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ULTRA HIGH ENERGY COSMIC RAY

SPECTRA IN TOP­DOWN MODELS

Roberto Aloisio

INFN – Laboratori Nazionali del Gran Sasso

In collaboration with: V.S. Berezinsky & M. Kachelriess

CRIS 2004 – Cosmic Ray International Seminar

Catania, May 31 – June 4 2004


AGASA HiRes

AGASA excess difficult to reconcile

with the Astrophysical sources

HiRes data compatible with

the GZK suppression

Astrophysical counterparts not seen

at eV

E5×10 19

Protons from uniform astrophysical sources good fit of the HiRes data and

AGASA data at E10 eV, required luminosities

20

L p≈10 46 erg/ Mpc 3 yr

(Berezinsky, Gazizov and Grigorieva (2002))


An Alternative to Acceleration

Decay of SH Relics

(Berezinsky, Kachelriess & Vilenkin 1997)

(Kuzmin & Rubakov 1997)

Topological Defects

(Hill & Schramm 1985)


Super Heavy Relics

Preheating

(Kofman, Linde & Starobinsky (1994))

Broad-resonance decay of X

M X m g m M Pl

SHDM is effectively produced at inflation

Supermassive particles with mass comparable with the inflaton

mass can be generated in the early universe through direct coupling

to the inflaton field or in the time-dependent gravitational field.

M X ≤10 14 GeV

Reheating

(Felder, Kofman & Linde (1998))

During graviton oscillations increasing of m =g

XX MX≤10 16 GeV overproduction: diluition

is needed (inflation)

Time Varying gravitational field

L= 1

2 ∂ 2

−V 1

2 ∂ X 2

− 1

2 2

MX− R X 2 − g2

2 2 X 2

Overproduction problem: to have

X =

M X nX 1 X ~M X nX ~a

t cr 0

−3 t

X-partilce production at inflation must

be extremely weak (diluition).

(Zeldovich & Starobinsky (1972), Chung, Kolb & Riotto (1998), Kuzmin & Tkachev (1998))

No coupling with inflation (g=0) X particle can be sterile

X-particle mass couples X to the expanding metric

creation occours when since H t≤m ~10 13 GeV

Ht~M X

M X ≤10 13 GeV M X ~2−310 13 GeV ⇔ X h 2 ~0.1


Discrete symmetry inhibits X-particles decay

Gauge discrete simmetry (remnant of the SSB gauge symmetry)

are respected by all interations (e.g. R-parity)

Long lifetime X ≫10 10 y

Decays of X-particles at the present epoch could arise in different models

Wormhole effect

(Berezinsky, Kachelriess & Vilenkin (1997))

Quantum Gravity through wormhole effect

could violate the discrete simmetry

Instanton induced decay

(Kuzmin & Rubakov (1997))

X-particles could decay through an

istanton transition

X ~ M 2

Pl

3

MX X ~ 1

M X

e2 S

exp 4

X

(S wormhole action)

(á gauge coupling)


1. The rare decays of SH relics may generate UHE particles the predicted mass of

the inflaton is about right!

2. As CDM, SH relics cluster in halos, in particular in the halo of our own Galaxy.

In this case the sources of UHECRs might be behind the corner (no GZK).

3. Photons are the expected UHECR primaries

In this talk: evidences that the spectrum of

UHECR from SHDM is now reliably predicted

Injection

QE~E −1.94

With this spectrum SHDM can explain only the

AGASA excess at E10 20 eV

For these AGASA events all arguments against the SHDM hypothesis do not work


How do we go from

X particles to UHECRs ?

Mainly π

Small fraction

nucleons

Hadronization

Hadronization

X

Cascade Cascade

Mainly π

Small fraction

nucleons

Mainly gammas

Neutrinos

nucleons

Discussion of the different techniques needed

to determine the UHECRs spectra, SUSY has to

be included

MC simulations

DGLAP equations


Monte Carlo Simulation

Perturbative QCD Parton Spectra UHECRs Spectra

h

Di x , MX =∑j=q ,g∫

x

Perturbative QCD

Angular Ordering

(coherent branching)

SUSY partons

(small correction)

2 2

QSUSY=1TeV 1 dz

Hadronization

z D j x

i

z , MX ,Q0 f h

j z ,Q0 Hadronization function

Independent of the scale

Determined from LEP data

MX =M Z

Minimal parton virtuality

2 2

Q =0.625GeV 0

Berezinsky & Kachelriess (2001)


LEP data fit

Hadronization Functions

Can be interpreted as FF at the scale

2 2

Q =0.625GeV 0

f h x ,Q 0 =N x a xx 0 −b 1−x c

x=

2 E

M X

R.A., Berezinsky & Kachelriess (2004)


SUSY-DGLAP equations

The FF at high scale can be calculated evolving them from a low scale. This evolution

is described by the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) equations. In the

general SUSY case, using the flavour singlet FFs for quark and squark, one has

h h

qx

,t Pq qx ,t Pgq x ,t Psq x ,t Pl qx ,t qx

,t

h h

D

∂ gx

,t 2n f Pq gx ,t Pg gx ,t 2 n f Ps gx ,t Pl gx ,t Dgx ,t

tD

h h

Ds x ,t Pq sx ,t Pg sx ,t Ps sx ,t Pl sx ,t Ds x ,t

h

x ,t=

2 n f Pq lx ,t Pg lx ,t 2 n f Ps lx ,t Pl lx ,t×D

h

x ,t

D l

t=ln s

s 0

Splitting function which describes the

emission of parton j by parton i

f ×g=∫ z

1 dx

2 2

SUSY is introduced at the threshold QSUSY=1TeV assuming SUSY FFs equal to

zero before this common threshold (Rubin (1999)).

