Fundamentals of Particle Physics
By Dr. Emmanuel Olaiya
Our Universe is 15 billion years old
It contains about 150 billion galaxies
Each galaxy has around 300 billion stars
This means there is a huge amount of matter containing an unimaginable amount of particles
How do we even begin to understand all of matter?
How many elementary particles does it take to describe matter around us?
We can actually describe the matter around us by using 3 particles:
Up Quark, Down Quark and the electron (lepton)
The up quark has a mass of 1.7 to 3.1 MeV/c^2 and a charge of +2e/3
The down quark has a mass of 4.1 to 5.7 MeV/c^2 and a charge of -1e/3
Protons and neutrons consist of up and down quarks
A proton is made up of two up quarks and a down quark which gives it a charge of +1e and a neutron is made up of two down quarks and an up which gives it a charge of 0.
All nuclei are constructed with up and down quarks
The electron is a lepton and has a charge of -1. Electrons orbit the nuclei and help to form molecules. These are classed as point like elementary particles.
We can build the world around us with these three particles. But how do they interact. To understand their interactions we have to introduce forces!
Consider two forces: nuclear and electromagnetic
The photon is the force carrier when experiencing forces such as electricity and magnetism
The gluon is the force carrier for the strong nuclear force. There is in fact eight different gluons.
Some familiar particles
The atom has a diameter of about 1 x E-10m
The nucleus is made up of protons and neutrons. Each proton has a +1 charge and energy of 938.3 MeV and each neutron has a 0 charge and energy of 939.6 MeV
Einstein’s famous equation E = mc2 tells us mass and energy are equivalent
Wave/Particle Duality (Quantum Mechanics)
Wave–particle duality is the concept that every elementary particle or quantic entity exhibits the properties of not only particles, but also waves. It addresses the inability of the classical concepts “particle” or “wave” to fully describe the behaviour of quantum-scale objects. As Einstein wrote “It seems as though we must use sometimes the one theory and sometimes the other, while at times we may use either. We are faced with a new kind of difficulty. We have two contradictory pictures of reality; separately neither of them fully explains the phenomena of light, but together they do”
The idea was initially put forward by Louis de Broglie, before the discovery of quantum mechanics, and developed later as the de Broglie-Bohm theory, the pilot wave interpretation does not regard the duality as paradoxical, seeing both particle and wave aspects as always coexisting.
Albert Einstein (14 March 1879 – 18 April 1955) was a German-born theoretical physicist.
Louis-Victor-Pierre-Raymond, 7th duc de Broglie (15 August 1892 – 19 March 1987) was a French physicist who made groundbreaking contributions to quantum theory. In his 1924 PhD thesis he postulated the wave nature of electrons and suggested that all matter has wave properties. This concept is known as the de Broglie hypothesis, an example of wave-particle duality, and forms a central part of the theory of quantum mechanics.
From Einstein’s work on the photoelectric effect we have the formula E = h f where E = photon energy, h = Planck’s constant and f = frequency of the wave (in time)
The photoelectric effect is the observation that many metals emit electrons when light shines upon them. Electrons emitted in this manner can be called photoelectrons.
From de Broglie’s work we have the formula p = h k where p is the momentum of the particle, h is Planck’s constant and k is frequency in space (k = 1/l where l = wavelength)
“low” momentum wave
“high” momentum wave
Heisenberg’s Uncertainty Principle
In quantum mechanics, the uncertainty principle, also known as Heisenberg’s uncertainty principle, is any of a variety of mathematical inequalities asserting a fundamental limit to the precision with which certain pairs of physical properties of a particle known as complementary variables, such as position x and momentum p, can be known simultaneously. Introduced first in 1927, by the German physicist Werner Heisenberg, it states that the more precisely the position of some particle is determined, the less precisely its momentum can be known, and vice versa.
There is a minimum for the product of the uncertainties of these two measurements. There is likewise a minimum for the product of the uncertainties of the energy and time.
Important steps on the way to understanding the uncertainty principle are wave-particle duality and the de Broglie hypothesis. As you proceed downward in size to atomic dimensions, it is no longer valid to consider a particle like a hard sphere, because the smaller the dimension, the more wave-like it becomes. It no longer makes sense to say that you have precisely determined both the position and momentum of such a particle. When you say that the electron acts as a wave, then the wave is the quantum mechanical wavefunction and it is therefore related to the probability of finding the electron at any point in space. A perfect sinewave for the electron wave spreads that probability throughout all of space, and the “position” of the electron is completely uncertain.
x is position of the particle and p is its momentum
It basically says that the combination of the error in position x the error in momentum must always be greater than Planck’s constant. So, you can measure the position of the particle to some accuracy, but then its momentum will be inside a very large range of values. Likewise, you can measure the momentum precisely, but then its position is unknown.
