Module 3. The Thermal History of the Universe




Pair Production and Particle Annihilation

In this chapter we will discuss the rapid evolution of the Universe in its very early stages. Most of this discussion will take place when the Universe is less than 2 seconds old. The basic framework for describing the thermal evolution of the Universe uses the principle of mass-energy equivalence, E = mc2 ; mass and energy are the same thing and can be converted from one form to the other. More specifically, the following reactions are possible in nature:

photon + photon --> particle + antiparticle

particle + anti-particle --> photon + photon

The top reaction represents the case of pair production. In this situation, two energetic photons collide to produce a particle plus its anti-particle. The bottom reaction represents the case of particle annihilation in which a particle plus its anti-particle meet and annihilate one another to produce energy (photons). In theory, this is the concept behind matter-anti matter propulsion. The problem is that there is little anti-matter left in the Universe, a subject to which we will later return.

In the early Universe, pair production and particle annihilation were occurring all the time. The key point, however, is the following: since the temperature of the Universe is steadily falling (due to its expansion) and since the average photon energy depends on the temperature, then the average energy per photon declines as the Universe expands and cools. The kinds of particle/anti-particle pairs that can be created depends strictly on the photon energy. For instance, the neutron has a rest mass energy given by mnc2, where mn represents the mass of the neutron. A neutron plus anti-neutron can only be created if the initial energy of the photon is in excess of this rest-mass energy. This is why very high temperatures are required for pair-production and why, therefore, it can only occur in the very early Universe.

Figure 3.1 Distribution of photon energies. The average photon energy (peak of the curve) depends only on temperature. Photons with wavelengths less than the wavelength at which this peak occurs have energies above average.


At any given time in the Universe, the distribution of photon energies is like that of a blackbody curve (see Figure 3.1). The peak in that curve depends upon the temperature but there are substantial numbers of photons with energies greater than this average value. Nonetheless, we still we have the general rule that if

Ephoton < mpc2

then that photon has insufficient energy to spontaneously convert itself to a particle plus anti-particle of mass mp .

What is a particle?

Most of us are familiar with electrons, protons and neutrons as being what makes up atoms. But the world of particle physics is a bit more complex than this. However, the big unknown in all of particle physics is the process that gives the particles the masses they have. Thus, while it's possible to ask - "What is a proton?" and get a sensible answer, it is not possible to ask and answer "how come the mass of a proton is 1.67 x 10-24 grams?" In discussing the early Universe we will refer to the following kinds of particles:

1. Hadrons: A hadron is any particle which is subject to the strong force. Generally these are "heavy" particles (they have high rest mass energy). All hadrons are composed of quarks. Those hadrons that are composed of 3 quarks are called baryons. Protons and neutrons are familiar forms of baryons. Hadrons that are composed of two quarks are called mesons, which are a relatively exotic form of matter.

2. Leptons: These are light particles with low rest mass energy. They are not subject to the strong force and they are not composed of any sub-particles (there are no leptonic-quarks). A familiar example of a lepton is an electron. Another example is the neutrino, discussed below. The neutrino is a very important particle in the early Universe.

3. Quarks: These are the fundamental building blocks of hadronic matter. There are 6 known quarks: up,down,top.bottom,charm, and strange. A baryonic particle such as a neutron or a proton is made of 3 quarks. Some quarks carry charges, particularly the up and down quarks. An up quark has a charge of +2/3 while a down quark has a charge of -1/3. A baryonic configuration composed of two up quarks and one down quark would have a charge of +1. This configuration we call a proton. If one of the up quarks changes to a down quark, the charge will be 0. Now we have a neutron. In symbolic form this would be expressed as

The remarkable thing about quarks is that if you try to take one out of a proton, for instance, to produce a particle that therefore has only 2 quarks, you can't. The force that holds the quarks together increases with increasing distance of the quarks. As you try to pull the quarks apart, their attractive bond increases. This is essentially the way the strong force works. It's called the strong force because it's very strong and allows atomic nuclei to stay together. That is, a Carbon nucleus has 6 protons in it. Why doesn't the nucleus fragment because the 6 protons with like charges all repel one another? The answer is the strong force. If you can confine protons to small spacings the strong force takes over and binds them together. Separating them requires a great deal more energy than can be supplied by simple electrostatic repulsion.

