Halpern scatter

The Halpern scattering is the scattering of photons to photons. It is based on quantum electrodynamics and was first described in 1931 by the Austrian physicist Otto Halpern , after whom it was also named. Since photons are the quanta of light, Halpern scattering is also called light-by-light scattering . Halpern scattering is an effect that cannot be described using the classical theory of electromagnetic waves.

description

Classical electromagnetism

In classical physics, the only possible interaction between electromagnetic waves is interference . Both the electric and the magnetic field of the interacting waves are added at each point in space; the result of the superposition is generally a beat . The beat can be clearly broken down into the original waves using a Fourier analysis .

Quantum electrodynamics

In quantum electrodynamics, light is described by light quanta, photons. These can form virtual particle-antiparticle pairs, which in turn can annihilate again to form photons . A scattering of photons on photons takes place when the virtual particle-antiparticle pair of one photon annihilates with that of another photon. This can be described diagrammatically using Feynman diagrams ; the simplest process shown is a so-called box diagram. There are also more complex processes in which more than two photons scatter on each other or the number of incoming and outgoing photons is not identical.

Halpern scattering is a process that only involves real photons, i.e. observable particles. A process in which real photons interact with virtual photons is called Delbrück scattering .

Details

Feynman diagram for the 2-2 process of Halpern scattering

With Halpern scattering, the sum of the incoming and outgoing photons is always even due to the Furry theorem . Therefore, the simplest case of Halpern scattering is a 2-2 process in which two photons interact with each other and are scattered again. Higher order processes with more photons involved are suppressed by the cross section by the factor of the fine structure constants . ${\ displaystyle \ alpha \ approx 1/137}$

The cross-section is also inversely proportional to the mass of the generated virtual particle-antiparticle pairs to the eighth power, so that the most dominant contribution comes from the lightest charged elementary particle, the electron .

The differential and total cross sections in the rest system of Halpern scattering are in the limit of low photon energies:

{\ displaystyle {\ frac {\ mathrm {d} \ sigma} {\ mathrm {d} \ Omega}} = {\ frac {139 \ alpha ^ {4} \ omega ^ {6}} {(180 \ pi) ^ {2} m _ {\ mathrm {e}} ^ {8}}} (3+ \ cos ^ {2} \ theta) ^ {2}}

{\ displaystyle \ sigma = {\ frac {973 \ alpha ^ {4} \ omega ^ {6}} {10125 \ pi m _ {\ mathrm {e}} ^ {8}}}}

Where:

${\ displaystyle \ omega}$ the angular frequency of the scattering photons in the rest system
${\ displaystyle m _ {\ mathrm {e}}}$ the electron mass
${\ displaystyle \ theta}$ the polar angle

Experimental evidence

Halpern scattering was first detected in 2015 by the ATLAS group of the Large Hadron Collider . In this lead ions at a mass energy of accelerated and in an integrated luminosity of detected 13 scattering processes. This amount is within the predictions of the Standard Model . ${\ displaystyle {\ sqrt {s}} = 5 {,} 02 \, {\ text {TeV}}}$ ${\ displaystyle \ int {\ mathcal {L}} \ mathrm {d} t = 4 {,} 80 \ cdot 10 ^ {- 4} {\ text {b}} ^ {- 1}}$

literature

Matthew D. Schwartz: Quantum field theory and the standard model . Cambridge University Press, New York 2014. ISBN 978-1-107-03473-0 .
The ATLAS Collaboration: Evidence for light-by-light scattering in heavy-ion collisions with the ATLAS detector at the LHC , arxiv : 1702.01625v1 .
Yi Liang and Andrzej Czarnecki: Photon-photon scattering: a tutorial , arxiv : 1111.6126v2 .