This is not a measurement problem in another form, the combination of position, energy (momentum) and time are actually undefined for a quantum particle until a measurement is made (then the wave function collapses).
Also notice that the uncertainty principle is unimportant to macroscopic objects since Planck’s constant, h, is so small (1 x E-34). For example, the uncertainty in position of a thrown cricket ball is 1 x E-30 millimetres.
The depth of the uncertainty principle is realised when we ask the question; is our knowledge of reality unlimited? The answer is no, because the uncertainty principle states that there is a built-in uncertainty, indeterminacy, unpredictability to Nature.
Werner Karl Heisenberg (5 December 1901 – 1 February 1976) was a German theoretical physicist and one of the key pioneers of quantum mechanics.
If Δx (the size of a nucleon) is about 1 x E-15m then Δp is about 1 GeV
Remember that nucleons are composites
All the above are fundamental (“pointlike”) particles
Quantum Field Theory (The Standard Model)
In theoretical physics, quantum field theory (QFT) is a theoretical framework for constructing quantum mechanical models of subatomic particles in particle physics and quasiparticles in condensed matter physics. A QFT treats particles as excited states of an underlying physical field, so these are called field quanta.
It sounds complicated but there are some simple points:
Interactions are described by underlying fields;
The “Quantum” means that the interaction takes place in discrete amounts. The interaction is not continuous, not all values are allowed;
The field “communicates” via particles. Therefore for every field there is a particle
What about the Higgs Boson?
When we consider the forces between particles as the interaction, there must be a particle associated with the field that transmits the force.
We would like to have a quantum field theory for the four fundamental forces; strong. Weak, electromagnetism and gravity
Unfortunately the current Standard Model doesn’t describe gravity
Matter Particles (Fermions)
In particle physics, a fermion (a name coined by Paul Dirac from the surname of Enrico Fermi) is any particle characterized by Fermi–Dirac statistics. These particles obey the Pauli exclusion principle. Fermions include all quarks and leptons, as well as any composite particle made of an odd number of these, such as all baryons and many atoms and nuclei. Fermions differ from bosons, which obey Bose–Einstein statistics.
A fermion can be an elementary particle, such as the electron, or it can be a composite particle, such as the proton. According to the spin-statistics theorem in any reasonable relativistic quantum field theory, particles with integer spin are bosons, while particles with half-integer spin are fermions.
The image above left is of Paul Adrien Maurice Dirac OM FRS (8 August 1902 – 20 October 1984). He was an English theoretical physicist who made fundamental contributions to the early development of both quantum mechanics and quantum electrodynamics.
The image above right is of Enrico Fermi (29 September 1901 – 28 November 1954). He was an Italian physicist, best known for his work on Chicago Pile-1 (the first nuclear reactor), and for his contributions to the development of quantum theory, nuclear and particle physics, and statistical mechanics.
The above 12 particles are fermions
Bosons are the force carrier particles
In quantum mechanics, a boson is a particle that follows Bose–Einstein statistics. Bosons make up one of the two classes of particles, the other being fermions. The name boson was coined by Paul Dirac to commemorate the contribution of the Indian physicist Satyendra Nath Bose in developing, with Einstein, Bose–Einstein statistics—which theorizes the characteristics of elementary particles.
Satyendra Nath Bose FRS (1 January 1894 – 4 February 1974) was an Indian physicist specialising in mathematical physics.
Remember that the 8 gluons (strong force carrier) and the photon (electromagnetic force carrier) have no mass
There are three weak force carriers: W+ with energy of 80385 MeV, Z0 with energy of 91187 MeV and W- with energy of 80385 MeV
Bosons are particles with whole number spin
Particles are described by their properties. They have: Mass, charge, intrinsic spin (0,1,2,3 etc. for Bosons and 1/2, 3/2, 5/2 etc. for fermions) and interact with specific forces.
Instead of talking about matter and forces, on a quantum level we talk about fermions and bosons.
How do we create particle?
From energy but we must not violate conservation laws – charge, momentum, etc.
Energy has no charge or angular momentum. So if we create an electron with negative charge and positive angular momentum, we must also create a particle with a positive charge and negative angular momentum (positron) for conservation’s sake.
Cosequently when you create a particle from energy you also create an antiparticle.