Figure 3.2 Schematic representation of a proton with 2U quarks (U) and 1D quark (D). The force between the quarks is provided by the gluons, represented as solid black balls on the force line arrows.


4. Gluons: These are mysterious sub-particles that are the carriers of the force between the quarks. There name is apropro as they literally are the "glue" that holds quarks together. As you try to separate the quarks, thus separating the gluons, the force provided by the gluons strongly increases. This is schematically shown in Figure 3.2.

5. Neutrinos: These are very light particles but there are lots of them in the Universe. They carry no charge and have a very small cross section for interaction with other forms of matter.

6. Antimatter: Antimatter has all the properties of normal matter but they are just reversed. For example, an anti-electron has exactly the same mass as an electron but has positive charge (and hence is called a positron).

Conservation Rules

Although the early Universe may appear to be quite chaotic, with matter and energy constantly changing forms, there is a set of conservation laws that strictly govern the kind of particle interactions which can occur. Specifically, there are three things that need to be conserved in any particle interaction. These are

Whatever these three numbers were in any initial state, they must be the same in a final state. But what do these numbers represent?

The Baryon number represents the initial baryon state. The units are +1, 0 , -1. A normal baryon, like a proton, would have a baryon number of +1. An anti-baryon would have a baryon number of -1. If the particle wasn't a baryon, its baryon number would be zero. Similar arguments hold for charge and lepton number. It is the strict adherence to these conservation rules that, for instance, allow for the spontaneous creation of some forms of antimatter during some particle decays, as in the case of neutrons which will decay with a 1/2 life of 900 seconds if they are not bound in an atomic nucleus.

Figure 3.3 Visualization of the decay of the neutron to its 3 decay products. The baryon number, lepton number and charge for each particle is indicated.


The decay path of the neutron is shown in Figure 3.3. Let's examine each of the decay steps in detail. The initial state is just that of a neutron. A neutron has a baryon number of +1, a lepton number of 0 (because its not a lepton), and a charge number of 0 (its neutral). Whatever the form of the decay products, their total baryon, lepton and charge numbers must sum to the initial condition:

Step 1: The neutron decays into a proton. The proton has baryon number = +1, lepton number = 0, and charge = +1. Now we have an immediate imbalance in the charge. Since conservation of charge is required (in order for the Universe to remain electrically neutral) we must balance this positive charge with a negative one. We cannot satisfy this condition with any negatively charged baryon because the total baryon number would be 2 instead of 1. Hence we require a negatively charged lepton.

Step 2: An electron is a negatively charged lepton. It has baryon number = 0 (because it's not a baryon), lepton number = +1, and charge = -1. Now we have balanced the charge but to do so required the creation of a lepton. So now we have a lepton number of +1 on the decay side when the initial value was zero.

Step 3: To satisfy the conservation laws, we need to create one more particle. This particle must have baryon number = 0 and charge =0. But it also must have lepton number = -1 and hence we must create anti-matter. A particle with these properties is the anti-neutrino. It is electrically neutral, it's not a baryon, but it is anti-matter and so its lepton number is -1.

Animated sequence of the decay of the free neutron

This is just one specific example but serves to illustrate the general rules. With our understanding of the conservation laws we can now see why a photon is a special particle. Consider when, say, a proton and an anti-proton annihilate. Since the anti -proton is a mirror image of the proton, then the combined baryon, lepton and charge numbers of the proton anti-proton pair must each be zero. Hence, the decay products must be 0. A photon is a unique particle in that it's neither a baryon or a lepton and it has no charge, so its value is zero. In that sense, a photon also acts as its own anti-particle. Because a photon is neither a baryon or a lepton it has no rest mass and hence can travel at the speed of light. Only photons or "photon-like" particles have this property.

Remember the key point here:

The ratio of photons to baryons in the Universe is one billion to one.

Hence, at early times when the Univere was hot and the average energy per photon was large the universe has to be radiation dominated!

The threshold for particle creation only depends on the temperature. If the rest mass energy (mc2) of a particle is higher than the average energy of a photon then that particle can't be created as shown in this animation: