Link to return to Modern Physics front page
Links to specific sections in the text:
15.a. Elementary Particles
15.b. Conservation Laws
15.c. Particle interactions
15.d. The standard model
The first elementary particle, the electron, was discovered by Thompson. But elementary particle physics as a separate area of physics was really started in the 1940's and 1950's, some time after the discovery of proton, neutron, and positron, that are all elementary particles (at least they were regarded as such until about 1970). There were two important reasons for the blossoming of elementary physics, one experimental and one theoretical.
The experimental impetus was given by the observation that very high energy particles, first observed in cosmic radiation, are able to initiate reactions, similar to nuclear interactions, when collide with the nuclei of O, N, H,... of the atmosphere. It was observed, using photographic emulsions flown at high altitude, that when particles of the cosmic radiation (mostly protons) collide with nuclei they produce a large number of new particles, at very narrow forward angles, sometimes a far larger number than the number of nucleons in the target nucleus. The large cross section for these collisons and the shear number of particles produced were a proof that the interaction between the nucleus and the incoming cosmic ray particle is very strong. Thus, it was immediately thought that most of the particles produced were not nucleons, but rather the quanta of the strong force. The existence of these quanta, called p-mesons, was predicted on purely theoretical grounds by Hideki Yukawa in the 1930's. It was soon proved that indeed most of the particles produced of these high energy collisions are p-mesons. Their approximate mass was also predicted successfully based on the structure of Yukawa interactions,
VYukawa = - g2e-m r c/ hbar / r = - g2e- r / R
where m is the mass of the particle communicating the interaction. Note that electromagnetic interactions are similar if we take g2 -> k e2 and m=0 (the mass of the photon is 0!). By estimating the range of nuclear interactions, which is equal to R = hbar /(m c) = hbar c / (m c2) one is able to come up with a number
m c2 = hbar c / R = 197.3 MeV f / 1.2 f = 164 MeV.
The true mass of p-mesons is 138 MeV, remarkably close to this crude estimate. The investigation of interactions of nucleons and p-mesons lead to the development of elementary particle physics.
The other ingredient in the emergence of elementary particle physics was the success of quantum field theory that became and still is the only successful framework of describing the interactions (creation, annihilation, and scattering) of elementary particles. Quantum field theory was started by Dirac around 1930 from the marriage of relativity and quantum mechanics. Though the theoretical framework was understood quanum field theory was useless for most practical reasons because calculations, beyond a trivial first approximation cannot be made any sense, they were plagued by divergences (infinities) that could not be eliminated. It took almost two decades until Tomonaga, Schwinger, and Feynman could device a self-consistent method of eliminating these divergences. This method is called renormalization.
The basic idea behind renormalization can be understood easiest in is the framework of Quantum electrodynamics, the quantum field theory describing the interaction of photons with charged particles, such as electrons. Quantum field theory implies that the vacuum is not really empty, but filled with "virtual" particles that are keep being produced and annihilated. Conservation of energy momentum is satisfied because the mass-energy of these virtual particles does not equal to the mass-energies observed for physical particles traveling in the vacuum. Virtual particles live for a very short time, before annihilating, thus the uncertainty relation between time and energy requires that their mass-energy is undetermined to a large degree.
The presence of these virtual particles on real electrons is profound and twofold. The mass-energy of the real electron is changed substantially by interactions with the bath of virtual particles around it. Note that even classically the self energy of a pointlike electron is infinite. It is also infinite, due to interactions with virtual particles, in quantum field theory. These interactions will give an infinite contribution to the mass energy of electrons. It turns out, however that if the mass-energy of the electron (the so-called bare mass-energy) without the interaction with virtual particles is chosen to be infinitely large and negative then the sum of contributions can be made finite and one can end up with a finite mass in a consistent series of approximations of arbitrary precision. Similarly, the other parameter describing electrons, their charge, can also be treated in a similar manner. Note that the presence of the negatively charged electron polarizes virtual particles, the total charge of which must be equal to zero. Thus, the electron sits in a polarized dielectric medium. Then, observed from practically infinite distance (that is what experimental observations practically do) the charge of the electron seems considerable smaller due to screening. In fact if, starting form infinity, one would be able to go closer and closer to the electron, one would observe a larger and larger negative charge. One can show that if one wishes to keep the observed charge (the one observed from infinite distance) finite then the charge one would observe at zero distance from the electron (the so-called bare charge), when all the layers of screening are peeled away, would have to be infinitely large negative. Conversely, chosing the "bare charge" to be infinite one can build up a scheme of systematic calculations that can in principle performed to arbitrary precision. Calculations performed following the method of Tomonaga, Schwinger, Feynman and Dyson had a tremendous success in explaining experiments of ultimate precision, such as the anomalous magnetic moment of electrons and the Lamb shift.