Quantum Electro-Dymamics (QED)
In particle physics, quantum electrodynamics (QED) is the relativistic quantum field theory of electrodynamics. In essence, it describes how light and matter interact and is the first theory where full agreement between quantum mechanics and special relativity is achieved. QED mathematically describes all phenomena involving electrically charged particles interacting by means of exchange of photons and represents the quantum counterpart of classical electromagnetism giving a complete account of matter and light interaction.
Electrical (and Magnetic) Forces explained by photon exchange!! A photon is a particle of light. Electrons repel each other via the exchange of a photon. Photon transfers momentum etc.
In theoretical physics, Feynman diagrams are pictorial representations of the mathematical expressions describing the behavior of subatomic particles. The scheme is named for its inventor, American physicist Richard Feynman, and was first introduced in 1948.
Richard Phillips Feynman, ForMemRS (May 11, 1918 – February 15, 1988) was an American theoretical physicist known for his work in the path integral formulation of quantum mechanics, the theory of quantum electrodynamics, and the physics of the superfluidity of supercooled liquid helium, as well as in particle physics (he proposed the parton model).
How do we know there are quarks inside the nucleons?
Ans: We can do electron-quark “scattering” and see
(e.g. at the HERA electron-proton collider)
A quark is an elementary particle and a fundamental constituent of matter. Quarks combine to form composite particles called hadrons, the most stable of which are protons and neutrons, the components of atomic nuclei. Due to a phenomenon known as colour confinement, quarks are never directly observed or found in isolation; they can be found only within hadrons, such as baryons (of which protons and neutrons are examples), and mesons. For this reason, much of what is known about quarks has been drawn from observations of the hadrons themselves.
The quark model was independently proposed by physicists Murray Gell-Mann and George Zweig in 1964. Quarks were introduced as parts of an ordering scheme for hadrons, and there was little evidence for their physical existence until deep inelastic scattering experiments at the Stanford Linear Accelerator Center in 1968. Accelerator experiments have provided evidence for all six flavours. The top quark was the last to be discovered at Fermilab in 1995.
The above left image is of Murray Gell-Mann (born September 15, 1929). He is an American physicist who received the 1969 Nobel Prize in physics for his work on the theory of elementary particles.
The above right image is of George Zweig (born May 30, 1937). He is an American physicist. He was trained as a particle physicist under Richard Feynman. He introduced, independently of Murray Gell-Mann, the quark model (although he named it “aces”).
Deep inelastic scattering is the name given to a process used to probe the insides of hadrons (particularly the baryons, such as protons and neutrons), using electrons, muons and neutrinos. It provided the first convincing evidence of the reality of quarks, which up until that point had been considered by many to be a purely mathematical phenomenon. It is a relatively new process, first attempted in the 1960s and 1970s. It is an extension of Rutherford scattering to much higher energies of the scattering particle and thus to much smaller resolution of the components of the nuclei.
The H1 experiment at the HERA accelerator
HERA (German: Hadron-Elektron-Ringanlage, English: Hadron-Electron Ring Accelerator) was a particle accelerator at DESY in Hamburg. It began operating in 1992. At HERA, electrons or positrons were collided with protons at a center of mass energy of 318 GeV. It was the only lepton-proton collider in the world while operating. Also, it was on the energy frontier in certain regions of the kinematic range. HERA was closed down on 30 June 2007.
When the quark (in the proton or neutron) was struck by the electrons a jet of mesons was formed. Some of the quark is replaced by energy.
meson = quark + anti-quark composite particle (“hadron”)
Quarks and gluons said to be “confined” in hadrons. Gluons self-interact and quarks can’t exist in isolation.
The strong force does not obey the inverse-square law.
In physics, an inverse-square law is any physical law stating that a specified physical quantity or intensity is inversely proportional to the square of the distance from the source of that physical quantity.
Confinement is a property of the strong force.
The strong force works by gluon exchange but at “large” distance the self-interaction of the gluons breaks the inverse square-law forming “flux tubes”:
Quarks and gluons carry “colour “ quantum numbers analogous to electric charge – but only “colourless” objects like baryons (3-quark states) and mesons (quark-antiquark states) escape confinement.
Quantum “Chromo”-Dynamics (QCD)
In theoretical physics, quantum chromodynamics (QCD) is the theory of strong interactions, a fundamental force describing the interactions between quarks and gluons which make up hadrons such as the proton, neutron and pion.
