Nick Connor

Quarks in the Standard Model

Quarks and electrons are some of the elementary particles. A number of fundamental particles have been discovered in various experiments. So many, that researchers had to organize them, just like Mendeleev did with his periodic table. This is summarized in a theoretical model (concerning the electromagnetic, weak, and strong nuclear interactions) called the Standard Model. In particle physics, an elementary particle or fundamental particle is a particle whose substructure is unknown, thus it is unknown whether it is composed of other particles.

In the present Standard Model, there are six “flavors” of quarks, six quarks, just as there are six leptons based on a presumed symmetry in nature. The three quarks originally proposed and accepted were labeled u (up quark), d (down quark), s (strange quark). The other three quarks are called charmed, bottom, and top. They can successfully account for all known mesons and baryons. The most familiar baryons are the proton and neutron, which are each constructed from up and down quarks.

See also:

Quarks

Antiquarks

In particle physics, corresponding to most kinds of particles there is an associated antiparticle. An antiparticle has the same mass and opposite charge (including electric charge). For example, for every quark there is a corresponding type of antiparticle. The antiquarks have the same mass, mean lifetime, and spin as their respective quarks, but the electric charge and other charges have the opposite sign. Up-type antiquarks have charges of −​2⁄3 e and down-type antiquarks have charges of +​1⁄3 e. Since the electric charge of a hadron is the sum of the charges of the constituent quarks, all hadrons have integer charges.

See also:

Quarks

Mass of Quark

The thermodynamics/thermodynamic-properties/what-is-mass-and-weight/what-is-mass/”>mass of the neutron is 939.565 MeV/c², whereas the mass of the three quarks is only about 10 MeV/c² (only about 1% of the mass-energy of the neutron). Like the proton, most of mass (energy) of the neutron is in the form of the strong nuclear force energy (gluons). The quarks of the neutron are held together by gluons, the exchange particles for the strong nuclear force. Gluons carry the color charge of the strong nuclear force.

Therefore, we have to distinguish between current quark mass (also called the mass of the ‘naked’ quarks) and constituent quark mass. Current quark mass refers to the mass of a quark by itself, while constituent quark mass refers to the current quark mass plus the mass of the gluon particle field surrounding the quark.

Noteworthy, because most of your mass is due to the protons and neutrons in your body, your mass (and therefore your weight on a bathroom scale) comes primarily from the gluons that bind the constituent quarks together, rather than from the quarks themselves. Mass is primarily a measure of the energies of the quark motion and the quark-binding fields any real object. It must be noted, gluons are inherently massless, they possess energy.

See also:

Quarks

Electric Charge of Quarks

The most familiar baryons are the proton and neutron, which are each constructed from up and down quarks.

The proton has a quark composition of uud, and so its charge quantum number is:

q(uud) = 2/3 + 2/3 + (-1/3) = +1

The neutron has a quark composition of udd, and its charge quantum number is therefore:

q(udd) = 2/3 + (-1/3) + (-1/3) = 0

Since the neutron has no net electric charge, it is not affected by electric forces, but the neutron does have a slight distribution of electric charge within it. This is caused by by its internal quark structure. This results in non-zero magnetic moment (dipole moment) of the neutron. Therefore the neutron interacts also via electromagnetic interaction, but much weaker than the proton.

See also:

Quarks

Properties of Quarks

Quarks are a type of elementary particles and fundamental constituents of matter. In the quark model, all hadrons are made of a few quarks. Today, the quark theory is well-accepted, and quarks are considered truly fundamental particles.

Properties of Quarks

Besides charge and spin (1/2 for the baryons), two other quantum numbers are assigned to these particles: baryon number (B) and strangeness (S). Baryons have a baryon number, B, of 1, while their antiparticles, called antibaryons, have a baryon number of −1. A nucleus of deuterium (deuteron), for example, contains one proton and one neutron (each with a baryon number of 1) and has a baryon number of 2.

Electric Charge of Quarks

The most familiar baryons are the proton and neutron, which are each constructed from up and down quarks.

The proton has a quark composition of uud, and so its charge quantum number is:

q(uud) = 2/3 + 2/3 + (-1/3) = +1

The neutron has a quark composition of udd, and its charge quantum number is therefore:

q(udd) = 2/3 + (-1/3) + (-1/3) = 0

Since the neutron has no net electric charge, it is not affected by electric forces, but the neutron does have a slight distribution of electric charge within it. This is caused by by its internal quark structure. This results in non-zero magnetic moment (dipole moment) of the neutron. Therefore the neutron interacts also via electromagnetic interaction, but much weaker than the proton.