After the discovery of pions, other elementary particles were discovered. Pions, or p-mesons, are unstable. That is why we do not see them under normal circumstances. The lifetime of p+ ( or p- ) mesons is not very short, by elementary particle standards, t = 2.6 x 10-8 s. That means, that relativistic p+ mesons can fly to a distance of hundreds of meters in the laboratory, if we take into the effect of time dilation. In fact, these days pion beams are produced from targets at accelerators provide an everyday experimental tool.
p+ -mesons decay into m+ mesons and neutrinos, p+ -> m+ + n. m+ are of course lighter than p+, but they are not strongly interacting, only electromagnetically (they are charged!) therefore they penetrate matter readily, they can traverse thick steel slabs without interactions. This property is used for their identification. In general, when elementary particles are studies it is extremely important to identify as many of the produced particles as possible. This helps understanding the basic laws of nature. The antiparticles of p+ mesons are p--mesons, they decay into p- -> m- + ncm (where this latter is a muon antineutrino, as distinguished form a muon neutrino, or an electron neutrino). Muons, or m-mesons, behave much the same way as electrons (or positrons). They only have electromagnetic and weak (like beta decay) interactions. Only their mass (106 MeV/c2) distinguishes them from electrons. It is still not understood why nature needs to duplicate electrons in this fashion. Along with nm they carry an additive quantum number, muon number that has been observed to conserve in all interactions. The electron number carried by electrons and electron neutrinos is also conserved (positrons and antineutrinos carry electron number +1). The muons decay as
m+ -> e+ + nm + ne
in about 10-6s. Muons and electrons, with their respective neutrinos are called leptons.
After the discovery of pions by Lattes, Occhialini, and Powell other particles were discovered in rapid pace. First, it was observed that near the collisions particle pairs, in the form of a narrow V diracted toward the collision center, seemed to emerge from nothing. This was immediately interpreted as the decay of a hitherto unknown neutral particle into two positive particles. These V-events were later identified as the decay of K-mesons and hyperons. While K-mesons (m= 494 MeV/c2) are similar to p -mesons, they do not carry a nucleon number, hyperons are different (The lightest hyperon is the L0 hyperon of m=1116 MeV/c2). This is shown by their decays:
K+ -> p+ + p0,
L0 -> p + p-, or n + p0
As if a hyperon would have nucleon inside, as this is already indicated by its large mass. Thus, we need to expand the notion of nucleon number to baryon number (baryos=heavy in greek). Nucleons and hyperons are baryons and it is not the nucleon number, A, that is conserved but the baryon number (B). This is clearly shown in production processes. Hyperons, just like nucleons, have s=1/2, while pions and kaons are s=0 bosons. As physicists learned how to build accelerators they succeeded in creating beams of various particles (by separating the products of p-p collisions by poweful magnets). Then they observed reactions as (that is a strong interaction with large cross section as 30 mb)
p+ + n -> L0 + K+
Obviously in the above process baryon number is conserved but nucleon number is not. It was remarkable that reactions like
p+ + n -> L0 + p +
were never observed. This required the introduction of a new quantum number, strangeness, by Gell-Mann and Pais, such that S( L0) = -1, S( K+) =1. At the same time in decay processes such as K-decay or hyperon decay strangeness was not conserved. This was the first case that some quantum numbers were conserved in strong interactions and electromagnetic interactions, but not in weak interactions. These are very well distinguishable, the characteristic reaction time of one is 10-23 s while for the other 10-10 s. Other hyperons were also discovered soon, S+, S-, and S0 hyperons that all had S=-1 (of course their antiparticles have S=+1), the X- and X0 hyperons that have S=-2. All these hyperon have B=1, just like the proton and the neutron, say B( X0) =1. Thus X0 is produced in a reaction like
K- + p -> X- + K+
Note that in this reaction both B ans S are conserved. Hyperons are all unstable, after a characteristic time of about 10-10 s they decay into nucleons and mesons or leptons. Example:
X- -> L0 + p - or L0 + m - + nm.