(more Feynman diagrams)
quarks come in 3 “colours” so there are three “red”, three “green” and three “blue” of each quark. You want to combine quarks to get colourless (red + blue + green)
As seen before there are eight types of gluon
Quark/gluon scattering in the UA1 p anti-p experiment at CERN
The UA1 experiment is famous for the discovery of the W and Z bosons – the carriers of the “weak force” in 1983. W± ≈ 80 GeV Z0 ≈ 91 GeV – heaviest particle known at the time (W and Z masses due to interaction with the Higgs field!)
The “weak force”: Beta decay
In particle physics, the weak interaction is the mechanism responsible for the weak force or weak nuclear force, one of the four known fundamental interactions of nature, alongside the strong interaction, electromagnetism, and gravitation. The weak interaction is responsible for both the radioactive decay of subatomic particles and nuclear fission. The theory of the weak interaction is sometimes called quantum flavordynamics (QFD), in analogy with the terms QCD and QED, but the term is rarely used because the weak force is best understood in terms of electro-weak theory (EWT).
In particle physics, the electroweak interaction is the unified description of two of the four known fundamental interactions of nature: electromagnetism and the weak interaction. Although these two forces appear very different at everyday low energies, the theory models them as two different aspects of the same force.
Radioactive β-decay n → p + e- + antineutrino is an example of the “weak force” in action!
In nuclear physics, beta decay (β decay) is a type of radioactive decay in which a proton is transformed into a neutron, or vice versa, inside an atomic nucleus. This process allows the atom to move closer to the optimal ratio of protons and neutrons. As a result of this transformation, the nucleus emits a detectable beta particle, which is an electron or positron.
β− decay in an atomic nucleus (the accompanying antineutrino is omitted). The inset shows beta decay of a free neutron. In both processes, the intermediate emission of a virtual W− boson (which then decays to electron and antineutrino) is not shown. The process is due to weak interaction.
The free neutron is an unstable particle. It can only exist for about 15 minutes
It beta-decays to a proton with the emission of an electron (e-) and an (anti-) neutrino
At the level of the quarks, a d-quark in the neutron is changing into an u-quark giving a proton instead:
Feynman diagram for beta decay: (at the quark level)
The weak force is here mediated by W exchange
The weak force only looks weak because the W is such a heavy particle ≈ 80 GeV (1983)
The photon and the gluon are both massless.
Why are the W and Z bosons not massless also?
Ans: the W and Z bosons get their masses via their interaction with the Higgs field
The W and Z bosons (together known as the weak bosons or, less specifically, the intermediate vector bosons) are the elementary particles that mediate the weak interaction; their symbols are W+, W− and Z. The W bosons have a positive and negative electric charge of 1 elementary charge respectively and are each other’s antiparticles. The Z boson is electrically neutral and is its own antiparticle. The three particles have a spin of 1, and the W bosons have a magnetic moment, while the Z has none. All three of these particles are very short-lived with a half-life of about 3 x E−25 s. Their discovery was a major success for what is now called the Standard Model of particle physics.
The two W bosons are best known as mediators of neutrino absorption and emission, where their charge is associated with electron or positron emission or absorption, always causing nuclear transmutation. The Z boson is not involved in the absorption or emission of electrons and positrons.
The Z boson mediates the transfer of momentum, spin, and energy when neutrinos scatter elastically from matter, something that must happen without the production or absorption of new, charged particles.
W to e and neutrino decay in the ATLAS experiment
The 4 LEP Experiments at the LEP e+ e – collider at CERN (Geneva) LEP was built to study the Z0
Remembering the 12 “matter” particles (fermions)
Although you could argue that there are 24 particles as each quark comes in three colours.
Identical fermions obey the “Pauli Exclusion Principle”
All these different masses of these fundamental particles come from their different interaction with the Higgs field!!
The Pauli exclusion principle is the quantum mechanical principle that states that two identical fermions (particles with half-integer spin) cannot occupy the same quantum state simultaneously. In the case of electrons, it can be stated as follows: it is impossible for two electrons of a poly-electron atom to have the same values of the four quantum numbers (Principal quantum number, Azimuthal quantum number, Magnetic quantum number, Spin quantum number).
This principle was formulated by Austrian physicist Wolfgang Pauli in 1925.
Wolfgang Ernst Pauli (25 April 1900 – 15 December 1958) was an Austrian-born Swiss theoretical physicist and one of the pioneers of quantum physics.
Particle Particle Collisions
How do we know about these elementary particle?
We collide particles together to generate new particles
The heavier particles are unstable and eventually decay to lighter particles
From Einstein’s equation E = mc^2, mass and energy are interchangeable. So we talk about a particle’s energy and not its mass
We need to collide particles with sufficient energy to create new particles
We identify these new generated particles using particle detectors
The Standard Model
Combining all of the elementary particles mentioned we get the standard model.
