Particle Physics_A Very Short Introduction

by Frank Close

  There are strange baryons and strange mesons. A strange baryon consists of three quarks at least one of which is a strange quark; the greater the number of strange quarks the baryon contains, the greater is the magnitude of its ‘strangeness’. A meson consists of a quark and an antiquark and so, by analogy, a strange meson is one that contains either a strange quark or a strange antiquark. The discovery of strange particles preceded by several years the discovery that baryons and mesons are made of quarks. The properties of the variety of strange particles led theorists to invent the concept of strangeness, which acted in many ways like charge: strangeness is conserved when the strong force acts on particles. Thus one could explain which processes were favoured or disfavoured by computing how much strangeness each of the participating particles carried. Various mesons were determined to carry strangeness of amount +1 or –1. Strange baryons were found by this scheme to carry amounts –1, –2, or –3. Today we understand what determines this. The amount of negative strangeness that a particle carries corresponds to the number of strange quarks within it. It might seem more natural to have defined strangeness such that each strange quark carried one unit of positive strangeness, and had we known of quarks before the idea of strangeness, that is how it would probably have been. But we are stuck with this accident of history whereby the number of strange quarks accounts for negative strangeness and the number of strange antiquarks accounts for positive strangeness. (A similar accident of history gave us a negative charge for the electron.)

  A strange quark is electrically charged, carrying an amount –1/3, as does the down quark. It is more massive than a down quark, having an mc2 of ~150 MeV. In all other respects the strange and down quarks appear to be the same. Due to the extra mass of the strange quark relative to an up or down quark, every time one of these in the proton or neutron, say, is replaced by a strange quark the resulting strange baryon is roughly 150 MeV more massive per unit of (negative) strangeness.

  25. a) Baryons with spin 1/2.

  b) Baryons with spin 3/2.

  The baryons that are like the proton and neutron, and have spin 1/2, are listed in Figure 25 a) along with their quark content, electric charge, strangeness, and magnitude of mass (or mc2 in MeV). The rule is not exact but is at least qualitatively true (the actual masses, as was the case for the proton and neutron, depend also on the different electrical forces among the constituents and the fact that their sizes, while approximately 10–15 m, are not all identical, due to the complicated nature of the forces acting on them). The rule is more precisely verified in the set of strange baryons with spin 3/2 that partner the Δ resonance, as seen in Figure 25, table b).

  There are mesons with strangeness +1, such as the , and –1, such as , with masses mc2 ~500 MeV. There are also mesons which contain both strange quark and antiquark, so that there is no net strangeness. This combination leads to a third electrically neutral meson, known as the eta-prime, η′, in addition to the πo and η that we met in Chapter 4.

  These mesons made of a quark and antiquark have a total spin of zero. There is also a set where the quark and antiquark spins combine to a total of one. The strange members in this case are known respectively as , and ; the analogues of the π, η, and η′ are known as ρ, ω, and φ (rho, omega, and phi).

  26. Spins of mesons made from quarks. Spins of the u and d quarks add together forming a positively charged ρ or cancel out, making a positively charged π. Similar combinations occur for any mixture of u, d, or s flavours with any of their antiquark counterparts. This picture extends to charm, bottom, and top flavours. Among the many resulting combinations we illustrate the ‘psi’ (ψ) where the spins add to a total of 1, and its partner the ‘eta-charm’ ηc, where the spins cancel to zero.

  Charm

  Not only does the down quark have its heavier cousin, the strange quark, but so does the up quark have a heavier version: the charm quark. A charm quark is electrically charged, carrying an amount +2/3, as does the up quark. It is more massive than the up quark, having an mc2 of ~1500 MeV. In all other respects the charm and up quarks appear to be the same.