Mass of Quark

The thermodynamics/thermodynamic-properties/what-is-mass-and-weight/what-is-mass/”>mass of the neutron is 939.565 MeV/c², whereas the mass of the three quarks is only about 10 MeV/c² (only about 1% of the mass-energy of the neutron). Like the proton, most of mass (energy) of the neutron is in the form of the strong nuclear force energy (gluons). The quarks of the neutron are held together by gluons, the exchange particles for the strong nuclear force. Gluons carry the color charge of the strong nuclear force.

Therefore, we have to distinguish between current quark mass (also called the mass of the ‘naked’ quarks) and constituent quark mass. Current quark mass refers to the mass of a quark by itself, while constituent quark mass refers to the current quark mass plus the mass of the gluon particle field surrounding the quark.

Noteworthy, because most of your mass is due to the protons and neutrons in your body, your mass (and therefore your weight on a bathroom scale) comes primarily from the gluons that bind the constituent quarks together, rather than from the quarks themselves. Mass is primarily a measure of the energies of the quark motion and the quark-binding fields any real object. It must be noted, gluons are inherently massless, they possess energy.

See also:

Quarks

Quarks

Quarks are a type of elementary particles and fundamental constituents of matter. In 1963, Gell-Mann and Zweig proposed that none of the hadrons, not even the proton and neutron, are truly fundamental, but instead are made up of combinations of three more fundamental pointlike entities called quarks. In the quark model, all hadrons are made of a few quarks. Today, the quark theory is well-accepted, and quarks are considered truly fundamental particles.

The hadrons are further sub-divided into baryons and mesons, according to the number of quarks they contain. Protons and neutrons each contain three quarks; they belong to the family of particles called the baryons. Other baryons are the lambda, sigma, xi, and omega particles. On the other hand mesons bosons and they are composed of two quarks: a quark and an antiquark. Besides charge and spin (1/2 for the baryons), two other quantum numbers are assigned to these particles: baryon number (B) and strangeness (S). Baryons have a baryon number, B, of 1, while their antiparticles, called antibaryons, have a baryon number of −1. A nucleus of deuterium (deuteron), for example, contains one proton and one neutron (each with a baryon number of 1) and has a baryon number of 2.

Electric Charge of Quarks

The most familiar baryons are the proton and neutron, which are each constructed from up and down quarks.

The proton has a quark composition of uud, and so its charge quantum number is:

q(uud) = 2/3 + 2/3 + (-1/3) = +1

The neutron has a quark composition of udd, and its charge quantum number is therefore:

q(udd) = 2/3 + (-1/3) + (-1/3) = 0

Since the neutron has no net electric charge, it is not affected by electric forces, but the neutron does have a slight distribution of electric charge within it. This is caused by by its internal quark structure. This results in non-zero magnetic moment (dipole moment) of the neutron. Therefore the neutron interacts also via electromagnetic interaction, but much weaker than the proton.

Mass of Quark

The thermodynamics/thermodynamic-properties/what-is-mass-and-weight/what-is-mass/”>mass of the neutron is 939.565 MeV/c², whereas the mass of the three quarks is only about 10 MeV/c² (only about 1% of the mass-energy of the neutron). Like the proton, most of mass (energy) of the neutron is in the form of the strong nuclear force energy (gluons). The quarks of the neutron are held together by gluons, the exchange particles for the strong nuclear force. Gluons carry the color charge of the strong nuclear force.

Therefore, we have to distinguish between current quark mass (also called the mass of the ‘naked’ quarks) and constituent quark mass. Current quark mass refers to the mass of a quark by itself, while constituent quark mass refers to the current quark mass plus the mass of the gluon particle field surrounding the quark.

Noteworthy, because most of your mass is due to the protons and neutrons in your body, your mass (and therefore your weight on a bathroom scale) comes primarily from the gluons that bind the constituent quarks together, rather than from the quarks themselves. Mass is primarily a measure of the energies of the quark motion and the quark-binding fields any real object. It must be noted, gluons are inherently massless, they possess energy.

