Manfred Hanke / Prof. Schäfer, Institut für theoretische Kern- und Teilchenphysik Compton-scattering of the cosmic background radiation off a ultrarelativsitic cosmic proton and pair production by a (back-scattered) photon Manfred Hanke, August 2005: QED- Project (guided by Prof. A. Schäfer)

Manfred Hanke / Prof. Schäfer, Institut für theoretische Kern- und Teilchenphysik 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 Contents of this talk:

Manfred Hanke / Prof. Schäfer, Institut für theoretische Kern- und Teilchenphysik 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) - follows Plancks formula for black-body-radiation with T = 2,725 K:

Manfred Hanke / Prof. Schäfer, Institut für theoretische Kern- und Teilchenphysik 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) - follows Plancks formula for black-body-radiation with T = 2,725 K:

Manfred Hanke / Prof. Schäfer, Institut für theoretische Kern- und Teilchenphysik Cosmic rays - high-energy particles (up to eV) - mostly (97%) nucleons, especially protons, -particles - discovered in 1912 by V. Hess (Nobelprize 1936)

Manfred Hanke / Prof. Schäfer, Institut für theoretische Kern- und Teilchenphysik Fluxes of Cosmic Rays (1 particle per m²·s) Knee (1 particle per m²·year) (1 particle per km²·year) Ankle Flux Energy

Manfred Hanke / Prof. Schäfer, Institut für theoretische Kern- und Teilchenphysik Cosmic rays - high-energy particles (up to eV) - mostly (97%) nucleons, especially protons, -particles - origin: solar eruptions, supernovae, cosmic jets (from black holes / pulsars),..., ? - Nucleons with energies higher than 5·10 19 eV loose their energy by the GZK-effect: (Greisen-Zatsepin-Kuzmin) + p + N + What is the energy-loss through Compton-scattering? - discovered in 1912 by V. Hess (Nobelprize 1936)

Manfred Hanke / Prof. Schäfer, Institut für theoretische Kern- und Teilchenphysik QED -Compton-scattering e + e + (Klein-Nishina) Easy calculation of the cross-section in the Dirac-theory: How to calculate Compton-scattering off a proton?

Manfred Hanke / Prof. Schäfer, Institut für theoretische Kern- und Teilchenphysik 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 Contents of this talk:

Manfred Hanke / Prof. Schäfer, Institut für theoretische Kern- und Teilchenphysik The cross-section To calculate the energy-loss through Compton-scattering, one needs... for Compton-scattering off a proton, with one finds: In Hildebrandt, Griesshammer, Hemmert, Pasquini: Signatures of Chiral Dynamics in Low Energy Compton Scattering off the Nucleon (nucl-th/ ) the A i s defined as page- long integrals over two Feynman parameters (!)

Manfred Hanke / Prof. Schäfer, Institut für theoretische Kern- und Teilchenphysik, for example, is given by: A1A1

Manfred Hanke / Prof. Schäfer, Institut für theoretische Kern- und Teilchenphysik Where do these expressions come from? EFT (Chiral Effective Field Theory) The Heavy Baryon Chiral Perturbation Theory only involves explicit πN degrees of freedom.

Manfred Hanke / Prof. Schäfer, Institut für theoretische Kern- und Teilchenphysik Where do these expressions come from? EFT (Chiral Effective Field Theory) The Heavy Baryon Chiral Perturbation Theory only involves explicit πN degrees of freedom, whereas the Small Scale Expansion formalism includes explicit spin 3/2 nucleon resonance degrees of freedom.

Manfred Hanke / Prof. Schäfer, Institut für theoretische Kern- und Teilchenphysik Where do these expressions come from? EFT (Chiral Effective Field Theory) The Heavy Baryon Chiral Perturbation Theory only involves explicit πN 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).

Manfred Hanke / Prof. Schäfer, Institut für theoretische Kern- und Teilchenphysik Here, the following abbreviations and constants are used: for > 0 - m 130 MeV, the values get imaginary due to the resonance, and zero-values cause numerical divergencies by the denominators! Problem:

Manfred Hanke / Prof. Schäfer, Institut für theoretische Kern- und Teilchenphysik numerical results for < 130 MeV 20 nbarn The cross-section

Manfred Hanke / Prof. Schäfer, Institut für theoretische Kern- und Teilchenphysik - for the energy-loss of the proton:, z := cos (proton, scattered photon) cm To calculate the energy-loss through Compton-scattering, one needs... 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 Kinematics

Manfred Hanke / Prof. Schäfer, Institut für theoretische Kern- und Teilchenphysik Now, one can calculate... k := energy of the cosmic background photon, := cos (proton, photon) lab, z := cos (proton, scattered photon) c Differential probabilities

Manfred Hanke / Prof. Schäfer, Institut für theoretische Kern- und Teilchenphysik one can look at the spectrum of interacting photons : Now, as one has calculated the differential probability

Manfred Hanke / Prof. Schäfer, Institut für theoretische Kern- und Teilchenphysik Do you see any difference to the Planck-spectrum? (E p = eV) Spectrum of interacting photons

Manfred Hanke / Prof. Schäfer, Institut für theoretische Kern- und Teilchenphysik Now, as one has calculated the differential probability, one can look at the For the numerical simulation, the -function is realized by a histogram. spectrum of energy-loss :

