michael kachelrieß ntnu, trondheimweb.phys.ntnu.no/~mika/tours12.pdfinternal discrepancy in pao:...

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Fundamental Physics at Extreme High Energies

Michael Kachelrieß

NTNU, Trondheim

Outline:

Introduction

Testing (new?) strong interactions

Lorentz invariance violation

Topological defects & superheavy dark matter

Summary

Michael Kachelrieß (NTNU Trondheim) Fundamental Physics at UHE 8th Tours Symposium 2 / 28

Determining nuclear composition: Xmax and RMS(Xmax)Bethe-Heitler model: Nmax ∝ E0 and Xmax ∝ ln(E0)



superposition model: nuclei = A shower with E = E0/A

⇒ Xmax ∝ − ln(A) and RMS(Xmax) reduced



superposition model: nuclei = A shower with E = E0/A

⇒ Xmax ∝ − ln(A) and RMS(Xmax) reduced

RMS(Xmax) has smaller theoretical error than Xmax


Restricting QCD: BFKL, Color Glass Condensates, . . .

550

600

650

700

750

800

850

108 109 1010 1011

Xm

ax [g

/cm

2 ]

energy [GeV]

Seneca 1.2

Sibyll (p,Fe)BBL r.c. (p)BBL f.c. (p)

Hires Stereo

[Drescher, Dumitru, Strikman ’04 ]


Nuclear composition via Xmax:

/decade] 18 19

]2>

[g/c

mm

ax<X

650

700

750

800

850

proton

iron

QGSJET01QGSJETIISibyll2.1EPOSv1.99

Auger 2009

HiRes ApJ 2005


Nuclear composition via RMS(Xmax) from Auger:

E [eV]

1810 1910

E [eV]

1810 1910

]2)

[g/c

mm

axR

MS

(X

10

20

30

40

50

60

70 proton

iron


Mixed composition:

Mean 744.8RMS 62.02

]2 [g/cmmaxX600 650 700 750 800 850 900 9500

0.02

0.04

0.06

0.08

0.1

0.12

Mean 744.8RMS 62.02

70% proton

30% iron

sum

σ2 =∑

i

fiσ2i +

∑

i<j

fifj(Xmax,i − Xmax,j)2


Nuclear composition from HiRes/TA:MC/Data (QGSJET-II)HiRes TA

Proton

Fe

•Proton

•Fe

Preliminary


What goes wrong?

internal discrepancy in PAO:

AGN correlations favor protons

RMS(Xmax) favors heavy

energy spectrum, Xmax and RMS(Xmax) difficult to fit

experimental discrepancy: HiRes/TA ⇔ Auger

Xmax

RMS(Xmax)

discrepancy experiment ⇔ theory:

energy ground array/fluoresence ∼ 1.2

muon number exp/MC ∼ 2


Comparison of MCs to LHC data: Energy flow

'()*'+),-)./00/1)+234/)05/6)7/1/)891024:;91;6)

./0PYTHIA as typical HEP model Cosmic ray interaction models


What can/should be changed?

/1"*,$:A$,G84)4I$;4:?($

G5/;+ #67+ H<

6-=I+ JK#

<6-=+

N:>B:()@:4&"+<)"8$ "$ #$D(&+33:#"8J$ #$D4+88:#"8J$

K)C"F$*:>B:()@:4$ "$D>"+4$:A$>)CJ$ #$D>"+4$:A$>)CJ$ "$D?8:+F"8$==$3:,(J$

N8:(($("*@:4$$"$ $$$===$ #$D(&+33:#"8J$ #$D4+88:#"8J$

H)18+*@<"$A8+*A"3#$ "$ #$D(&+33:#"8J$ #$D4+88:#"8J$

KG3@B3)*),'$"$ "$ #$D(&+33:#"8J$ #$D4+88:#"8J$

kW$A8+*@:4$$$#$ "$ $===$ $===$

O,8+4I"4"((X$Q=Q?+8$ $===$ $===$ $===$


What can/should be changed?

