Feynman Diagrams Rosie Cavalier 2012 Edited by Mr Catchpole 2014

What is a Feynman diagram? A Feynman diagram is used by to illustrate and calculate probabilities of reactions between elementary particles. The diagram shows particle interactions and the idea is to use interaction vertices* in order to build up possible physical processes

Interaction and exchange particles To understand the Feynman diagram you must first look at interactions and exchange particles A free electron can emit a (virtual) photon provided the photon is very quickly absorbed This diagram shows the exchange of a virtual photon in the interaction between electrons. As the first electron emitted a photon, it changes direction slightly in order to conserve momentum. The second photon also changed direction, since it absorbed a photon.

The change in direction of the two electrons can be interpreted as the result of a force or interaction between the two electrons. The two electrons will exert repelling forces on each other according to Coulomb’s law The particle physics view of the situation is that Coulomb’s law is the exchange of a virtual photon between the electrons. This electromagnetic interaction is the exchange of a virtual photon between charged particles. The exchanged photon is not observable.

Basic Interaction Vertices There are four fundamental forces (or Interactions) in nature. The interactions and the particles involved, as well as their relative strength are shown below. InteractionInteraction acts onExchange particle(s)Relative strength ElectromagneticParticles with electric charge Photon1/137 WeakQuarks and leptons only W and Z bosons10 -6 Strong (colour)Quarks onlyGluons1 GravitationalParticiples with mass Graviton However, the electromagnetic and weak nuclear reactions have been shown to be two faces of the same interactions, called the electroweak interaction. Therefore there are in fact three fundamental interactions

Interaction The electroweak interaction The strong (colour interaction) The gravitational interaction – Least relevant for particle physics as the masses of the particles are so small.

Interaction vertices At a fundamental level, particle physics views an interaction between two elementary particles in terms of interaction vertices The wavy line represents a photon The arrow to the right represents an electron An arrow to the left would represent a positron

In the electron-electron scattering process, there are two interaction vertices so the amplitude of the diagram is proportional to:

Calculating a Feynman diagram

Building Feynman diagrams You need: Basic interaction vertex Lines with arrows to represent electrons and positrons (or “real” particles) Wavy lines to represent photons (or “virtual” exchange particles)

Vertices examples Electromagnetic interaction is simple as it only has one interaction vertex The weak and strong interaction are more complex as they have many vertices

Weak and Strong interactions Basic interaction vertices for the weak interaction involve the W or Z boson along with two fermions (quarks or leptons) These vertices are given if needed in the exam so you don’t have to remember them.

Weak Interactions These are examples of interaction vertices for weak interaction The d quark turns into a u quark by emitting a virtual W - boson. The total charge is conserved as the charge going in is -1/3e, the charge leaving the vertex is +2/3e for the u quark and –e for the W -. Therefore the total charge is -1/3e.

Strong interaction One interaction vertex is similar to electromagnetic vertex where electrons are replaced by quarks and photons by gluons The flavour of the quark does not change so if the incoming quark is a u quark then the outgoing quark will also be u.

Calculating the range of interaction The range of a particle is given by: R = h/4πmc m is the rest mass of the virtual particle which is why photons have long range and W and Z bosons have a very short range

Calculating the range of strong force Since the individual gluons and quarks are contained within the proton or neutron, the masses attributed to them cannot be used in the range relationship to predict the range of the force. When something is viewed as emerging from a proton or neutron, then it must be at least a quark-antiquark pair, so it is then plausible (Yukawa’a prediction) that the pion as the lightest meson should serve as a predictor of the maximum range of the strong force between nucleons.