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The evolving Universe
The evolving Universe

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1.6 The quark-lepton era (contd)

The next stage of the story is to look at how and when the original mixture of all types of quark and lepton that were present when the Universe was 10−11 s old, gave rise to the Universe today, which seems to be dominated by protons, neutrons and electrons.

Question 8

In particle accelerators, how much energy is required in order to 'create' a particle and an antiparticle of a given mass?


Broadly speaking, an amount of energy equivalent to (or greater than) the mass energy of the particle and antiparticle concerned needs to be supplied. For example, the mass energy of an electron is about 500 keV, so to create an electron-positron pair, at least 2 × 500 keV = 1 MeV of energy must be available.

In the early Universe, when the mean energy per particle was greater than the mass energy of a given particle plus antiparticle, those particles and antiparticles existed in abundance, and survived in equilibrium with radiation. When the mean energy per particle dropped below this value, annihilations became more likely than pair creations, and so the number of particles and antiparticles of a given type reduced.

Massive quarks and leptons also decay into less massive ones, and these decays became more likely as the available energy fell.

Question 9

In the early Universe, what was the mean energy per particle when the following particles decayed into their less massive counterparts? (a) Top quarks with a mass energy of around 180 GeV. (b) Tauons with a mass energy of around 1.8 GeV.


(a) Top quarks decayed when the mean energy per particle fell below about 180 GeV. (b) Tauons decayed when the mean energy per particle fell below about 1.8 GeV.

Broadly speaking, when the temperature of the Universe fell below that at which the mean energy per particle was similar to the mass energy of the particles concerned, then the particles decayed into other less massive particles. So, by the time the Universe had cooled to a temperature of 3 × 1012 K, equivalent to a mean energy per particle of about 1 GeV, when the Universe was 10−5 s old, several important changes had taken place. First, many of the tauons and antitauons, muons and antimuons had decayed into their less massive lepton counterparts: electrons and positrons. Also, the temperature had fallen such that annihilation was favoured rather than pair creation for tauons and muons, so any remaining massive leptons had mutually annihilated, producing photons. The only leptons that remained in the Universe in any significant number were therefore electrons and neutrinos (with their antiparticles in approximately equal numbers).

Similarly, the massive quarks (strange, charm, top and bottom) had mostly decayed into their less massive counterparts (up and down), via a variety of transformations, some of which are shown in Figure 4. Notice that all of these decays are weak interactions, since they involve W bosons. In each case quarks change flavour with the emission of a lepton-antilepton pair.

All types of quark and antiquark also underwent mutual annihilations — with a particularly crucial result. In discussing the relative numbers of particles and antiparticles earlier, the phrase approximately equal was used deliberately. If the Universe had contained exactly equal numbers of quarks and antiquarks, then these would have all annihilated each other, leaving a Universe that contained no baryons — so no protons and neutrons — no atoms and molecules — no galaxies, stars, planets or people. Clearly that is not what we observe around us!

In fact the Universe now seems to consist almost entirely of matter (rather than antimatter) in the form of protons, neutrons, electrons and electron neutrinos, plus photons. And there are believed to be roughly one billion photons for every baryon (proton or neutron) in the Universe today. This implies that, just before the quark-antiquark annihilations took place, for every billion antimatter quarks there must have been just over a billion matter quarks. Running the Universe forward from this point, for every billion quarks and billion antiquarks that annihilated each other producing photons, a few quarks were left over to build baryons in order to make galaxies, stars, planets and people.

Why did the Universe produce this slight imbalance of matter over antimatter? Maybe it was just 'built-in' from the start, like any other constant of nature? This is rather unsatisfactory to many cosmologists and particle physicists, who prefer to believe that the imbalance arose after the Universe had got started. It has been suggested that the decays of X bosons into quarks and leptons may slightly favour the production of matter particles over antimatter particles. As you saw in Equation 2, a matter or antimatter X boson can decay into either matter particles or antimatter particles. So, if there is an imbalance in the rates, starting with equal numbers of matter and antimatter X bosons will not lead to the production of equal numbers of matter and antimatter quarks and leptons. Such matter-antimatter asymmetry has actually already been observed with experiments on Earth that measure the decay of particles called K mesons. Of the two possible routes for this reaction, one is favoured over the other by seven parts in a thousand. Perhaps something similar, to the tune of a few parts in a billion, occurs with X boson decays? The answer to this question is not yet known — but it's a rather important one, since without it none of us would be here to discuss the matter!

Figure 4
Figure 4 Feynman diagrams showing some examples of processes by which massive quarks decay into less massive quarks. In each case, electric charge, the number of quarks minus the number of antiquarks, and the number of leptons minus the number of antileptons are all conserved.