/1"*,$:A$,G84)4I$;4:?($

G5/;+ #67+ H<

6-=I+ JK#

<6-=+

N:>B:()@:4&"+<)"8$ "$ #$D(&+33:#"8J$ #$D4+88:#"8J$

K)C"F$*:>B:()@:4$ "$D>"+4$:A$>)CJ$ #$D>"+4$:A$>)CJ$ "$D?8:+F"8$==$3:,(J$

N8:(($("*@:4$$"$ $$$===$ #$D(&+33:#"8J$ #$D4+88:#"8J$

H)18+*@<"$A8+*A"3#$ "$ #$D(&+33:#"8J$ #$D4+88:#"8J$

KG3@B3)*),'$"$ "$ #$D(&+33:#"8J$ #$D4+88:#"8J$

kW$A8+*@:4$$$#$ "$ $===$ $===$

O,8+4I"4"((X$Q=Q?+8$ $===$ $===$ $===$

only option: reduce π0

“restoration of chiral symmetry?” [Farrar ’12 ]


High energy is not enough

Generically, new physics requires not only large s, but also largemomentum transfer t




0

1

2

0 2 4 6 b, Fm

b σ

inel

(b)

p+14N (1 PeV) QGSJET II-03




0

1

2

0 2 4 6 b, Fm

b σ

inel

(b)

p+14N (1 PeV) QGSJET II-03

Exceptions: large extra dimensions, classicalisation, . . .


Large extra dimensions

t chanel exchange of KK gravitons σ ∼ s2/M6D

black hole production, if b <∼ Rs with σ ∼ πR2s


Large extra dimensionst chanel exchange of KK gravitons σ ∼ s2/M6

D



Large extra dimensions

t chanel exchange of KK gravitons σ ∼ s2/M6D


no deviations from SM at LHC


Lorentz invariance violation (LIV):

motivation: has Planck length LPl =√

~G/c3 any role for space-timedespite SR?





if yes: modifies dispersion relation

E2 = m2 + p2 + f(E, p, MPl)

= m2 + p2 + η(1)|p|MPl + η(2)|p|2 + η(3)|p|3/MPl + . . .





if yes: modifies dispersion relation

E2 = m2 + p2 + f(E, p, MPl)

= m2 + p2 + η(1)|p|MPl + η(2)|p|2 + η(3)|p|3/MPl + . . .

⇒ ToF delays (Opera, GRBs, AGN flares, SN1987a)⇒ reaction thresholds: changes lower, introduces upper, opens new

channels⇒ vacuum birefringence⇒ generically preferred reference frame⇒ sideral anisotropies⇒ generically breaking of CPT



implementation:

EFT: SM plus composite operators of SM⊕ tensor fields withnon-zero vev ⇒ preferred reference system



implementation:


Example: gauge-invariant, CPT-even modification of QED

L = −1

4(ηµρηνσ − κµνρσ) (∂µAν − ∂νAµ) (∂ρAσ − ∂σAρ)

κ : 20 − 1 = 19 independent dimensionless numbers to be limited10 lead to birefringence, |κ| < 10−32, 9 constraint by UHECR



implementation:


Example: gauge-invariant, CPT-even modification of QED

L = −1

4(ηµρηνσ − κµνρσ) (∂µAν − ∂νAµ) (∂ρAσ − ∂σAρ)

κ : 20 − 1 = 19 independent dimensionless numbers to be limited10 lead to birefringence, |κ| < 10−32, 9 constraint by UHECR

Double special relativity (DSR): GR: laws of physics do not contain any scale of length or velocity ER: laws of physics do not contain any scale of length, but one

fundamental velocity, c DSR: laws of physics contain a fundamental scale of length and of

velocity


Lorentz invariance violation:

LIV becomes important, when

m2

p2∼

pn−2

Mn−2Pl

or

pcr ∼n

√

m2Mn−2Pl

n pcr for ν pcr for e− pcr for p

2 p ∼ mν ∼ 1 eV p ∼ me p ∼ mp

3 ∼GeV ∼ 10 TeV ∼ 1 PeV

4 ∼ 100 TeV ∼ 100 PeV ∼ 3 EeV


Bounds on LIV parameters from UHECRs:

threshold for GZK may be changed

GZK photons: upper threshold Emax for γγ → e+e− introduced

if Emax ≪ 1020 eV, photon fraction too large

if some UHE photons observed, photon decay γ → e+e− can belimited


Bounds on dim=5 LIV parameters: ξ ↔ e and η ↔ γ

If LIV exists, then probably not of EFT typeMichael Kachelrieß (NTNU Trondheim) Fundamental Physics at UHE 8th Tours Symposium 19 / 28