Antiquarks

In particle physics, corresponding to most kinds of particles there is an associated antiparticle. An antiparticle has the same mass and opposite charge (including electric charge). For example, for every quark there is a corresponding type of antiparticle. The antiquarks have the same mass, mean lifetime, and spin as their respective quarks, but the electric charge and other charges have the opposite sign. Up-type antiquarks have charges of −​2⁄3 e and down-type antiquarks have charges of +​1⁄3 e. Since the electric charge of a hadron is the sum of the charges of the constituent quarks, all hadrons have integer charges.

Quarks in the Standard Model

Quarks and electrons are some of the elementary particles. A number of fundamental particles have been discovered in various experiments. So many, that researchers had to organize them, just like Mendeleev did with his periodic table. This is summarized in a theoretical model (concerning the electromagnetic, weak, and strong nuclear interactions) called the Standard Model. In particle physics, an elementary particle or fundamental particle is a particle whose substructure is unknown, thus it is unknown whether it is composed of other particles.

In the present Standard Model, there are six “flavors” of quarks, six quarks, just as there are six leptons based on a presumed symmetry in nature. The three quarks originally proposed and accepted were labeled u (up quark), d (down quark), s (strange quark). The other three quarks are called charmed, bottom, and top. They can successfully account for all known mesons and baryons. The most familiar baryons are the proton and neutron, which are each constructed from up and down quarks.

See also:

Fundamental Particles

What is Matter

The physical world is composed of combinations of various subatomic or fundamental particles. These are the smallest building blocks of matter. All matter except dark matter is made of molecules, which are themselves made of atoms. The atoms consist of two parts. An atomic nucleus and an electron cloud. The electrons are spinning around the atomic nucleus. The nucleus itself is generally made of protons and neutrons but even these are composite objects. Inside the protons and neutrons, we find the quarks.

Quarks and electrons are some of the elementary particles. A number of fundamental particles have been discovered in various experiments. So many, that researchers had to organize them, just like Mendeleev did with his periodic table. This is summarized in a theoretical model (concerning the electromagnetic, weak, and strong nuclear interactions) called the Standard Model. In particle physics, an elementary particle or fundamental particle is a particle whose substructure is unknown, thus it is unknown whether it is composed of other particles. Known elementary particles include the fundamental fermions and the fundamental bosons.

Matter vs. Antimatter

Particles and Antiparticles

Quarks and electrons are some of the elementary particles. A number of fundamental particles have been discovered in various experiments. So many, that researchers had to organize them, just like Mendeleev did with his periodic table. This is summarized in a theoretical model (concerning the electromagnetic, weak, and strong nuclear interactions) called the Standard Model. In particle physics, an elementary particle or fundamental particle is a particle whose substructure is unknown, thus it is unknown whether it is composed of other particles.

In particle physics, corresponding to most kinds of particles there is an associated antiparticle. An antiparticle has the same mass and opposite charge (including electric charge).

For example, for every quark there is a corresponding type of antiparticle. The antiquarks have the same mass, mean lifetime, and spin as their respective quarks, but the electric charge and other charges have the opposite sign.

The original idea for antiparticles came from a relativistic wave equation developed in 1928 by the English scientist P. A. M. Dirac (1902-1984). He realised that his relativistic version of the Schrödinger wave equation for electrons predicted the possibility of antielectrons. These were discovered by Paul Dirac and Carl D. Anderson in 1932 and named positrons. They studied cosmic-ray collisions via a cloud chamber – a particle detector in which moving electrons (or positrons) leave behind trails as they move through the gas. Positron paths in a cloud chamber trace the same helical path as an electron but rotate in the opposite direction with respect to the magnetic field direction due to their having the same magnitude of charge-to-mass ratio but with opposite charge and, therefore, opposite signed charge-to-mass ratios. Although Dirac did not himself use the term antimatter, its use follows on naturally enough from antielectrons, antiprotons, etc.

It was predicted that other particles also would have antiparticles. In 1955 the antiparticle to the proton, the antiproton, which carries a negative charge, was discovered at the University of California, Berkeley. Since then, the antiparticles of many other subatomic particles have been created in particle accelerator experiments. On the other hand, a few, like the photon and π⁰, do not have distinct antiparticles. These particles are their own antiparticles.

Matter and Antimatter – Laws of Conservation in Nuclear Reactions

In analyzing nuclear reactions, we apply the many conservation laws. Nuclear reactions are subject to classical conservation laws for charge, momentum, angular momentum, and energy (including rest energies).  Additional conservation laws, not anticipated by classical physics, are are electric charge, lepton number and baryon number. Certain of these laws are obeyed under all circumstances, others are not.

At this point, we describe especially the relationship between antimatter and the following laws of conservation:

• Law of Conservation of Lepton Number
• Law of Conservation of Baryon Number
• Law of Conservation of Electric Charge

Law of Conservation of Lepton Number

In particle physics, the lepton number is used to denote which particles are leptons and which particles are not. Each lepton has a lepton number of 1 and each antilepton has a lepton number of -1. Other non-leptonic particles have a lepton number of 0. The lepton number is a conserved quantum number in all particle reactions. A slight asymmetry in the laws of physics allowed leptons to be created in the Big Bang.

The conservation of lepton number means that whenever a lepton of a certain generation is created or destroyed in a reaction, a corresponding antilepton from the same generation must be created or destroyed. It must be added, there is a separate requirement for each of the three generations of leptons, the electron, muon and tau and their associated neutrinos.

Consider the decay of the neutron. The reaction involves only first generation leptons: electrons and neutrinos:

Since the lepton number must be equal to zero on both sides and it was found that the reaction is a three-particle decay (the electrons emitted in beta decay have a continuous rather than a discrete spectrum),  the third particle must be an electron antineutrino.

Law of Conservation of Baryon Number

In particle physics, the baryon number is used to denote which particles are baryons and which particles are not. Each baryon has a baryon number of 1 and each antibaryon has a baryon number of -1. Other non-baryonic particles have a baryon number of 0. Since there are exotic hadrons like pentaquarks and tetraquarks, there is a general definition of baryon number as:

where n_q is the number of quarks, and n_q is the number of antiquarks.

The baryon number is a conserved quantum number in all particle reactions.

The law of conservation of baryon number states that:

The sum of the baryon number of all incoming particles is the same as the sum of the baryon numbers of all particles resulting from the reaction.

For example, the following reaction has never been observed:

even if the incoming proton has sufficient energy and charge, energy, and so on, are conserved. This reaction does not conserve baryon number since the left side has B =+2, and the right has B =+1.

On the other hand, the following reaction (proton-antiproton pair production) does conserve B and does occur if the incoming proton has sufficient energy (the threshold energy = 5.6 GeV):

As indicated, B = +2 on both sides of this equation.

From these and other reactions, the conservation of baryon number has been established as a basic principle of physics.

This principle provides basis for the stability of the proton. Since the proton is the lightest particle among all baryons, the hypothetical products of its decay would have to be non-baryons. Thus, the decay would violate the conservation of baryon number. It must be added some theories have suggested that protons are in fact unstable with very long half-life (~10³⁰ years) and that they decay into leptons. There is currently no experimental evidence that proton decay occurs.

Law of Conservation of Electric Charge

The law of conservation of electric charge can be demonstrated also on positron-electron pair production. Since a gamma ray is electrically neutral and sum of the electric charges of electron and positron is also zero, the electric charge in this reaction is also conserved.

Ɣ → e^– + e⁺

It must be added, in order for electron-positron pair production to occur, the electromagnetic energy of the photon must be above a threshold energy, which is equivalent to the rest mass of two electrons. The threshold energy (the total rest mass of produced particles) for electron-positron pair production is equal to 1.02MeV (2 x 0.511MeV) because the rest mass of a single electron is equivalent to 0.511MeV of energy. If the original photon’s energy is greater than 1.02MeV, any energy above 1.02MeV is according to the conservation law split between the kinetic energy of motion of the two particles. The presence of an electric field of a heavy atom such as lead or uranium is essential in order to satisfy conservation of momentum and energy. In order to satisfy both conservation of momentum and energy, the atomic nucleus must receive some momentum. Therefore a photon pair production in free space cannot occur.

See also:

Fundamental Particles

Matter – Antimatter Creation and Annihilation

At the beginning of the 20th century, the notion of mass underwent a radical revision. Mass lost its absoluteness. One of the striking results of Einstein’s theory of relativity is that mass and energy are equivalent and convertible one into the other. Equivalence of the mass and energy is described by Einstein’s famous formula E = mc². In words, energy equals mass multiplied by the speed of light squared.

