The Strong Interaction Michael Mattern

Contents The fundamental forces History The need of a strong force The Therory from Yukawa The pion as the mediator QCD Quantum chromodynamics (QCD) SU(3) and color blindness Color charge of particles Flow of color charge QED vs. QCD Confinement Asymptotic freedom Nuclear force Proseminar "The Strong Interaction" ( ) 2 Michael Mattern

The fundamental forces Proseminar "The Strong Interaction" ( ) 3 Michael Mattern ForceStrengthRange (m) strong electromagnetic 1/137infinite weak gravity6 x infinite

History: The need of a strong force Classical period ( ): discovery of protons, neutrons in a compact cluster (the nucleus/core) and electrons around in a shell Problem: Why do positive charged protons & electrically neutral neutrons bind together in the nucleus of an atom? Electromagnetic  protons should repel one another violently, no force on neutrons Gravity  weaker than electromagnetic force  need of another strong force Proseminar "The Strong Interaction" ( ) 4 Michael Mattern

Proseminar "The Strong Interaction" ( ) 5 Michael Mattern History: The therory 1934: first significant theory of the strong force proposed by Yukawa Proton and neutron are attracted by some sort of properly quantized field Exchange particle 300 times heavier than electron and a sixth of a proton Yukawa (Source: Wikipedia) Particle called meson because of it´s middle-weight 1947: Powell discovered two middle-weight particles in cosmic rays (pion and muon) The true Yukawa meson is the pion

6 Michael Mattern History Source: David Griffiths (2008) Introduction to Elementary Particles, Second Edition. Proseminar "The Strong Interaction" ( )

History: The pion as the mediator in 1947 it seemed that the job of elementary particle physics was essentially done The proposed theory allows easier calculations and more descriptive representations, but it is valid only within a limited energy range During the 1950´s discovery of a large and ever- growing number of particles called hadrons It seemed that this large number of particles could not all be fundamental Proseminar "The Strong Interaction" ( ) 7 Michael Mattern

History: QCD First, the particles were classified by charge and isospin 1953: classification according to strangeness 1961: hadrons were sorted into groups having similar properties and masses using the eightfold way 1963: explaining the structure of the groups by the existence of three flavors of smaller particles inside the hadrons: the quarks In 1965: proposal that quarks have an additional degree of freedom (the color charge) and that quarks might interact via an octet of vector gauge bosons: the gluons Proseminar "The Strong Interaction" ( ) 8 Michael Mattern

History: Summary Quarks are fundamental particles Hadrons made of quarks ▫ Baryons (made of three quarks)  for example proton and neutron ▫ Mesons (made of one quark and one antiquark)  for example pion Hadrons held together by the strong force Gluons mediator of the strong force Quarks are color “charged” (equivalent to the electrical charge) Proseminar "The Strong Interaction" ( ) 9 Michael Mattern

History: QCD Free quark searches consistently failed Gell-Mann thought that quarks were just mathematical constructs and strong interactions could not be fully described by quantum field theory Feynman argued that high energy experiments showed quarks are real particles Difference caused split in the physics community 1969 S-matrix Theorie 1973 Discovery of the asymptotic freedom  rehabilitating of the quantum field theory Proseminar "The Strong Interaction" ( ) 10 Michael Mattern

Quantum chromodynamics (QCD) It is the study of the SU(3) Yang–Mills theory Is a quantum field theory of a special kind called a non-abelian gauge theory, consisting of a 'color field' mediated by a set of exchange particles (the gluons) Describing the interactions between color charged particles (quarks and gluons) which make up hadrons Two strange properties: Confinement Asymptotic freedom Proseminar "The Strong Interaction" ( ) 11 Michael Mattern

SU(3) and color blindness Color charge is associated with the Strong Interaction But: the properties of the strong interaction do not depend on the color of the quark Color is associated with some abstract space Rotations in this space changes the color of the quarks Strong Interaction is “color-blind”  symmetry space The rotations (“symmetry transformations”) are mathematically equivalent to rotations in three complex dimensions Proseminar "The Strong Interaction" ( ) 12 Michael Mattern green blue red