In decay processes (weak interactions) the strangeness can only change by only one unit. Note the second of these decay processes, it is just like beta decay. Even more similar to beta decay are two modes of L0 decay (they happen very rarely)
L0 -> p + e- + ne
L0 -> p + m - + nm
There are other additive quantum numbers, called flavors that are similar to strangeness and are also conserved in strong interactions. We will discuss them later.
Another important quantum number conserved in strong intreractions is isotopic spin. It has an important role in nuclear physics, as well. It was noticed very early that just like nucleons (p,n) all strongly interactive particles come in multiplets having equal, or almost equal mass. Examples are ( p -, p0, p +), ( K+, K0), L0 (alone), (S+, S0, S-), ( X-, X0), ... These multiplets (singulet, doublet, triplet,...) have the important property that their members have the same spin, baryon number, strangeness, and approximate mass. They have identical strong interactions. Apart from their small mass differences they are distinguished by their charge (and consequently electromagnetic interactions). In this respect they are very similar to a system with a fixed spin that can have states with different spin projections. E.g. we have a s=1 system that can have sz= -1,0, and 1. Pions, having three charge states have I = 1, so they can have I3 = -1,0 and 1, corresponding to the states of p -, p0, and p +. Experiments showed that isotopic spin is conserved in all strong interactions. E.g. in the collision of a p + and a p the total I can either be I=1/2 or I=3/2. Then the final state products must also have either I=1/2 or I=3/2.
Nucleons have isotopic spin I=1/2, since they have 2I+1 = 2 charge states, p and n. Then isotopic spin is very relevant for nuclear physics, because nuclear physics is mostly a study of strong interactions. Then combining two nucleons can lead to I=0, or 1. The only two nucleon state is d. Then d has I=0. Nuclear forces depend strongly on isospin there are no nn or pp bound states. One could explain away the state pp by invoking the Coulomb repulsion, but there is no other good reason to forbid the nn state.
Since the introduction of isotopic spin is the recognition that p and n are just two charge states of the same particle, the Pauli exclusion principle should also be applied to them. Investigate the d from the point of view of antisymmetry of the two nucleons. The p and the n, being in I=0 state, is antisymmatric for the exchange of the p and n. (remember that s=1 is a symmetric state and s=0 is an antisymetric state). Then their wave function must be symmetric in spin, because the overall wavefunction must be antisymmetric for fermions. If the spin wavefunction is symmetric then the spin must be s=1. Indeed, the s(d)=1.
If one goes to heavier nuclei, then it is obvious that the pair (32He, 31H) forms an isodoublet. Their collision with d can only produce an I=1/2 state in strong interactions. So
d + 32He -> 42He + p
happens because I( 42He) =0. Electromagnetic interactions violate I conservation, though I3 is still conserved.
