QED-Project

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QED-Project
Manfred Hanke, August 2005
(guided by Prof. A. Schäfer)
Compton-scatteringof the cosmic background
radiation off a ultrarelativsitic cosmic proton
andpair productionby a (back-scattered) photon
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Contents of this talk
0. Introduction- Cosmic background radiation-
Cosmic rays- Compton-scattering 1. Energy-loss
of a cosmic proton due to Compton-scattering-
Cross-section- Kinematics- Differential
probabilities- Mean energy-loss- Result 2. Mean
free path of a back-scattered photon-
Cross-section- Differential probabilities and
mean free path- Result 3. Summary
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Cosmic background radiation

• predicted by G. Gamow and R. Alpher in the 1940s

• discovered by A. Penzias and R. W. Wilson in
  1964 (Nobelprize in 1978)

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Cosmic background radiation

• predicted by G. Gamow and R. Alpher in the 1940s

• discovered by A. Penzias and R. W. Wilson in
  1964 (Nobelprize in 1978)

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Cosmic rays
- discovered in 1912 by V. Hess (Nobelprize 1936)
- high-energy particles (up to 1020 eV)
- mostly (97) nucleons, especially protons,
?-particles
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Fluxes of Cosmic Rays
Flux
(1 particle per m²s)
Knee(1 particle per m²year)
Ankle
(1 particle per km²year)
Energy
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Cosmic rays
- discovered in 1912 by V. Hess (Nobelprize 1936)
- high-energy particles (up to 1020 eV)
- mostly (97) nucleons, especially protons,
?-particles
- origin solar eruptions, supernovae,
cosmic jets (from black holes / pulsars), ..., ?

• Nucleons with energies higher than 51019 eV
  loose their energy by the GZK-effect
  (Greisen-Zatsepin-K
  uzmin)
• ? p ? ? ? N ?

What is the energy-loss through
Compton-scattering?
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QED -Compton-scattering
How to calculate Compton-scattering off a proton?
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Contents of this talk
0. Introduction- Cosmic background radiation-
Cosmic rays- Compton-scattering 1. Energy-loss
of a cosmic proton due to Compton-scattering-
Cross-section- Kinematics- Differential
probabilities- Mean energy-loss- Result 2. Mean
free path of a back-scattered photon-
Cross-section- Differential probabilities and
mean free path- Result 3. Summary
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The cross-section
To calculate the energy-loss through
Compton-scattering,one needs...
for Compton-scattering off a proton
the Ais defined as page-long integrals over two
Feynman parameters (!)
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A1
, forexample, is given by
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Where do these expressions come from?

• ?EFT (Chiral Effective Field Theory)
• The Heavy Baryon Chiral Perturbation Theory
• only involves explicit pN degrees of freedom.

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Where do these expressions come from?

• ?EFT (Chiral Effective Field Theory)
• The Heavy Baryon Chiral Perturbation Theory
• only involves explicit pN degrees of freedom,
  whereas the Small Scale Expansion
  formalism includes
• explicit spin 3/2 nucleon resonance degrees of
  freedom.

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Where do these expressions come from?

• ?EFT (Chiral Effective Field Theory)
• The Heavy Baryon Chiral Perturbation Theory
• only involves explicit pN degrees of freedom,
  whereas the Small Scale Expansion
  formalism includes
• explicit spin 3/2 nucleon resonance degrees of
  freedom (and within that in my opinion very
  exotic couplings,
• like ? N ? or ? ? N N, for which the
  parameters have
• been fitted from experimental cross section
  data).

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Problem
Here, the following abbreviations and constants
are used
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The cross-section
20 nbarn ?
numericalresults for ? lt 130 MeV
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Kinematics
To calculate the energy-loss through
Compton-scattering,one needs...
- for the energy-loss of the
proton
, z cos ?(proton, scattered
photon)cm
In the relativistic limit, one gets - for the
photon-energy in the center-of-mass-frame
Here is k energy of the cosmic background
photon, ? cos ?(proton, photon)lab
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Differential probabilities
Now, one can calculate...
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the differential probability
Now, as one has calculated
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Spectrum of interacting photons
(Ep 1019 eV)
Do you see any difference to the Planck-spectrum?
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spectrum of energy-loss
Now, as one has calculated
the differential probability,
one can look at the
For the numerical simulation, the ?-function is
realized by a histogram.
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Spectrum of energy-loss
(Ep 1019 eV)
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Spectrum of energy-loss
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Spectrum of energy-loss
(Ep 1019 eV)
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The mean energy-loss
? 5.3 MeV / ly for proton with Ep 1019 eV
Ep2
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Result
1. Energy-loss of a cosmic proton

• The low energy-loss is due to the small
  cross-section for Compton-scattering.

• A mean energy-loss of 5.3 MeV / ly for 1019 eV-
  protons corresponds to a mean free path of 1.9
  1012 ly. (The mean distance between galaxies
  is of order 106 ly.)