In special theory of relativity certain types of matter may be created or destroyed, but in all of these processes, the mass and energy associated with such matter remains unchanged in quantity. As a result of the conservation of lepton and baryon numbers,  antimatter (antiparticles) can be created out of energy, but only if a particle counterpart for every antiparticle is created as well. It will be demonstrated in the following sections.

Matter – Antimatter Annihilation

As was written, a particle and its antiparticle have the same mass as one another, but opposite electric charge, and other differences in quantum numbers. That means a proton has positive charge while an antiproton has negative charge and therefore they attract each other. A collision between any particle and its antiparticle partner is known to lead to their mutual annihilation. Since matter and antimatter carry an immense amount of energy (due to E = mc²), their mutual annihilation is associated with production of intense photons (gamma rays), neutrinos, and sometimes less-massive particle–antiparticle pairs.

One of best known processes is electron-positron annihilation. Electron–positron annihilation occurs when a negatively charged electron and a positively charged positron collide.When a low-energy electron annihilates a low-energy positron (antiparticle of electron), they can only produce two or more photons (gamma rays). The production of only one photon is forbidden because of conservation of linear momentum and total energy. The production of another particle is also forbidden because of both particles (electron-positron) together do not carry enough mass-energy to produce heavier particles. When an electron and a positron collide, they annihilate resulting in the complete conversion of their rest mass to pure energy (according to the E=mc² formula) in the form of two oppositely directed 0.511 MeV gamma rays (photons).

e⁻ + e⁺ → γ + γ (2x 0.511 MeV)

This process must satisfy a number of conservation laws, including:

• Conservation of electric charge. The net charge before and after is zero.
• Conservation of linear momentum and total energy. T
• Conservation of angular momentum.

See also:

Antimatter

Matter – Antimatter Creation and Annihilation

At the beginning of the 20th century, the notion of mass underwent a radical revision. Mass lost its absoluteness. One of the striking results of Einstein’s theory of relativity is that mass and energy are equivalent and convertible one into the other. Equivalence of the mass and energy is described by Einstein’s famous formula E = mc². In words, energy equals mass multiplied by the speed of light squared.

In special theory of relativity certain types of matter may be created or destroyed, but in all of these processes, the mass and energy associated with such matter remains unchanged in quantity. As a result of the conservation of lepton and baryon numbers,  antimatter (antiparticles) can be created out of energy, but only if a particle counterpart for every antiparticle is created as well. It will be demonstrated in the following sections.

Matter – Antimatter Creation

Matter – Antimatter creation occurs naturally in high-energy processes involving cosmic rays, and also in high-energy experiments in accelerators in Earth. High-energy cosmic rays impacting Earth’s atmosphere (or any other matter in the Solar System) produce minute quantities of antiparticles in the resulting particle jets, which are immediately annihilated by contact with nearby matter. The presence of the resulting antimatter is detectable by the two gamma rays (with 511 keV) produced every time positrons annihilate with nearby matter.

Antimatter creation is also very common in nuclear decay of many isotopes. Let assume a decay of potassium-40. Naturally occurring potassium is composed of three isotopes, of which ⁴⁰K is radioactive. Traces of ⁴⁰K are found in all potassium, and it is the most common radioisotope in the human body. ⁴⁰K is a radioactive isotope of potassium which has a very long half-life of 1.251×10⁹ years and undergoes both types of beta decay.

• About 89.28% of the time (10.72% is by electron capture), it decays to calcium-40 (⁴⁰Ca) with emission of a beta particle (β⁻, an electron) with a maximum energy of 1.33 MeV and an antineutrino, which is an antiparticle to the neutrino.
• Very rarely (0.001% of the time) it will decay to ⁴⁰Ar by emitting a positron (β+) and a neutrino.

Another very interesting source of antimatter is, in fact, a nuclear reactor. Nuclear reactors are the major source of human-generated antineutrinos. This is due to the fact that antineutrinos are produced in a negative beta decay. In a nuclear reactor occurs especially the β⁻decay, because the common feature of the fission fragments is an excess of neutrons. Please note that billions of solar neutrinos per second pass (mostly without any interaction) through every square centimeter (~6×10¹⁰) on the Earth’s surface and antineutrino radiation is by no means dangerous.