Color charge There are three color values (found experimentally) they were assigned as (red green and blue) quarks carry SU(3)-color charge  also antiquarks and anitcolors  unlike Electromagnetism, we find that the mediator of the strong force (the gluon) also carries color charge Gluons carry a color and a anticolor Proseminar "The Strong Interaction" ( ) 13 Michael Mattern qqq qqq gg

Color of hadrons Baryons (red + blue + green = white or colorless) Mesons green + antigreen = colorless red + antired = colorless blue + antiblue = colorless Proseminar "The Strong Interaction" ( ) 14 Michael Mattern q q q qqqqqq

Color of gluons It seems to give 9 types of gluon: red anti-redred anti-bluered anti-green blue anti-redblue anti-blue blue anti-green green anti-redgreen anti-bluegreen anti-green Just 8 gluons  no red anti-red Proseminar "The Strong Interaction" ( ) 15 Michael Mattern gg g

Flow of color charge Emission of a gluon: red  red anti-blue + blue Re-absorption of a gluon: Proseminar "The Strong Interaction" ( ) 16 Michael Mattern g qq gq q

Color flow inside hadrons Proseminar "The Strong Interaction" ( ) Michael Mattern 17 Source:

QED vs. QCD Proseminar "The Strong Interaction" ( ) 18 Michael Mattern PropertyQEDQCD mediatorphotongluon mediator mass00 mediator charge0color charged charge types+,-red,green,blue interaction with electrical charged objects color charged objects rangeinfinite10^-14 m

QED vs. QCD (feynman diagrams) Proseminar "The Strong Interaction" ( ) 19 Michael Mattern Normal particle (quark): Antiparticle (antiquark): Interaction by gluon: Analogous to photon exchange of QED 3-gluon vertex4-gluon vertex

QED vs. QCD (feynman diagrams) Proseminar "The Strong Interaction" ( ) 20 Michael Mattern The first vertex produces the following set of combinations: Source:

QED vs. QCD Summary QCD more difficult because: Additional vertices (gluon-gluon interaction) Coupling constant of QED is 1/137  this small value limits the sum of more and more complicated feyman diagrams In QCD coupling constant is close to 1  effects of simple and complicated diagrams are both strong No separated quarks in QCD  difficult calculations Proseminar "The Strong Interaction" ( ) 21 Michael Mattern

Confinement Proseminar "The Strong Interaction" ( ) 22 Michael Mattern Source: Phenomenon that color charged particles cannot be separated  direct observation impossible Quarks are only seen confined in colorless combinations Strong force gets stronger with the distance What happens if we try to separate a quark-aniquark-pair Gluon-tube between quarks elongates Strong force gets stronger with the distance As soon as there is enough energy inside the system a new quark-antiquark pair will be created

Hadronization Proseminar "The Strong Interaction" ( ) 23 Michael Mattern Source:

Asymptotic freedom Proseminar "The Strong Interaction" ( ) 24 Michael Mattern Phenomenon that strong force gets weaker with decreasing distance Asymptotically approaches zero for close confinement (or high energy) Quarks in close confinement can move “freely”  quark gluon plasma Described qualitatively as resulting from the penetration of the gluon cloud surrounding the quarks

Running coupling constant of QCD Proseminar "The Strong Interaction" ( ) 25 Michael Mattern distance strength 1 radius of a proton 0

But what holds the nucleus together? Before the introduction of the quark model, the strong interaction was the force between the nucleons Now it is the force acts on quarks and gluons (or QCD) We know that hadrons does not have a color charge (so they do not exchange gluons)  there must be an other explanation Today we understand the problem as a residual effect of the even more powerful strong interaction We call it nuclear force Proseminar "The Strong Interaction" ( ) 26 Michael Mattern

Nuclear force Proseminar "The Strong Interaction" ( ) 27 Michael Mattern Like Yukawa proposed, the mediator of the nuclear force is the meson Today we know that this mesons which are transmitted between hadrons are combinations of quarks and gluons Strength and range of the nuclear force limit the maximum size of the nucleus (because of the short range of the nuclear force and the infinite range of the elecromagnetic force, after a certain number of nucleons, the elecromagnetic force dominates)

Nuclear force Proseminar "The Strong Interaction" ( ) 28 Michael Mattern Source:

Thank you for your attention Proseminar "The Strong Interaction" ( ) 29 Michael Mattern