinsky, Toldra, Sarkar, Barbot, Drees: results not drastically different.

Fold in meson decay spectra into neutrinos and -rays to obtain injection spectra for nucleons, neutrinos, and

QCD

SUSY-QCD

The X-particle decay cascade

At the highest energies fluxes in increasing order are: nucleons, -rays,neutrinos, neutralinos.

Kalashev, Kuzmin, Semikoz, Sigl, PRD 66 (2002) 063004

3

-1214

with sources shomogeneou

,G 10, GeV102 ,

t

BmqqX

X

X

A typicalexample:

310-

14

on with distributi source shomogeneou ,G 10B

,Earth of Mpc 5 within 50y overdensit of neutrinos relic eV,1 , eV1.0

, GeV10 ,

t

mmm

mX

X

X

e

Another example only involving neutrino primaries

Bhattacharjee, Sigl, LNP 542 (2001) 275

Motivated by possible correlations with high redshift objects:

Farrar, Biermann radio-loud quasars ~1%

Virmani et al. radio-loud quasars ~0.1%

Tinyakov, Tkachev BL-Lac objects ~10-5

G.S. et al. radio-loud quasars ~10%

If this is confirmed, one can only think of 3 possibilities:

1.) Neutrino primaries but Standard Model interaction probability in atmosphere is ~10-5.

resonant (Z0) secondary production on massive relic neutrinos: needs extreme parameters and huge neutrino fluxes.

2.) New heavy neutral (SUSY) hadron X0: m(X0) > mN increases GZK threshold. but basically ruled out by constraints from accelerator experiments.

3.) New weakly interacting light (keV-MeV) neutral particle electromagnetic coupling small enough to avoid GZK effect; hadronic coupling large enough to allow normal air showers: very tough to do.

In all cases: more potential sources, BUT charged primary to be accelerated toeven higher energies.

strong interactions above ~1TeV: only moderate neutrino fluxes required.

New Particles and New InteractionsThe Z-burst eff ect

A Z-boson is produced at theneutrino resonance energy

mE

eVeV 104 21res

“Visible” decay products haveenergies 10-40 times smaller.

Fargion, Weiler, Yoshida

Main problems of this scenario:* sources have to accelerate upto ~1023eV.

* -rays emitted f rom thesources and produced byneutrinos during propagationtend to over-produce diff usebackground in GeV regime.

The Z-burst mechanism: Relevant neutrino interactions

The Z-burst mechanism: Sources emitting neutrinos and -rays

Sources with constant comoving luminosity density up to z=3, with E-2 -rayinjection up to 100 TeV of energy fluence equal to neutrinos, mν=0.5eV, B=10-9 G.

Kalashev, Kuzmin, Semikoz, Sigl, PRD 65 (2002) 103003

The Z-burst mechanism: Exclusive neutrino emitters

Sources with comoving luminosity proportional to (1+z)m up to z=3, mν=0.5eV,B=10-9 G.

Kalashev, Kuzmin, Semikoz, Sigl, PRD 65 (2002) 103003

Probes of Neutrino Interactions beyond the Standard Model

Note: For primary energies around 1020 eV:Center of mass energies for collisions with relic backgrounds ~100 MeV – 100 GeV ―> physics well understood

Center of mass energies for collisions with nucleons in the atmosphere ~100 TeV – 1 PeV ―> probes physics beyond reach of accelerators

Example: microscopic black hole production in scenarios with a TeV string scale:

For neutrino-nucleon scattering withn=1,…,7 extra dimensions,from top to bottom

Standard Model cross section

Feng, Shapere, hep-ph/0109106

This increase is not sufficientto explain the highest energycosmic rays, but can be probedwith deeply penetrating showers.

However, the neutrino flux from pion-production of extra-galactic trans-GZK cosmic rays allows to put limits on the neutrino-nucleon cross section:

Future experiments will either close the window down to the Standard Modelcross section, discover higher cross sections, or find sources beyond thecosmogenic flux. How to disentangle new sources and new cross sections?

Comparison of this N- (“cosmogenic”) flux with the non-observation ofhorizontal air showers results in the present upper limit about 103 above theStandard Model cross section.

Ringwald, Tu, PLB 525 (2002) 135

Sensitivities of LHC and the Pierre Auger project tomicroscopic black hole production in neutrino-nucleon scattering

Ringwald, Tu, PLB 525 (2002) 135

LHC much more sensitive than Auger, but Auger could “scoop” LHC

MD = fundamental gravity scale; Mbhmin = minimal black hole mass

Sensitivities of LHC, future air shower arrays, and neutrino telescopes tomicroscopic black hole production in neutrino-nucleon scattering

Ringwald, Kowalski, Tu, PLB 529 (2002) 1

Contained events: Rate ~ Volume Through-going events: Rate ~ Area

Ultra-High Energy Neutrino Detection: Traditional and New Ideas

Mostly uses the charged-current reactions: ,, , eiNlN ii

1.) detect Cherenkov radiation from muons in deep sea or ice AMANDA, ANTARES, BAIKAL, NESTOR aims at 1 km3 for E> 100 GeV to 1 TeV

2.) horizontal air showers for electron and τ-neutrinos PIERRE AUGER, MOUNT for E> 1018 eV, increased efficiency for τ-neutrinos if surrounded by mountains on 100 km scale which is decay length of produced taus.