In January 2011, research by the American Astronomical Society discovered antimatter (positrons) originating above thunderstorm clouds.  It is suggested that these positrons are formed in terrestrial gamma-ray flashes (TGF). These positrons are produced in gamma-ray flashes created by electrons accelerated by strong electric fields in the clouds. TGFs are brief bursts occurring inside thunderstorms and associated with lightning. The streams of positrons and electrons collide higher in the atmosphere to generate more gamma rays. About 500 TGFs may occur every day worldwide, but mostly go undetected.

Matter – Antimatter Annihilation

As was written, a particle and its antiparticle have the same mass as one another, but opposite electric charge, and other differences in quantum numbers. That means a proton has positive charge while an antiproton has negative charge and therefore they attract each other. A collision between any particle and its antiparticle partner is known to lead to their mutual annihilation. Since matter and antimatter carry an immense amount of energy (due to E = mc²), their mutual annihilation is associated with production of intense photons (gamma rays), neutrinos, and sometimes less-massive particle–antiparticle pairs.

One of best known processes is electron-positron annihilation. Electron–positron annihilation occurs when a negatively charged electron and a positively charged positron collide.When a low-energy electron annihilates a low-energy positron (antiparticle of electron), they can only produce two or more photons (gamma rays). The production of only one photon is forbidden because of conservation of linear momentum and total energy. The production of another particle is also forbidden because of both particles (electron-positron) together do not carry enough mass-energy to produce heavier particles. When an electron and a positron collide, they annihilate resulting in the complete conversion of their rest mass to pure energy (according to the E=mc² formula) in the form of two oppositely directed 0.511 MeV gamma rays (photons).

e⁻ + e⁺ → γ + γ (2x 0.511 MeV)

This process must satisfy a number of conservation laws, including:

• Conservation of electric charge. The net charge before and after is zero.
• Conservation of linear momentum and total energy. T
• Conservation of angular momentum.

See also:

Antimatter

Particles and Antiparticles

Quarks and electrons are some of the elementary particles. A number of fundamental particles have been discovered in various experiments. So many, that researchers had to organize them, just like Mendeleev did with his periodic table. This is summarized in a theoretical model (concerning the electromagnetic, weak, and strong nuclear interactions) called the Standard Model. In particle physics, an elementary particle or fundamental particle is a particle whose substructure is unknown, thus it is unknown whether it is composed of other particles.

In particle physics, corresponding to most kinds of particles there is an associated antiparticle. An antiparticle has the same mass and opposite charge (including electric charge).

For example, for every quark there is a corresponding type of antiparticle. The antiquarks have the same mass, mean lifetime, and spin as their respective quarks, but the electric charge and other charges have the opposite sign.

The original idea for antiparticles came from a relativistic wave equation developed in 1928 by the English scientist P. A. M. Dirac (1902-1984). He realised that his relativistic version of the Schrödinger wave equation for electrons predicted the possibility of antielectrons. These were discovered by Paul Dirac and Carl D. Anderson in 1932 and named positrons. They studied cosmic-ray collisions via a cloud chamber – a particle detector in which moving electrons (or positrons) leave behind trails as they move through the gas. Positron paths in a cloud chamber trace the same helical path as an electron but rotate in the opposite direction with respect to the magnetic field direction due to their having the same magnitude of charge-to-mass ratio but with opposite charge and, therefore, opposite signed charge-to-mass ratios. Although Dirac did not himself use the term antimatter, its use follows on naturally enough from antielectrons, antiprotons, etc.

It was predicted that other particles also would have antiparticles. In 1955 the antiparticle to the proton, the antiproton, which carries a negative charge, was discovered at the University of California, Berkeley. Since then, the antiparticles of many other subatomic particles have been created in particle accelerator experiments. On the other hand, a few, like the photon and π⁰, do not have distinct antiparticles. These particles are their own antiparticles.

What is Antimatter

Antimatter is a term referring to material that would be made up of “antiatoms” in which antiprotons and antineutrons would form the nucleus around which positrons (antielectrons) would move. The term is also used for antiparticles in general.

Antimatter particles bind with one another to form antimatter, just as ordinary particles bind to form normal matter. For example, a positron and an antiproton can form an antihydrogen atom. Physical principles indicate that complex antimatter atomic nuclei are possible, as well as anti-atoms corresponding to the known chemical elements.