  In the case of strange quarks we formed strange baryons and mesons which were a few hundred MeV more massive than their up and down flavoured counterparts. A similar story happens with the charm quark, but due to its greater mass, the analogous charmed mesons and baryons weigh in correspondingly heavier, the lightest being found around ~1900 MeV or nearly 2 GeV. In part as a result of this greater mass, they are not easily produced in cosmic rays, and it was only with the advent of dedicated experiments at high-energy particle accelerators that the existence of charmed particles, and the charm quark, became known in the final quarter of the 20th century.

  Charm quarks can link in threes with any combination of up, down, or strange quarks to make baryons with charm, or even with both charm and strangeness. A few examples have even been seen where two charmed quarks have joined with an up, down, or strange quark. We expect that three charmed quarks can join to make a baryon with three units of charm, but clear evidence for its existence is still awaited.

  A charmed quark can link with a single antiquark that can be any of (anti)- up, down, or strange. The most celebrated examples, though, are where a charmed quark joins with a charmed antiquark, , leading to yet another electrically neutral partner, adding to the pion and etas, made from ; or that we already met. The resulting ‘eta-c’, written ηc, has a mass of just below 3,000 MeV, 3 GeV, and as such is the lightest example of a whole spectroscopy known as ‘charmonium’.

  It was through charmonium that the charm property was first discovered. The ηc is formed when the c and , each having spin ½, couple their spins to a total of zero (see Figure 26). They can also couple their spins to give a total value of one; this forms a slightly heavier state at 3.1 GeV known as the psi: ψ. When an electron and a positron meet and annihilate, they do so most readily when their spins are correlated to make spin one. In such a reaction both the energy and also the amount of spin are conserved; this has the effect that, if the combined energy of the electron and positron matches the mc2 of a meson with spin one, made of a quark and its antiquark (hence electrically neutral), then that meson will be produced from the energy left from the annihilation of the electron and positron. So, for example, if an electron and positron collide head on with a combined energy of about 0.8 GeV, which is the mass of the spin-one ρ and ω, either of these mesons can be formed; around 1 GeV the analogous meson made of , namely the φ, appears; and at 3.1 GeV we meet whence a ψ can be formed. That is how this first example of charmonium was found in 1974, and how the spectrum of particles was gradually uncovered.

  Particles with either charm or strangeness are not stable. Their masses are greater than those of baryons or mesons without charm or strangeness and hence their intrinsic energy, represented by mc2, is greater. Thus although strange and charmed particles can be made in high-energy collisions at accelerators, or even in the extreme energies that were prevalent immediately following the Big Bang, they rapidly decay leaving ultimately up and down quarks within the ‘conventional’ baryons, which survive in our day to day world; mesons ultimately self-destruct due to quark and antiquark annihilation, producing photons or electrons and neutrinos as their stable endproducts.

  27. Mesons with spin 1 that can be made easily in e+e– annihilation. In addition a photon or Zo, which are not made from quarks, can be made this way.

  Bottom and top

  We have seen above how Nature has duplicated its basic quark flavours making a second set, the strange and charm, with the same electric charges but greater mass than their down and up cousins. One may well ask why? This is not the end of the story; Nature has availed itself of a third set of yet more massive quarks, with the same electric charges as those that went before. Thus we have the bottom quark (b), mc2 ~ 4.5 GeV, electric charge –1/3; and there is the top quark (t), mc2 ~ 180 GeV (this is not a misprint!), electric charge +2/3. How it is that Nature packs so much mass, compara
ble to that of an entire atom of gold, into a space of at most 10–18 m is one of the great mysteries for the 21st century. In some articles these attributes are called truth and beauty instead of top and bottom; it is the latter that are now rather generally agreed on and so I shall refer to top and bottom here.

  Baryons and mesons containing bottom quarks or antiquarks occur and are in effect heavier analogues of those containing the lighter strange quark of the same charge. The lightest bottom mesons have mass, or mc2, at around 5 GeV. Similarly bottom baryons occur. There is little to be gained in writing out all their characteristics; however, if you want to do so, go to the table of strange particles, replace s by b and add about 4.5 GeV mass for every b quark or antiquark and you will have it. Bottom mesons have proved interesting in that their behaviour may give clues to the puzzle of why the universe is made of matter to the exclusion of antimatter. There is also a spectroscopy of ‘bottomonium’ states analogous to the charmonium spectroscopy; bottomonium consists of , the lightest example having a mass around 9.5 GeV.