Starting point FFs at the scale Q=M Z computed with MC, reliable assumption as

follows form the comparison with experimental data (R.A., Berezinsky & Kachelriess (2004)).

x

D l

f xg x

z


MC - DGLAP comparison

QCD SUSY - QCD

Disagreement at smallest and largest x values

x3×10 −5

small x coherent branching not included in DGLAP evolution

x1×10 −1

large x sensitive to the adronization scheme,

uncertanties in the measured FFs

DGLAP evolution not much sensitive to the value of

Q SUSY

R.A., Berezinsky & Kachelriess (2004)


Photon Nucleon Spectra

Using the MC approach we have determined (from exp. data) the hadronization

functions of charged pions and nucleons and the spectra of these particles at any scale

D x , MX = 2

3 ∫ 1 dy

x y Dh y , M X


D x , MX = 2

3 R∫

1 dy

x R y Dh y , MX

e

D x , MX = 2

3 R∫

1 dy

x y qy∫ x /ry dz

x /y z Dh z , MX

N x , M X = D N x , M X

D h x , M X

At large eV

M X 10 12

x , M X = D x , M X

D h x , M X

≈0.73±0.03 N ≈0.12±0.02

ã í N Spectra

Photon spectrum dominant component of the radiation by SHDM

R.A., Berezinsky & Kachelriess (2004)


Gamma rays

Nucleons

New determination of the ratio ã/N ~ 2 - 3

Fraction of Nucleons in SHDM models increased

Photons dominates (Nã > 50%) at E5×10 eV

19

(R.A., Berezinsky and Kachellriess (2004))

previous results based on DGLAP evolution

(Barbot & Drees 2002/03) (Sarkar & Toldrà 2002).

small differences due to the diffenrences in the

starting FFs

Good agreement: Spectra as signature

of the model

Injection

QE~E −1.94

Ratio ã/N


UHECR in SHDM models

SHDM particle are accumulated

in the halo with an overdenensity

halo component

= halo

X

extr = halo

DM

CDM cr X

(Berezinsky, Kachelriess & Vilenkin (1997))

≈2.1×10 5

No GZK suppression

SHDM SHDM + Astrophysical

extragalactic

component

(protons)

halo SHDM source

(gamma rays)

Uniform Astrophysical

sources (protons)

L p n s ≈10 46 erg/ Mpc 3 y

R.A., Berezinsky & Kachelriess (2004)


Extragalactic component subdominant

Halo component only AGASA excess.

Observed UHECR flux

X

X

r X = X

CDM

t 0

X

relic abundance (cosmology: Mass

& Reheating Temperature)

lifetime (particle physics model)

M X ,T R , X

≈10 −11

UHECR flux selects a subspace of compatible with

the SHDM hypothesis (no fine tuning, measure of )

r X


Topological Defects

Regions of unbroken symmetry surrounded by

broken symmetry regions

Stable because of non-trivial winding of the Higgs

field around the defect (solid sate physics: vortex lines in

superfluid He, magnetic flux tubes in superconductors.....)

TD could be produced in non-thermal phase

transition during the preheating stage after

inflation

mX ~~10 16 GUT phase transition

GeV

TD “ constitued” by “ trapped” quanta of the massive

gauge, Higgs fields generically called X-particles.

TD stable but X-particles can be released through

collapse, annihilation, intersecting, chopping..........

Common idea:

X q q hadrons gamma rays

=〈 H 〉 0 ~T c

Vacuum expectation value of the

Higgs field in the broken phase,

phase transition critical

temperature

Core size ~ −1

UHECR


Cosmic Strings

Monopolonia

Superconducting Strings

Vortons

Necklaces

Small separation between TDs

Dneck ≥10 Kpc

monopole mass m X ~ 4 m

e

string mass density

2

~2 s

String intersection Chopping Cusp annihilation

Observed UHECR spectra difficult to reconcile

with the expected density of these TD, distance

between defects larger than attenuation lengths

D TD ≫R p R

monopoles

(Berezinsky, Blasi & Vilenkin (1998))

m

connecting strings

G H×U1 H×Z 2

r~ mX d ≫1

evolution parameter Monopoles and anti-monopoles trapped in necklaces

inevitably annihilate producing X-particles

(Berezinsky & Vilenkin (1997))

s


ate of X-particle production

˙n X = r2

t 3 m X

EGRET limit (Strong, Moskalenko & Reimer (2003))

obs ≈2×10 −6 eV /cm 3

(R.A., Berezinsky & Kachekriess (2004))

r 2 ≤9×10 27 GeV 2

e-m cascade energy density

cas = 1

2 f r2 t0 dt

∫0 t 3

D neck ~

3 f 1/4

10

2

4t cas

0

Observed UHECR flux:

1

1z 4=34

f r


2

r 2 =4.7×10 27 GeV 2

Consequence on the new spectrum:

UHECR from necklaces can explain

only the AGASA excess somewhat

above the prediction

UHE particle from necklaces can serve

only as an additional component in the

observed UHECR flux

2

t0

10 6 GeV 2 1/4

Kpc


Conclusions

1. UHECRs have an unprecedented potential to test the existence of new physics:

Super Heavy Dark Matter hypothesis

Topological Defects hypothesis

Lorentz Invariance violations (see Galante talk)

2. UHECRs spectrum in top-down models reliably computed (signatures of the

model):

Injection

QE~E −1.94

3. From the data already available (AGASA & HiReS)

4. Exciting future with Auger and EUSO

Ratio ã/N ~ 2 – 3 decreased respect to previous results

SHDM hypothesis compatible with the AGASA excess

Necklaces subdominant

Determination of the chemical composition (ã/N ratio)

Data from the Galactic Center, expected overdensity of SHDM

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