Quantum Chromodynamics

Quantum Chromodynamics (QCD) is a branch of theoretical physics that is part of the Standard Model of particle physics. It is the theory that describes the strong nuclear force, one of the four fundamental forces of nature (along with gravity, electromagnetism, and the weak nuclear force). QCD specifically deals with the interactions between quarks and gluons, which are the fundamental building blocks of protons, neutrons, and other hadrons.

Here are some key points about Quantum Chromodynamics:

1. Quarks: Quarks are elementary particles that come in six different "flavours": up, down, strange, charm, bottom, and top. They are never found in isolation but are always confined within larger particles called hadrons (like protons and neutrons) due to the strong force.

2. Gluons: Gluons are the force carriers of the strong nuclear force. They are massless and carry the "colour charge" (analogous to electric charge in electromagnetism) that governs the strong interactions between quarks. Gluons can exchange colour charge between quarks, mediating the strong force that binds them together.

3. Color Charge: In QCD, quarks and gluons are said to have a "colour charge" because of their interactions. However, this has nothing to do with the coloureen, and blue (plus their corresponding anticolours: cyan, magenta, and yellow). Quarks and gluons can combine in ways that ensure the resulting particles are "colour-neutral."

4. Confinement: One of the key features of QCD is confinement, which means that quarks and gluons cannot exist as isolated particles but are always bound together within hadrons. This explains why we never observe free quarks or gluons in nature.

5. Asymptotic Freedom: QCD also exhibits a phenomenon known as asymptotic freedom, discovered by David Gross, Frank Wilczek, and David Politzer, which means that at very short distances or high energies, quarks and gluons behave almost like free particles. This is in contrast to the behavior of the strong force at larger distances, where quarks are tightly confined within hadrons.

6. Lattice QCD: Because of the complexity of QCD calculations, physicists often use numerical simulations on a lattice (grid) to study the behavior of quarks and gluons within the strong force. This approach, known as lattice QCD, helps to understand the properties of hadrons and other aspects of QCD.

Quantum Chromodynamics plays a crucial role in our understanding of the structure of atomic nuclei, the behavior of matter at extreme temperatures and densities (such as in the early universe and in neutron stars), and the interactions of particles in high-energy physics experiments conducted at facilities like the Large Hadron Collider (LHC). It is a fundamental theory that has been tested and confirmed through numerous experimental observations and measurements.

Harald Fritzsch, one of the pioneers of quantum chromodynamics, recalls some of the background to the development of the theory 40 years ago.

The observed hadrons are members of specific representations of SU(3). The baryons are octets and decuplets, the mesons are octets and singlets. The baryon octet contains the two nucleons, the three Σ hyperons, the Λ hyperon and the two Ξ hyperons (see figure 1). The members of the meson octet are the three pions, the η meson, the two K mesons and the two K mesons.

Quark Jets

In electron–positron annihilation, the virtual photon creates a quark and an antiquark, which move away from each other with high speed. Because of the confinement property, mesons – mostly pions – are created, moving roughly in the same direction. The quark and the antiquark “fragment” to produce two jets of particles. The sum of the energies and momenta of the particles in each jet should be equal to the energy of the original quark, which is equal to the energy of each colliding lepton. These quark jets were observed for the first time in 1978 at DESY. They had already been predicted in 1975 by Feynman.

An event with quark jets observed at DESY. Image credit: Oxford University PPU.

If a quark pair is produced in electron–positron annihilation, then QCD predicts that sometimes a high-energy gluon should be emitted from one of the quarks. The gluon would also fragment and produce a jet. So, sometimes three jets should be produced. Such events were observed at DESY in 1979.

A three-jet event observed at DESY. Image credit: Oxford University PPU.

The basic quanta of QCD are the quarks and the gluons. Two colour-octet gluons can form a colour singlet. Such a state would be a neutral gluonium meson. The ground state of the gluonium mesons has a mass of about 1.4 GeV. In QCD with only heavy quarks, this state would be stable but in the real world it would mix with neutral quark–antiquark mesons and would decay quickly into pions. Thus far, gluonium mesons have not been identified clearly in experiments.

Scattering and Resonances in Quantum Chromodynamics

GENERAL FORMULA:

QCD in 1+1 dimensions, bosonized in the scheme

Is given by the action

where

Equation of motion, as coefficient of (δg)g†,

We adopt the approach of Ref. [7] for deriving the meson-baryon scattering S-matrix.

Expanding in small fluctuations around a given static classical solution

Quarks

Quarks are the matter particles. Gluons are the force particles. There are 6 known quarks with fanciful names. The names have no relation to the properties of the particles. (The physics Hypertextbook)

• up

• down

• charm

• strange

• top

• bottom

Quarks and gluons exist only in groups (in the "low" temperature realm below 1012 K).

• meson: quark-antiquark pair (qq)

• hadron: quark triplet (qqq)

• tetraquark: two quarks-two antiquarks (qqqq) or a meson "molecule" (qq qq)

• pentaquark: four quarks and one antiquark (qqqqq) or a hadron-meson "dimer" (qqq qq)

Ordinary matter is composed of up and down quarks.

• proton: up up down

• neutron: up down down

In conclusion, Quantum Chromodynamics (QCD) is a fundamental branch of theoretical physics that forms a vital part of the Standard Model. It serves as the theoretical framework for understanding the strong nuclear force, which governs the interactions between quarks and gluons---the elementary particles responsible for composing protons, neutrons, and other hadrons. QCD introduces the concept of colour charge, mediates the confinement of quarks within particles, and exhibits phenomena like asymptotic freedom. This theory is essential for explaining the behavior of matter at both the smallest scales within atomic nuclei and the highest energies in particle physics experiments, contributing significantly to our understanding of the fundamental forces and particles that make up the universe.

Citations

Encyclopædia Britannica, inc. (n.d.). Quantum Chromodynamics. Encyclopædia Britannica. https://www.britannica.com/science/quantum-chromodynamics

Formulas

Quantum Chromodynamics. Quantum Chromodynamics - an overview | ScienceDirect Topics. (n.d.). https://www.sciencedirect.com/topics/physics-and-astronomy/quantum-chromodynamics