  You might at this point expect that mesons and baryons containing top quarks will occur, with properties analogous to those of the charmed particles, (as top and charm have the same charge), and that their main distinguishing feature is that they are nearly 200 GeV more massive than their charmed counterparts. And this might indeed be the case, but no one yet knows as we do not have a facility capable of making such massive particles in enough quantity to study them in sufficient detail. However, there is strong doubt that these particles will actually occur. The problem is that the top quark, being so massive, is so unstable that it decays in less than 10–25 s, probably before it has time to grip other quarks or antiquarks to form the bound states that we call mesons and baryons.

  The decay occurs by a process analogous to that familiar in beta radioactivity. As a neutron turns into a proton when a down quark turns into the (lighter) up quark, emitting energy in the form of an electron and a neutrino (technically, an antineutrino),

  so do the heavier quarks imitate this. The difference between the electric charges of any quarks is either zero or ±1. In the latter case, a decay can occur from the heavier to the lighter by emitting an electron or a positron respectively (along with a neutrino or antineutrino). So we can have a cascade of decays

  and at the final step one can have a stable particle left, such as a proton. It is possible, though less likely, that a decay chain might miss a step, e.g. . It is also quite probable that the charmed quark takes an alternate route ; . The d and u quarks have such similar masses, reflected in the similar masses of the neutron and proton, that the process is slow, for example the half life of a free neutron is as long as ten minutes. The other mass differences are larger and the processes occur faster, in the case of the top, we suspect, so fast that top mesons and baryons do not have time to form.

  28. Dominant weak decays of quarks. Each downward arrow emits e+ν; each upward arrow emits . Two less probable paths are also shown with dotted arrows.

  Who ordered that?

  Our world consists of up and down quark, the electron and a neutrino. The latter is known as the ‘electron-neutrino’, symbol νe to denote the fact that it is a sibling of the electron. Nature triplicates the quarks, with charm and strange, and also top and bottom as heavier versions of these electrically charged +2/3 and –1/3 particles. It is not just with the quarks that nature does this; there are three varieties of each of the leptons too.

  There is a heavier version of the electron, known as the muon, symbol μ–. This is negatively charged, like the electron. The muon (and its antiparticle version the μ+) are apparently in all respects the same as electron or positron except that they are 207 times more massive, with an mc2 ~ 105 MeV. In weak decays, the muon is accompanied by a neutrino, but a different neutrino from the νe. We call this the muon-neutrino, symbol νμ (there is, of course, an antineutrino too: ).

  There is a third set of leptons. This consists of the tau, a negatively charged analogue of the electron but weighing in at some 2 GeV, (this is denoted τ–, its antiparticle version being τ+) and the associated neutrino (antineutrino) being .

  The neutrinos are distinguished by their masses, which are too small to measure though we are beginning to get a measure of their nugatory differences in masses. In a nutshell, it seems to be mass that is the essential feature distinguishing the corresponding members of the three ‘generations’ of basic particles. From the study of the Zo boson we know that there are no more light neutrino varieties in nature. This is because we can measure how long the Zo lives, which turns out to be the same as theorists calculated should be the case so long as there are only three distinct varieties of neutrinos that can be produced when it decays. The more varieties there are, the faster the Zo would decay as each available path would make the Zo more and more unstable. If there are any more light neutrinos, they would shorten the Zo life, in disagreement with what is observed in practice. So the inference is that there are only three distinct varieties of such light neutrinos.