• Compton-scattering of the cosmic background
  radiation off such a ultra-high-energy cosmic
  proton therefore does not lead to a noticeable
  decceleration of cosmic rays.

The result is, that there is no result.
(what concerns the decceleration of cosmic
protons)
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2. Mean free path of a back-scattered photon
But
The protons energy-loss (up to 1018 eV for Ep
1019 eV) is added to the photons energy. (This
is known as Compton-back-scattering / inverse
Compton-scattering,which is one way to produce
ultra-high-energy cosmic ?-rays.)
What happens with these high-energetic photons?
e / e - pair production from single photons is
not allowed, but they can interact with the
cosmic background radiation.
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Contents of this talk
0. Introduction- Cosmic background radiation-
Cosmic rays- Compton-scattering 1. Energy-loss
of a cosmic proton due to Compton-scattering-
Cross-section- Kinematics- Differential
probabilities- Mean energy-loss- Result 2. Mean
free path of a back-scattered photon-
Cross-section- Differential probabilities and
mean free path- Result 3. Summary
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The total cross-section
for e / e - pair production from two photons
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The total cross-section
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Differential probabilities
k0 3.21 109 MeV
kmax(CMB) ? kmax(?) ? maximum
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Differential probabilities
k0 5 107 MeV
kmax(CMB) lt kmax(?) ? suppression by the
exp-factor
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Differential probabilities
k0 1011 MeV
kmax(?) lt kmax(CMB)? suppression by the
k²-factor
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Mean free path
rapid decrease of probability for k0 lt 5 108 MeV
dW/dL(k0 109 MeV) 2.52 10-5/ly dW/dL(k0
108 MeV) 2.28 10-9/ly dW/dL(k0 107 MeV)
1.60 10-54/ly
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Mean free path
(slow) decrease of probability for k0 gt 1011 MeV
dW/dL(k0 1010 MeV) 3.0 10-5/lydW/dL(k0
1011 MeV) 9.4 10-6/ly dW/dL(k0 1012 MeV)
2.0 10-6/ly
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Mean free path
minimal probability at k0 3.21 109 MeV

• dW/dL 3.8 10-5/ly
• maximal mean free pathltLgt 26 103 ly

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Result
2. Mean free path of a back-scattered photon
The universe should be almost transparent for
very-high-energy ?-rays with k0 lt 1014 eV (at
least what concerns e/e-pair production) the
mean free paths are billions of lightyears!
Photons with ultra-high energies 21014 eV
lt k0 lt 1019 eV should interact with the cosmic
background radiationand create e/e-pairs
within less than 3 million ly, what is
approximately the mean distance of galaxies.
There should be no ultra-high-energy
extragalactic ?-rays! (Back-scattered photons
with these energies cant be observed.)
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3. Summary
Contents of this talk
0. Introduction- Cosmic background radiation-
Cosmic rays- Compton-scattering 1. Energy-loss
of a cosmic proton due to Compton-scattering-
Cross-section- Kinematics- Differential
probabilities- Mean energy-loss- Result 2. Mean
free path of a back-scattered photon-
Cross-section- Differential probabilities and
mean free path- Result
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Contents of this talk
0. Introduction- Cosmic background radiation-
Cosmic rays- Compton-scattering 1. Energy-loss
of a cosmic proton due to Compton-scattering-
Cross-section- Kinematics- Differential
probabilities- Mean energy-loss- Result 2. Mean
free path of a back-scattered photon-
Cross-section- Differential probabilities and
mean free path- Result 3. Summary
from ?EFT ? 20 nbarn
spectrum of energy-loss
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Spectrum of a protons energy-loss due to
Compton-scattering
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Contents of this talk
0. Introduction- Cosmic background radiation-
Cosmic rays- Compton-scattering 1. Energy-loss
of a cosmic proton due to Compton-scattering-
Cross-section from ?EFT ? 20 nbarn -
Kinematics- Differential probabilities spectrum
of energy-loss- Mean energy-loss -
Result 2. Mean free path of a back-scattered
photon- Cross-section- Differential
probabilities and mean free path-
Result 3. Summary
Ep2, but only 5.3 MeV / ly for Ep 1019
eV
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Contents of this talk
0. Introduction- Cosmic background radiation-
Cosmic rays- Compton-scattering 1. Energy-loss
of a cosmic proton due to Compton-scattering-
Cross-section from ?EFT ? 20 nbarn -
Kinematics- Differential probabilities spectrum
of energy-loss- Mean energy-loss Ep2, but
only 5.3 MeV / ly for Ep 1019 eV -
Result 2. Mean free path of a back-scattered
photon- Cross-section- Differential
probabilities and mean free path-
Result 3. Summary
? 26 103 ly
(k0,min 3.21015 eV)
no ?-rays with 21014 eV lt k0 lt 1019 eV
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Thats it!
Thank you very muchfor your attention!