Our visible Universe is almost entirely composed of matter, and very little antimatter has existed since the Big Bang. This problem is known as the baryon asymmetry. This asymmetry of matter and antimatter in the visible universe is one of the great unsolved problems in physics.

Matter – Antimatter Creation and Annihilation

At the beginning of the 20th century, the notion of mass underwent a radical revision. Mass lost its absoluteness. One of the striking results of Einstein’s theory of relativity is that mass and energy are equivalent and convertible one into the other. Equivalence of the mass and energy is described by Einstein’s famous formula E = mc². In words, energy equals mass multiplied by the speed of light squared.

In special theory of relativity certain types of matter may be created or destroyed, but in all of these processes, the mass and energy associated with such matter remains unchanged in quantity. As a result of the conservation of lepton and baryon numbers,  antimatter (antiparticles) can be created out of energy, but only if a particle counterpart for every antiparticle is created as well. It will be demonstrated in the following sections.

Matter – Antimatter Creation

Matter – Antimatter creation occurs naturally in high-energy processes involving cosmic rays, and also in high-energy experiments in accelerators in Earth. High-energy cosmic rays impacting Earth’s atmosphere (or any other matter in the Solar System) produce minute quantities of antiparticles in the resulting particle jets, which are immediately annihilated by contact with nearby matter. The presence of the resulting antimatter is detectable by the two gamma rays (with 511 keV) produced every time positrons annihilate with nearby matter.

Antimatter creation is also very common in nuclear decay of many isotopes. Let assume a decay of potassium-40. Naturally occurring potassium is composed of three isotopes, of which ⁴⁰K is radioactive. Traces of ⁴⁰K are found in all potassium, and it is the most common radioisotope in the human body. ⁴⁰K is a radioactive isotope of potassium which has a very long half-life of 1.251×10⁹ years and undergoes both types of beta decay.

• About 89.28% of the time (10.72% is by electron capture), it decays to calcium-40 (⁴⁰Ca) with emission of a beta particle (β⁻, an electron) with a maximum energy of 1.33 MeV and an antineutrino, which is an antiparticle to the neutrino.
• Very rarely (0.001% of the time) it will decay to ⁴⁰Ar by emitting a positron (β+) and a neutrino.

Another very interesting source of antimatter is, in fact, a nuclear reactor. Nuclear reactors are the major source of human-generated antineutrinos. This is due to the fact that antineutrinos are produced in a negative beta decay. In a nuclear reactor occurs especially the β⁻decay, because the common feature of the fission fragments is an excess of neutrons. Please note that billions of solar neutrinos per second pass (mostly without any interaction) through every square centimeter (~6×10¹⁰) on the Earth’s surface and antineutrino radiation is by no means dangerous.

In January 2011, research by the American Astronomical Society discovered antimatter (positrons) originating above thunderstorm clouds.  It is suggested that these positrons are formed in terrestrial gamma-ray flashes (TGF). These positrons are produced in gamma-ray flashes created by electrons accelerated by strong electric fields in the clouds. TGFs are brief bursts occurring inside thunderstorms and associated with lightning. The streams of positrons and electrons collide higher in the atmosphere to generate more gamma rays. About 500 TGFs may occur every day worldwide, but mostly go undetected.

Matter – Antimatter Annihilation

As was written, a particle and its antiparticle have the same mass as one another, but opposite electric charge, and other differences in quantum numbers. That means a proton has positive charge while an antiproton has negative charge and therefore they attract each other. A collision between any particle and its antiparticle partner is known to lead to their mutual annihilation. Since matter and antimatter carry an immense amount of energy (due to E = mc²), their mutual annihilation is associated with production of intense photons (gamma rays), neutrinos, and sometimes less-massive particle–antiparticle pairs.

One of best known processes is electron-positron annihilation. Electron–positron annihilation occurs when a negatively charged electron and a positively charged positron collide.When a low-energy electron annihilates a low-energy positron (antiparticle of electron), they can only produce two or more photons (gamma rays). The production of only one photon is forbidden because of conservation of linear momentum and total energy. The production of another particle is also forbidden because of both particles (electron-positron) together do not carry enough mass-energy to produce heavier particles. When an electron and a positron collide, they annihilate resulting in the complete conversion of their rest mass to pure energy (according to the E=mc² formula) in the form of two oppositely directed 0.511 MeV gamma rays (photons).

e⁻ + e⁺ → γ + γ (2x 0.511 MeV)

This process must satisfy a number of conservation laws, including:

• Conservation of electric charge. The net charge before and after is zero.
• Conservation of linear momentum and total energy. T
• Conservation of angular momentum.