After the discovery of mesons and hyperons experimentalists found a large number of excited states of these particles as well. The typical example of these resonances is the D particle that has four charge states (isotopic spin, I=3/2) D++, D+ , D0, and D-. This resonance was found by Fermi in an experiment in which he bombarded protons (hydrogen) by a newly created p-meson been at the Bevatron accelerator in Berkeley. The reaction he observed was
p- + p -> D0 -> p- + p
Now the intermediate state, D0 is of extremely short lifetime. In fact, t ~ 10-23 s. Direct observation of such a particle is impossible. The uncertainty relation between time and energy, however, implies that the energy of the D is uncertain to about 100 MeV. The p- p cross section increases when the total energy-momentum squared E2 = (Ep + Ep)2- c2 (pp + pp)2 = mD2 c4 This is so because there is a new channel throgh which the scattering can happen. Due to the uncertainty of mD, d mD~ hbar / ( c2 t ), the maximum in the p- p cross section is not sharp, but smeared over a region of about 100Mev in the primary energy of p-. Thus, if we plot the cross section as a function of the energy of the pion (performing the experiment at a series of different energies) then we will see a large bump at E2 = mD2 c4. The width of the bump provides the lifetime of the D particle. This particle is a baryon if you require baryon number conservation. It also turns out that the spin of this particle is s=3/2. The mass of D is mD=1232 MeV/ c2
As time went by many more particle resonances were discovered. These resonances can be regarded as new particles on their own right. They just happen to have large enough masses so that conservation laws allow them to decay via strong interactions into strongly interacting particles. That is the reason why their lifetime are so short. As an example the mass of D happens to satisfy mD > mp + mp so D is allowed to decay into p + p. After literally hundeds of resonances with exactly the same quantum numbers as some other particles were discovered the situation became untenable. This looked more or more as the a system of states with the excitations of the same system, like an atom or a nucleus. The existence of such excitations is a sure sign of composite nature. Clearly atoms and nuclei are composite. This gave the idea to Nambu and Gell-Mann to postulate the existence of constituents for strongly interacting particles: quarks.
The most economic choice (due to Gell-Mann) turned out to be very strange: All normal and strange strongly interacting particles in every charge mode can be constructed out of three quarks, and their antiparticles (antiquarks). The three quarks are u (up), d (down), and s (strange) quarks. Their charge are not integer times e.
|
quark |
charge |
spin |
Baryon number |
Strangeness |
Isotopic spin |
I3 |
|
u |
2/3 e |
1/2 |
1/3 |
0 |
1/2 |
1/2 |
|
d |
-1/3 e |
1/2 |
1/3 |
0 |
1/2 |
-1/2 |
|
s |
- 1/3 e |
1/2 |
1/3 |
-1 |
0 |
0 |
If one uses these quantum numbers then all states known at that time could be built from the combination of these quarks. Examples: p- = d uc (where I denote antiparticles by superscript c. Ususal notation is a bar above the u, or d, or s), p=uud, n=udd, D++=uuu, K-=suc, L0 = sdu, etc. Note that one gets the right spins and isotopic spins as well. Baryons, made of three quarks, must be fermions. In the ground state (zero orbital momentum) they must have spins of s=1/2 or s=3/2. Indeed the nucleons have s=1/2 and the D baryons have s=3/2. Since both of these states are made of three I=1/2 quarks (u and d) their isospin must be 1/2 or 3/2 as well. Of course, we know that I(N) = 1/2 and I(D)=3/2, because they have 2 and four charge states respectively. Anyway, the existence of D++ demands I=3/2, because I3 is an additive quantum number and D++ =uuu. Each u has I3 = 1/2 so the total I3=3/2. But in that case I cannot be smaller than I=3/2. Similarly, S+ = uus, so, since I(s) = 0, it must have I=1. Indeed it has three charge states. Finally, the starngeness of X S(X) = -2 so it must contain 2 strange quarks. Concequently, X- = ssd, X0 = ssu, they have isospin I( X) =1/2 , because they contain one I=1/2 quark (u or d) and two I=0 quarks (s). The above list conatins all ground states of baryons constructed from the three quarks u, d , and s, except sss. This state was predicted by Gell-Mann and subsequently discovered and was called W-.
