# Fundamental Interactions and Feynman Diagrams

Back to Standard Model

#### Fundamental Interactions

• All forces of nature derive from four Fundamental Interactions (or Forces), which govern how particles interact and, in some cases, decay:
• Electromagnetism
• Strong Force
• Weak Force
• Gravity
• The Standard Model governs the first three; General Relativity the last.
• The forces differ regarding:
• The kinds of particles experiencing the force
• The nature of the particle mediating the force
• The relative strength of the force
• The effective range of the force

#### Feynman Diagrams

• A Feynman Diagram represents particle interactions.
• The horizontal axis represents space in one dimension, with particles moving left and right along the horizontal line.
• The vertical axis represents time.
• At right is a Feynman diagram representing the reaction e+ ee+ e
• The left electron e moves to the right (blue line) along the horizontal line.
• The right electron e then moves to the left (other blue line) along the horizontal line.
• At vertex V1 the left electron emits a photon γ and recoils, moving to the left (red line).
• At vertex V2 the right electron absorbs the photon γ and recoils, moving to the right (red line).
• Lines with arrows, denoting the direction of travel, represent Matter Particles (electrons, neutrinos, quarks, protons, etc)
• Antiparticles have reversed arrows (which doesn’t mean they travel back in time).
• Wavy lines with no arrows represent Exchange Particles (photons, gluons, W and Z bosons).
• A vertex is a junction of three lines.
• Vertices obey the conservation laws for charge, baryon number, and lepton number.
• Only lines entering or leaving the diagram represent observable particles

#### Electromagnetic Interaction

• The electromagnetic force manifests itself as the attraction and repulsion among electrically-charged particles
• The force is responsible for
• electrons orbiting atomic nuclei
• ionic and covalent bonds
• chemical reactions
• electricity and magnetism
• electromagnetic waves
• Its exchange particle is the photon (γ).
###### Annihilation
• When a particle and its antiparticle collide, they annihilate each other, releasing energy.
• Positrons (e+) don’t live long because they are attracted to negatively-charged electrons (e).  When they collide, their masses are converted into energy in the form of a high-energy photon per E=mc2.
• Positron e+ and electron e  approach each other on the horizontal axis, collide, and are annihilated, releasing the photon 𝛾, which splits into a muon (𝜇) and an antimuon (𝜇+)
• [Arrows for antimatter particles are always reversed]
• The reaction is:  e+ + e→ 𝜇 + 𝜇+
###### Pair Production
• Pair production is the creation of a particle and its antiparticle from a high-energy photon. An electron and a positron are created, for example, when a gamma-ray photon passes near the electric field of a large atom such as lead or uranium.
• The energy of the photon is converted into the masses of the electron and positron per E=mc2
• Any excess energy is converted to kinetic energy of the electron and positron.
• Conserved in the process are electric charge (0), energy, and momentum.

#### Strong Interaction

• The Strong Force manifests itself as the attraction and repulsion among color-charged particles.
• Color-Charge
• A quark has a color-charge of red, green, or blue
• An antiquark has a color-charge of antired, antigreen, or antibluel
• Quarks with different color-charges attract
• Quarks with the same color-charge repel
• A hadron is a particle built from quarks:
• A baryon consists of three quarks: red, blue, green.
• An antibaryon consists of three antiquarks: antired, antiblue, antigreen
• A meson (mezz-on) consists of a quark and an antiquark

Proton

Neutron

Antiproton

Antineutron

Pion

###### Residual Strong Force

The Residual Strong Force, also known as the Nuclear Force, keeps protons and neutrons together in atomic nuclei, overcoming the electromagnetic repulsion among protons.

#### Weak Interaction

• The Weak Force manifests itself as a short-range force by which subatomic particles decay or change flavor
• The force is responsible for
• nuclear fusion
• nuclear fission
• decay of unstable subatomic particles
• Its exchange particles are the W+, W, and Z0 Bosons
###### Free Neutron Decay (Electron Emission Beta Decay)

Neutrons are typically bound in the nuclei of atoms, where they are stable. But a neutron on on its own spontaneously decays into a proton, an electron, and an antineutrino, per the weak force.  A free neutron, as it’s called, has an average lifetime of only 14 minutes 42 seconds. The type of decay is called Electron Emission Beta Decay. A neutron is made up of two down quarks and an up quark.  In the decay, a down quark (d) spontaneously emits a W-, an exchange particle of the weak force, which splits into an electron and an antineutrino.

###### Carbon Dating (Electron Emission Beta Decay)
• Carbon has three naturally-occurring isotopes
• C-12 makes up 99% of natural carbon
• C-13 makes up about 1%
• C-14, making up a tiny percent, is radioactive, spontaneously decaying into nitrogen.
• Through photosynthesis, plants absorb carbon in the form of carbon dioxide.  The carbon is passed onto animals when they eat the plants.
• The ratio of C-14 to C-12 remains constant as long as the organism is alive, since C-14, though decaying, is constantly replenished.
• When the organism dies, however, C-14 is no longer replenished and the ratio of C-14 to C-12 decreases as C-14 atoms decay.
• The ratio of C-14 to C-12 in a fossil can then be used to estimate how long ago the organism died.
• A carbon-14 nucleus, with 6 protons and 8 neutrons, spontaneously decays into nitrogen-14, with 7 protons and 7 neutrons, with a half-life of 5,730 years, emitting an electron and antineutrino in the process.  (The mean lifetime of a Carbon-14 atom is 8267 years.)
• This happens when a neutron in the carbon-14 nucleus decays into a proton, through Electron Emission Beta Decay.  In this process, a down quark (d) changes flavor into an up quark (u), emitting an electron (e) and an antineutrino (𝜈e).
###### Radioactivity (Positron Emission Beta Decay)

In Positron Emission Beta Decay an up quark in a proton changes flavor into a down quark, changing the proton to a neutron and emitting a neutrino (𝜈e) and a positron (e+). The process thus produces a daughter nucleus with an atomic number one less than its parent but with the same mass number. Positron emission was first observed by Irène and Frédéric Joliot-Curie in 1934.

###### Radioactivity (Electron Capture Beta Decay)

In Electron Capture Beta Decay an orbital electron in an atom’s inner shell is captured by the nucleus where it combines with a proton, which decays into a neutron and emits a neutrino. The atom is therefore lowered by one atomic number, e.g. from Carbon with 6 protons to Boron with 5