Matter and Antimatter – Laws of Conservation in Nuclear Reactions

In analyzing nuclear reactions, we apply the many conservation laws. Nuclear reactions are subject to classical conservation laws for charge, momentum, angular momentum, and energy (including rest energies).  Additional conservation laws, not anticipated by classical physics, are are electric charge, lepton number and baryon number. Certain of these laws are obeyed under all circumstances, others are not.

At this point, we describe especially the relationship between antimatter and the following laws of conservation:

• Law of Conservation of Lepton Number
• Law of Conservation of Baryon Number
• Law of Conservation of Electric Charge

Law of Conservation of Lepton Number

In particle physics, the lepton number is used to denote which particles are leptons and which particles are not. Each lepton has a lepton number of 1 and each antilepton has a lepton number of -1. Other non-leptonic particles have a lepton number of 0. The lepton number is a conserved quantum number in all particle reactions. A slight asymmetry in the laws of physics allowed leptons to be created in the Big Bang.

The conservation of lepton number means that whenever a lepton of a certain generation is created or destroyed in a reaction, a corresponding antilepton from the same generation must be created or destroyed. It must be added, there is a separate requirement for each of the three generations of leptons, the electron, muon and tau and their associated neutrinos.

Consider the decay of the neutron. The reaction involves only first generation leptons: electrons and neutrinos:

Since the lepton number must be equal to zero on both sides and it was found that the reaction is a three-particle decay (the electrons emitted in beta decay have a continuous rather than a discrete spectrum),  the third particle must be an electron antineutrino.

Law of Conservation of Baryon Number

In particle physics, the baryon number is used to denote which particles are baryons and which particles are not. Each baryon has a baryon number of 1 and each antibaryon has a baryon number of -1. Other non-baryonic particles have a baryon number of 0. Since there are exotic hadrons like pentaquarks and tetraquarks, there is a general definition of baryon number as:

where n_q is the number of quarks, and n_q is the number of antiquarks.

The baryon number is a conserved quantum number in all particle reactions.

The law of conservation of baryon number states that:

The sum of the baryon number of all incoming particles is the same as the sum of the baryon numbers of all particles resulting from the reaction.

For example, the following reaction has never been observed:

even if the incoming proton has sufficient energy and charge, energy, and so on, are conserved. This reaction does not conserve baryon number since the left side has B =+2, and the right has B =+1.

On the other hand, the following reaction (proton-antiproton pair production) does conserve B and does occur if the incoming proton has sufficient energy (the threshold energy = 5.6 GeV):

As indicated, B = +2 on both sides of this equation.

From these and other reactions, the conservation of baryon number has been established as a basic principle of physics.

This principle provides basis for the stability of the proton. Since the proton is the lightest particle among all baryons, the hypothetical products of its decay would have to be non-baryons. Thus, the decay would violate the conservation of baryon number. It must be added some theories have suggested that protons are in fact unstable with very long half-life (~10³⁰ years) and that they decay into leptons. There is currently no experimental evidence that proton decay occurs.

Law of Conservation of Electric Charge

The law of conservation of electric charge can be demonstrated also on positron-electron pair production. Since a gamma ray is electrically neutral and sum of the electric charges of electron and positron is also zero, the electric charge in this reaction is also conserved.

Ɣ → e^– + e⁺

It must be added, in order for electron-positron pair production to occur, the electromagnetic energy of the photon must be above a threshold energy, which is equivalent to the rest mass of two electrons. The threshold energy (the total rest mass of produced particles) for electron-positron pair production is equal to 1.02MeV (2 x 0.511MeV) because the rest mass of a single electron is equivalent to 0.511MeV of energy. If the original photon’s energy is greater than 1.02MeV, any energy above 1.02MeV is according to the conservation law split between the kinetic energy of motion of the two particles. The presence of an electric field of a heavy atom such as lead or uranium is essential in order to satisfy conservation of momentum and energy. In order to satisfy both conservation of momentum and energy, the atomic nucleus must receive some momentum. Therefore a photon pair production in free space cannot occur.

See also:

Antimatter