After the identification of the ground state baryons the previously discovered resonances of higher mass and frequently higher spin were also identified as excited states of these meson and baryon states, with nonzero orbital angular momenta between quarks. Subsequently, heavier and heavier states were investigated, mostly in e+ - e- colliders. On theoretical grounds, the existence of another quark, the charmed quark was predicted. c- anti c bound states were found as tremendously high peaks in the e+ - e- cross sections near total energy (in the CMS) 3 GeV. These peaks were very narrow O(100 keV), which cannot be explained any other way but by the interpretation that such a new state, so called charmonium was produced (Richter and Ting got the Nobel prize for the discovery). The fact is that the decay is from strongly interacting particles to strongly interacting particles should be much faster (i.e. have larger width). QCD, the theory of strong interactions, that will be discussed in the next section can explain it why this decay rate so small. While the u d and s quarks are light, M(c) ~ 1.5 GeV/c2
Subsequently, and unexpectedly, two more quarks, b (bottom) and t (top) (other two Nobel prizes) were discovered in similar typ of experiments. Their masses are large M(b) = 5 GeV/c2 and M(t) = 170 GeV/c2 (as heavy as a A=180 nucleus). Furthermore, a third lepton family was also discovered (also Nobel prize winner), with the t (positive and negative) lepton and corresponding neutrino. There is fairly strong (astrophysical, and accelerator physics) evidence that there are no more quarks or leptons. The known leptons and quarks can be grouped into three families. First family: d, u, e, ne, Second family: s, c, m, nm and the third family: b, t, t, nt. These are listed in order of increasing mass (except possible neutrinos, whose mass is consistent with zero). All ordinary matter, including radioactive decay products are made of the members of the first family. As we see it, the world would not be substantially different if the second and third families would not exist. It is still a mistery why the first family is duplicated twice. The additive quantum numbers distinguishing the six quarks, charge, strangness, char, and the bottom and top quantum numbers are called flavors. They are all conserved in strong and electromagnetic interactions, but with the exception of charge they all can be violated in weak interactions.
There is a substantial problem with the quark assignments of baryons. Take for example the W- hyperon. Its assignment is sss and its spin is s( W-) = 3/2 This spin state is completely symmetric for the exchange of the s quarks (all the three spins are parallel). Consequently the wave function of the W- hyperon is a completely symmetric combination of the wavefunctions of the three s quarks. Similarly the D baryons have isospin I=3/2 and spin I=3/2, both of these states are completely symmetric, i.e the three quark wavefunctions are completely symmetric. In fact, assuming that the three quark wavefunctions are completely symmetric one can prove that the baryon ground states formed from threee u and d quarks are exactly the observed isospin I=3/2 and spin I=3/2 state ( D) and an I=1/2 and spin I=1/2 state (the nucleons). This is very troublesome because it requires the symmetrizations of wavefuncions in fermions, while according to the Pauli exclusion principle the wavefunctions should be completely antisymmetric.
Now the symmetry properties of wavefunctions and their relation to the bosonic and fermionic nature of particles is a very basic law of physics and should not be violated. This gave a lot of headache to theorists, who finally came up with the right solution. The only way to solve the situation is that the the three s quarks that make up W- , or the three u quarks that make up D++ differ in an additional, hitherto unknown, quantum number, so they can be antisymmetrized in that quantum number. Gell-Mann called this quantum number color (he also named quarks). Thus there are three colors: say red, blue, and yellow and then the wavefunctions of the three quarks inside the baryon can be completely antisymmetrized in color, requiring that the three quarks are completely symmetrized in the remainging quantum numbers, such as spin and isospin. One can show using group theory, that such an antisymmetric combination of color states is "colorless" does not have any color quantum numbers. In a similar way mesons are constructed by equal combination red-antired, blue-antiblu, and yellow-antiyellow quarks, that is also a colorless state. Furthermore, one can see that the baryon and meson states of this kinds are the only colorless states one can construct from three quarks and a quark antiquark pair respectively. Since free quarks have never been seen in nature the challange is to construct a theory of quarks that allows the existence of colorless physical states constructed from quarks only. Such a theory is quantum chromodynamics (QCD).
Quantum chromodynamics is built based on the analogy of Quantum electrodynamics, the theory of interaction of photons with charged particles. The strength of electromagnetic interactions is given by e. In field theory , so a similar "strong coupling constant," g, is defined. Since g is much larger than e, strong interactions are stronger than electromagnetic interactions. The role of photons is to generate interactions among charged particles. There should be particles call gluons, that create interactions among particles that have the color quantum number. The difference is that while there is only one kind of a conserved charge in electromagnetism, in QCD there are three colors to play a similar role. Accordingly, there are much more kinds of gluons (eight) that communicate interactions among objects having color quantum numbers. While in Quantum electrodynamics an photon can turn into an electron positron pair, gluons can turn into quark-antiquark pairs. So there is one gluon that can turn into a blue-antired quark pair, etc. The great difference is that while photons themselves are not charged (the total charge of the electron positron pair is zero), gluons themselves carry color. Since photons interact with charged objects only, tnot being charged, they do not directly interact with each other. At the same time gluons, carrying color charges do have direct interactions with each other.
