the strong interaction michael mattern. contents the fundamental forces history the need of a strong...

The Strong InteractionMichael 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 forceProseminar "The Strong Interaction" (18.04.23)

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The fundamental forces

Proseminar "The Strong Interaction" (18.04.23)

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Force Strength Range (m)

strong 1 10-15

electromagnetic 1/137 infinite

weak 10-6 10-18

gravity 6 x 10-39 infinite

History: The need of a strong force •Classical period (1897-1932): 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


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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

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History

Source: David Griffiths (2008) Introduction to Elementary Particles, Second Edition.


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


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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 gluonsProseminar "The Strong Interaction" (

18.04.23)8Michael 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)


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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


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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


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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


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greenblue

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


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q q q

q q q

g g

Color of hadrons

•Baryons (red + blue + green = white or colorless)

•Mesonsgreen + antigreen = colorless red + antired = colorlessblue + antiblue = colorless


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q qq

qq qq qq

Color of gluons

• It seems to give 9 types of gluon:

red anti-red red anti-blue red anti-greenblue anti-red blue anti-blue blue anti-greengreen anti-red green anti-blue green anti-green

• Just 8 gluons no red anti-red


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g g

g

Flow of color charge

•Emission of a gluon:

red red anti-blue + blue

•Re-absorption of a gluon:


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gq q

g qq

Color flow inside hadrons


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Source: http://en.wikipedia.org/wiki/Color_charge

QED vs. QCD


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Property QED QCD

mediator photon gluon

mediator mass 0 0

mediator charge 0 color charged

charge types +,- red,green,blue

interaction with electrical charged objects

color charged objects

range infinite 10^-14 m

QED vs. QCD (feynman diagrams)


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•Normal particle (quark):•Antiparticle (antiquark):• Interaction by gluon:

Analogous to photon exchange of QED

3-gluon vertex 4-gluon vertex

QED vs. QCD (feynman diagrams)


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The first vertex produces the following set of combinations:

Source: http://teachers.web.cern.ch

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


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Confinement


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Source: http://www.rug.nl/

•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 pairwill be created

Hadronization


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Source: http://en.wikipedia.org/

Asymptotic freedom


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•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


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distance

strength

1

radius of a proton0

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


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Nuclear force


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• 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


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Source: http://en.wikipedia.org/

Thank you for your attention


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