If LIV exists, then probably not of EFT typeMichael Kachelrieß (NTNU Trondheim) Fundamental Physics at UHE 8th Tours Symposium 19 / 28


If LIV exists, then probably not of EFT type


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 ↔ DM non-thermal or thermal point particle or non-perturbative solutions stable or decaying

fragmentation products: mainly photons, neutrinos


Top-Down Models

UHECR primaries are produced by decays of supermassive particle X withMX >∼ 1012 GeV.

topological defects: monopoles, strings, . . .

superheavy metastable particles

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

ϕk +[

k2 + m2eff(τ)

]

ϕk = 0




ϕk +[

k2 + m2eff(τ)

]

ϕk = 0

If meff is time dependent, vacuum fluctuations will be transformedinto real particles.




ϕk +[

k2 + m2eff(τ)

]

ϕk = 0


⇒ expansion of Universe,

m2eff = M2a2 + (6ξ − 1)

a′′

a

leads to particle production




ϕk +[

k2 + m2eff(τ)

]

ϕk = 0


⇒ expansion of Universe,

m2eff = M2a2 + (6ξ − 1)

a′′

a

leads to particle production

In inflationary cosmology

ΩXh2 ∼

(

MX

1012GeV

)2 TRH

109GeV

dependent only on cosmology, for MX <∼ HI


Signatures of SHDM decays

flat spectra dE/E1.9 up to mX/2

E3J(E

)/m

−2s−

1eV

2

E/eV

1e+23

1e+24

1e+25

1e+26

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




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

threshold energy [eV]

1910 2010

phot

on fr

actio

n

−210

−110

1

threshold energy [eV]

1910 2010

phot

on fr

actio

n

−210

−110

1

SHDM

SHDM’

TD

Z Burst

GZK

HP HP

A1

A1 A2

AY

Y

Y

Auger SD

Auger SD

Auger SD

Auger HYB




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

galactic anisotropy:

0 20 401

10

NFW

1020 eV 6x1019 eV 3x1019 eV 1019 ev


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

matterepoch

scalingregime


Topological defect models

+ “generic” in SUSY-GUTs

+ produced during reheating

- typical density: one per horizon/correlation length

- main energy loss low-energy radiation?

favourable models for UHECRs:

monopole-antimonopole pairs

hybrid defects: cosmic necklaces


Topological defect models

+ “generic” in SUSY-GUTs

+ produced during reheating

- typical density: one per horizon/correlation length

- main energy loss low-energy radiation?

favourable models for UHECRs:

monopole-antimonopole pairs

hybrid defects: cosmic necklaces G → H ⊗ U(1) → H ⊗ Z2

monopoles M ∼ ηm/e connected by strings µs ∼ η2

s

parameter r = M/(µd): r ≪ 1 normal string dynamics r ≫ 1 non-rel. string network


Status of topological defect models – necklaces:

E3J(E

)/m

−2s−

1eV

2

E/eV

ν

p γ

p+γ

1e+22

1e+23

1e+24

1e+25

1e+26

1e+27

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


Status of topological defect models – necklaces:

E3J(E

)/m

−2s−

1eV

2

E/eV

ν

p γ

p+γ

1e+22

1e+23

1e+24

1e+25

1e+26

1e+27

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

• large neutrino fluxes possible• UHE photon fraction reduced


Summarycomposition of UHECR is crucial both for astrophysics and stronginteractions

exremely strong limits on ETF-like LIV

LHC limits on large extra dimensions

no positive evidence for superheavy dark matter from its three keysignatures:

spectral shape photons galactic anisotropy

SHDM remains an interesting DM candidate

topological defects are generic prediction of (SUSY-) GUTs

⇒ both should be searched for as subdominant sources of UHECRs;potential for UHE neutrinos


michael kachelrieß ntnu, trondheimweb.phys.ntnu.no/~mika/tours12.pdfinternal discrepancy in pao:...

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