  Given this result, and as we suspect that every variety of such a neutrino is partnered by a negatively charged lepton, and these in turn partnered by two varieties of quark, the +2/3 and –1/3 variety, then we have identified the full set of such basic pieces. Every one of these leptons and quarks has a spin 1/2. Thus Nature appears to have made three generations of fundamental particles with spin 1/2. Why three? We do not know. Why was it not satisfied with one? Here again we do not know for certain but we suspect that the answer may be related to another puzzle: why is there an imbalance between matter and antimatter in the universe?

  29. Quarks and leptons. The up and down quarks’ masses are ~5–10 MeV and the strange ~150 MeV. When trapped inside hadrons they gain extra energy and act as if they have masses of ~350 MeV and ~500 MeV, respectively. The effective masses of the heavier quarks are not so dramatically affected by their entrapment inside hadrons. Their masses are charm ~1.5 GeV, bottom ~4.5 GeV, and top ~180 GeV.

  Antimatter puzzle

  Antimatter has an aura of mystery, the promise of a natural Tweedledum to our Tweedledee, where left is right, north is south, and time runs in reverse. Its most celebrated property is its ability to destroy matter in a flash of light, converting the stuff that we are made of into pure energy. In science fiction, antiplanets tempt travellers to their doom even as antihydrogen powers the engines of astrocruisers. In science fact, according to everything that decades of experimental physics has taught us, the newborn universe was a cauldron of energy where matter and antimatter emerged in perfect balance. Which begs a question: how is it that matter and antimatter did not immediately destroy each other in an orgy of mutual annihilation? How is it that today, some 14 thousand million years later, there is anything left in the universe at all?

  This conundrum touches on our very existence. We are made of matter, as is everything we know of in the universe. There are no antimatter mines on Earth, which is just as well as they would be destroyed by the matter surrounding them with catastrophic results. Somehow, within moments of the Big Bang, matter had managed to emerge victorious; the antimatter having been annihilated, the heat energy from the destruction remaining (today being a cool 3 degrees above absolute zero in temperature and known as the microwave background radiation) and the surfeit of matter eventually clumping into galaxies of stars. Something must distinguish matter from antimatter so that matter emerged victorious.

  The sequence of events that enabled the basic pieces of matter to be cooked within stars, eventually to form bulk matter as we find it today, will be described in the next chapter. Here we discuss the question of how matter and antimatter might differ.

  This question has plagued physicists and cosmologists for years. An essential clue turned up in 1964 and it is only recently, following further discoveries and advances in technology, that it has become possible to exploit the clue and perhaps identify the culprit. The clue was the discovery that Nature contains a tiny imba
lance, a tendency for the behaviour of certain ‘strange’ particles, such as the electrically neutral Ko not to be mimicked precisely by the antimatter counterpart, the .

  The strange particles had been discovered in 1947 among the debris arising when cosmic rays hit the upper atmosphere. The realization that there is exotic stuff in the universe had helped inspire the building of particle accelerators, which were capable of producing strange particles, such as K-mesons, in abundance. Thus it was that in 1964 a team of physicists at Brookhaven National Laboratory in New York discovered that about one in a million times, the matter and antimatter accounts in the K-meson decays failed to balance.

  The nature of this asymmetry is so subtle that investigating it has been one of the most demanding and delicate measurements in modern physics. The breakthrough came following the discovery in 1977 of the first examples of ‘bottom’ particles and the realization that they are in effect heavier versions of strange particles. As the strange particles can distinguish between matter and antimatter, so the bottom particles might too. Indeed, when the discovery of bottom and top quarks confirmed that nature has indeed made three generations of quarks, and of antiquarks, the resulting equations surprisingly seemed to imply that an asymmetry between matter and antimatter for bottom particles was almost inevitable. The subtle asymmetry between Ko and was predicted to be rather large for their bottom analogues, the Bo and . Could the existence of three generations, and in particular of bottom quarks, somehow hold the key to the conundrum? As bottom particles are abundant in the first moments of the universe, could they hold the secret of how the lopsided universe, where matter dominates today, has emerged?