The Standard Model of particle physics is a theory concerning the electromagnetic, weak, and strong nuclear interactions, as well as classifying all the subatomic particles known. It was developed throughout the latter half of the 20th century, as a collaborative effort of scientists around the world. The current formulation was finalized in the mid-1970s upon experimental confirmation of the existence of quarks. Since then, discoveries of the top quark (1995), the tau neutrino (2000), and more recently the Higgs boson (2013), have given further credence to the Standard Model. Because of its success in explaining a wide variety of experimental results, the Standard Model is sometimes regarded as a “theory of almost everything”.
The Standard Model of elementary particles (more schematic depiction), with the three generations of matter, gauge bosons in the fourth column, and the Higgs boson in the fifth.
The standard model describes the particle interactions to a very high precision. But there are some problems.
The Higgs Boson
We have seen that the standard model particles have different masses.
How do they acquire that mass?
The standard model particles acquire their mass by interacting with a field that acts over all space. This field is the Higgs field.
Therefore there must be a particle associated with the field. The Higgs Boson.
If you provide enough energy to the field then you will be able to generate the Higgs Boson from the field. This is how physicists look for the Higgs Boson.
Interaction with the ambient all-pervasive Higgs field gives mass to the fundamental particles:
The Higgs field is non-zero even in the vacuum.
Interaction with the non-zero Higgs field gives masses to the fundamental particles
Waves in the Higgs field correspond to a new kind of “force” particle: The Higgs boson!!
Peter Ware Higgs CH FRS FRSE (born 29 May 1929) is a British theoretical physicist, Nobel Prize laureate and emeritus professor at the University of Edinburgh.
Higgs Boson Analogy
Imagine pulling a light object. Then imagine pulling the same object through water. In water the object seems “heavier” when you pull it. The analogy is that the water is like the Higgs Field and in water the object acquires mass (“feels heavier”)
Our understanding of gravity is impressive
Using Einstein’s theory of general relativity we can describe the behaviour of gravity very well
General relativity is a theory of gravitation that was developed by Albert Einstein between 1907 and 1915. According to general relativity, the observed gravitational effect between masses results from their warping of spacetime.
General relativity, also known as the general theory of relativity, is the geometric theory of gravitation published by Albert Einstein in 1915 and the current description of gravitation in modern physics. General relativity generalises special relativity and Newton’s law of universal gravitation, providing a unified description of gravity as a geometric property of space and time, or spacetime. In particular, the curvature of spacetime is directly related to the energy and momentum of whatever matter and radiation are present. The relation is specified by the Einstein field equations, a system of partial differential equations.
Gravity explains the duplication of galaxies – gravitational lensing
A gravitational lens refers to a distribution of matter (such as a cluster of galaxies) between a distant source and an observer, that is capable of bending the light from the source, as it travels towards the observer. This effect is known as gravitational lensing and is one of the predictions of Albert Einstein’s general theory of relativity.
Bending light around a massive object from a distant source. The orange arrows show the apparent position of the background source. The white arrows show the path of the light from the true position of the source.
Abell 2744 galaxy cluster – extremely distant galaxies revealed by gravitational lensing (16 October 2014)
Still our understanding of gravity is very good. It helps point out another problem with the standard model.
From the orbits of galaxies and other bodies we can calculate the mass of the central body. In space we can see that the mass calculated is much greater than what we can detect. There is missing matter out there that we cannot detect.
A famous illustration of this is the Bullet Cluster
The Bullet Cluster (1E 0657-558) consists of two colliding clusters of galaxies. Strictly speaking, the name Bullet Cluster refers to the smaller subcluster, moving away from the larger one. It is at a co-moving radial distance of 1.141 Gpc (3.721 Gly)
X-ray photo by Chandra X-ray Observatory. Exposure time was 140 hours. The scale is shown in megaparsecs. Redshift (z) = 0.3, meaning its light has wavelengths stretched by a factor of 1.3.
The red shows that matter is detected by X-rays (standard model particles). They colide and progress no further.
The blue shows the matter detected by gravitational lensing. They pass right through each other uninterrupted and continue to the ends of the picture.
We have a great understanding of fundamental physics
Our understanding has grown with the discovery of the Higgs Boson
Though there are some interesting questions still to be answered:
What is Dark Matter?
What about Dark Energy?
What about Gravity?
The LHC has started taking data again but at much higher energy than before.
Hopefully some of these questions will be answered there!