Manfred Hanke / Prof. Schäfer, Institut für theoretische Kern- und Teilchenphysik Spectrum of energy-loss (E p = eV)

Manfred Hanke / Prof. Schäfer, Institut für theoretische Kern- und Teilchenphysik One can rewrite the -function and perform the integral over z to get an analytic expression for that is only an integral over k and, which can more easily be numerically determined. Spectrum of energy-loss

Manfred Hanke / Prof. Schäfer, Institut für theoretische Kern- und Teilchenphysik Spectrum of energy-loss (E p = eV)

Manfred Hanke / Prof. Schäfer, Institut für theoretische Kern- und Teilchenphysik The mean energy-loss 5.3 MeV / ly for proton with E p = eV ~ E p 2

Manfred Hanke / Prof. Schäfer, Institut für theoretische Kern- und Teilchenphysik Result - The low energy-loss is due to the small cross-section for Compton-scattering. 1. Energy-loss of a cosmic proton - A mean energy-loss of 5.3 MeV / ly for eV- protons corresponds to a mean free path of 1.9 · ly. (The mean distance between galaxies is of order 10 6 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)

Manfred Hanke / Prof. Schäfer, Institut für theoretische Kern- und Teilchenphysik But: The protons energy-loss (up to eV for E p = 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. 2. Mean free path of a back-scattered photon

Manfred Hanke / Prof. Schäfer, Institut für theoretische Kern- und Teilchenphysik 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 Contents of this talk:

Manfred Hanke / Prof. Schäfer, Institut für theoretische Kern- und Teilchenphysik The total cross-section for e + / e – - pair production from two photons (Breit-Wheeler) It is. As a result from kinematics:,

Manfred Hanke / Prof. Schäfer, Institut für theoretische Kern- und Teilchenphysik The total cross-section

Manfred Hanke / Prof. Schäfer, Institut für theoretische Kern- und Teilchenphysik Differential probabilities k 0 = 3.21 · 10 9 MeV k max(CMB) k max( ) maximum

Manfred Hanke / Prof. Schäfer, Institut für theoretische Kern- und Teilchenphysik Differential probabilities k 0 = 5 · 10 7 MeV k max(CMB) < k max( ) suppression by the exp-factor

Manfred Hanke / Prof. Schäfer, Institut für theoretische Kern- und Teilchenphysik Differential probabilities k 0 = MeV k max( ) < k max(CMB) suppression by the k²-factor

Manfred Hanke / Prof. Schäfer, Institut für theoretische Kern- und Teilchenphysik rapid decrease of probability for k 0 < 5 · 10 8 MeV Mean free path dW / dL ( k 0 = 10 9 MeV) = 2.52 · / ly dW / dL ( k 0 = 10 8 MeV ) = 2.28 · / ly dW / dL ( k 0 = 10 7 MeV ) = 1.60 · / ly

Manfred Hanke / Prof. Schäfer, Institut für theoretische Kern- und Teilchenphysik Mean free path (slow) decrease of probability for k 0 > MeV dW / dL ( k 0 = MeV ) = 3.0 · / ly dW / dL ( k 0 = MeV ) = 9.4 · / ly dW / dL ( k 0 = MeV ) = 2.0 · / ly

Manfred Hanke / Prof. Schäfer, Institut für theoretische Kern- und Teilchenphysik Mean free path minimal probability at k 0 = 3.21 · 10 9 MeV dW / dL = 3.8 · / ly maximal mean free path = 26 · 10 3 ly

Manfred Hanke / Prof. Schäfer, Institut für theoretische Kern- und Teilchenphysik Result 2. Mean free path of a back-scattered photon The universe should be almost transparent for very-high-energy -rays with k 0 < eV (at least what concerns e + /e – -pair production) – the mean free paths are billions of lightyears! Photons with ultra-high energies 2·10 14 eV < k 0 < eV should interact with the cosmic background radiation and 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.)

Manfred Hanke / Prof. Schäfer, Institut für theoretische Kern- und Teilchenphysik 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 Contents of this talk: 3. Summary

Manfred Hanke / Prof. Schäfer, Institut für theoretische Kern- und Teilchenphysik from EFT: 20 nbarn 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 : spectrum of energy-loss

Manfred Hanke / Prof. Schäfer, Institut für theoretische Kern- und Teilchenphysik Spectrum of a protons energy-loss due to Compton-scattering

Manfred Hanke / Prof. Schäfer, Institut für theoretische Kern- und Teilchenphysik 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 : ~ E p 2, but only 5.3 MeV / ly for E p = eV

Manfred Hanke / Prof. Schäfer, Institut für theoretische Kern- und Teilchenphysik 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: ~ E p 2, but only 5.3 MeV / ly for E p = eV - Result 2.Mean free path of a back-scattered photon - Cross-section - Differential probabilities and mean free path - Result 3.Summary : 26 · 10 3 ly : no -rays with 2·10 14 eV < k 0 < eV (k 0,min = 3.2·10 15 eV)

Manfred Hanke / Prof. Schäfer, Institut für theoretische Kern- und Teilchenphysik Thank you very much for your attention! Thats it!