3.) detection of inclined showers from space for E>1020 eV EUSO, OWL

4.) acoustic detection in water: hydrophonic arrays

5.) detection of radio emission from negative charge excess of showers produced in air, water, ice, or in skimming rock. RICE (in South-pole ice), GLUE (radio-telescope observing the moons rim)

6.) Earth-skimming events in ground arrays or fluorescence detectors.

Effective detector mass for some future neutrino detectors

Filled arrowheads: optical Cherenkov in water or iceOpen arrowheads: air shower techniquesDots without arrowheads: radio Cherenkov experiments

Seckel, astro-ph/0103300

Future neutrino flux sensitivities

Kalashev, Kuzmin, Semikoz, Sigl, hep-ph/0205050

Telescope Array

HiRes (mono)

Fly’s Eye

Feng et al., PRL 88 (2002) 161102

Earth-skimming τ-neutrinos

Air-shower probability per τ-neutrinoat 1020 eV for 1018 eV (1) and1019 eV (2) threshold energy forspace-based detection.

Effective aperture for τ-leptons.Tau-flux ~8.5x10-4 x τ-neutrino fluxindependent of σνN for ground-baseddetectors.

Kusenko, Weiler, PRL 88 (2002) 121104

Comparison of earth-skimming andhorizontal shower rates allows tomeasure the neutrino-nucleon crosssection in the 100 TeV range.

Signatures of ultra-high energy neutralinos in neutrino telescopes

LSP flux predicted from X-particles in thegalactic halo for mX=2x1021 eV (left) andmX=2x1025 eV (right). Decay modes arequark+antiquark (solid), quark+squark(dot-dash), SU(2) doublet lepton+slepton(dots), and 5 quark+5 squarks (dashes)

Inverse fraction of neutrinos orneutralinos passing through Earthwith zenith angle < 85o. Regenerationeffects are not included.

Barbot, Drees, Halzen, Hooper, hep-ph/0207133s

For certain ranges and energies the neutrino-nucleon cross section can bemeasured in the atmosphere

For demonstration assume:

Neutrino-induced showers with E>E1(θ)peak above the ground.

θ θ

E1(θ

)/10

20 e

V

E2(θ

)/10

20 e

V

Neutrino-induced showers with E<E2(θ)are not absorbed and thus observableabove the ground.

Tyler, Olinto, Sigl, PRD 63 (2001) 055001

4SM

4

D

NM

s

Dashed line: MD=1.4 TeV, solid line: MD=1.2 TeV.Note that above ~1020 eV σνN is not constrained by the cosmogenic flux.

Probes of Lorentz symmetry violations

Dispersion relation between energy E, momentum p, and mass m may bemodified by non-renormalizable effects at the Planck scale MPl,

...,2Pl

4

Pl

3222

M

p

M

pmpE

where most models, e.g. critical string theory, predict ξ=0 for lowest order.

,4

2 2

0 mmm

p N

the threshold momentum pth in the modified theory is given by

1...32)()2( 0

th

4

0

th

Pl

0

3

0

th2

Pl2

30

p

p

p

p

M

p

p

p

mm

mm

Mmmm

p

N

N

N

Coleman, Glashow, PRD 59 (1999) 116008; Alosio et al., PRD 62 (2000) 053010

Attention: this assumes standard energy-momentum conservation which isnot necessarily the case.

Introducing the standard threshold momentum for pion production, N+->Nπ,

For ξ ~ ζ ~ 1 this equation has no solution => No GZK threshold!

For ζ ~ 0, ξ ~ -1 the threshold is at ~1 PeV!For ξ ~ 0, ζ ~ -1 the threshold is at ~1 EeV!

Confirmation of a normal GZK threshold would imply the following limits:

|ξ| ‹ 10-13 for the first-order effects.|ζ| ‹ 10-6 for the second-order effects.

Energy-independent (renormalizable) corrections to the maximal speedVmax= limE―>∞ ∂E/∂p = 1-d can be constrained by substitutingd―>(ξ/2)(E/MPl)+(ζ/2)(E/MPl)2.

The modified dispersion relation also leads to energy dependent group velocityV=∂E/∂p and thus to an energy-dependent time delay over a distance d:

sec TeVMpc 100

ED

M

EDt

for ζ = 0. GRB observations in TeV -rays can therefore probe quantum gravity.The current limit is M/ξ > 8x1015 GeV (Ellis et al.).

Conclusions

1.) The origin of very high energy cosmic rays is one of the fundamental unsolved questions of astroparticle physics. This is especially true at the highest energies, but even the origin of Galactic cosmic rays is not resolved beyond doubt.2.) Pion-production establishes a very important link between the physics of high energy cosmic rays on the one hand, and -ray and neutrino astrophysics on the other hand. All three of these fields should be considered together.

4.) At energies above ~1018 eV, the center-of mass energies are above a TeV and thus beyond the reach of accelerator experiments. Especially in the neutrino sector, where Standard Model cross sections are small, this probes potentially new physics beyond the electroweak scale.

3.) Acceleration and sky distribution of cosmic rays are strongly linked to the in part poorly known strength and distribution of cosmic magnetic fields.

5.) The coming 3-5 years promise an about 100-fold increase of ultra-high energy cosmic ray data due to experiments that are under either construction or in the proposal stage.6.) Many new ideas on a modest cost scale, especially for ultra-high energy neutrino detection, are currently under discussion.