The fact that gluons interact directly with each other has far reaching consequences in strong interactions. Remember, that the vacuum screening of charges gets stronger and stronger as one goes farther and farther away from the electron. The consequence is that the effective charge is decreasing with distance. Alternatively, using the uncertainty relation that says that large distance corresponds to low energy and short distance corresponds to high energy. The one can show that the effective charge has an energy dependence, i.e. at low energies a lower effective charge can be used in calculations (of cross sections, decay rates, etc.), but that increases at high energies the effective charge is larger. Now in QCD, due to the self interaction of gluons the screening situation is entirely different. The gluons that pop out from the vacuum generate antisceening, because the like color charges and anticharges repel each other. The end result is that at large distances (or at low momentum) the effective color charge (g) increases, while at short distances (high momentum) the effective color charge, g decreases. One can also show that in the limit of of infinite momentum (or energy) the effective charge vanishes. This property is called asymptotic freedom.
If the effective charge is very small at high energies then the basic calculational method of field theory of expansion in a power series of charge works very well. Indeed very highenergy experiments confirm this they agree completely with the predictions of QCD, though the precision is far less than the experimental agreement with predictions of QED. At low energies the effective charge is large and the calculations break down. The only results at low energies are from crude numerical symulations that confirm the property of confinement: all states that carry a color quantum number (single quark, single gluon, diquark) are non existent in the free form, quarks and gluons are permanently confined inside mesons and baryons.
The picture of strongly interactive particles is then the following: If we bombard a proton with very high energy probes then it behaves as a collection of three free quarks. This can be clearly seen in experiements. The very high energy probes (think of the uncertainty relation again) probe the proton at very short distances. So if the quarks are close they interact very little. Then when we try to separate them their interaction is getting stronger. When they are at a larger distance, the attractive energy between themm increases proportionally to the distance. To separate them to infinite distance we must supply infinite energy. Thus, they are permanently confined inside mesons and baryons.
If quarks are never seen in nature in the free form the question can be raised whether they exist at all or they are some kind of a mathematical concept only, a mnemonic that tells you how to construct elementary particles. There is extensive evidence for the existence of quarks. I just mention two experiments. One is the bombardment of protons by very high energy electrons. Electrons do not participate in strong interactions, only in electromagnetic and weak interactions. Negelecting weak interactions, the scattering is purely electromagnetic. At very high energy the proton looks like a collection of free quarks. Scattering on free quarks can be easily calculated (something like Rutherford scattering) and the calculated cross sections agree precisely with the experimentally observed ones. More direct and specttacular evidence comes from high energy e+ - e- colliders. When these particles collide in th eCMS (which is the laboratory) they create a virtual photon at rest in the laboratory, but having an enormous mass. The photon (if it is not polarized) loses the directionality of the original e+ and e- comlpetely. Then it is spectacular to see that the large number of strongly interacting particles produced and observed in the final state come out in two narrowly focused jets in oppositie direction. Without quarks one would expect a more or less isotropic distribution for these produced particles. Now how do quarks explain the existence of jets? At very high energy quarks interact with the photon (they are charged!) but their strong interactions are "weak" so the only thing that happens is that the virtual photon can decay into quark-antiquark pairs, which, due to energy-momentum conservation fly out in opposite directions with very high momentum. As long as the quarks are not very far from each other they continue to fly and have still weak interactions. When the distance between them is increasing the potential energy also increases and try to stop them. Instead of stopping them virtual quark -antiquark pairs and gluons are produced from the vacuum and join the initial quarks in a way that they become colorless object that are now free to go out to infinite distance. Since this happens after the original quarks were produced their directionality is conserved and two jets are produced. More precise calculations in QCD confirm this scenario. There is no other known theory that could produce jets as QCD does.