Particles, Patterns, and Conservation Laws

The positron was only the first example of antimatter. Every particle in nature has an antimatter counterpart, although some particles, like the photon, are their own antiparticles. Antimatter has charge opposite to that of matter (for example, the positron is positive while the electron is negative) but is nearly identical otherwise, having the same mass, intrinsic spin, half-life, and so on. When a particle and its antimatter counterpart interact, they annihilate one another, usually totally converting their masses to pure energy in the form of photons as seen in Figure 14.13.2. Neutral particles, such as neutrons, have neutral antimatter counterparts, which also annihilate when they interact. Certain neutral particles are their own antiparticle and live correspondingly short lives. For example, the neutral pion ${\pi }^0$ is its own antiparticle and has a half-life about ${\text{10}}^{-8}$ shorter than ${\pi }^{+}$ and ${\pi }^{-}$, which are each other’s antiparticles. Without exception, nature is symmetric—all particles have antimatter counterparts. For example, antiprotons and antineutrons were first observed in accelerator experiments in 1955 and 1956, respectively and the antiproton is negative. Antihydrogen atoms, consisting of an antiproton and antielectron, were observed in 1995 at CERN, too. Antiprotons can be stored in electromagnetic traps that use electric and magnetic fields to keep them away from ordinary matter. Repulsion between the trapped antiprotons limits how densely they can be confined for given trapping fields. Maintaining the required vacuum, low temperatures, and stable confinement presents substantial technical challenges, so storing macroscopic quantities remains impractical. At any rate, we now see that negative charge is associated with both low-mass (electrons) and high-mass particles (antiprotons) and the apparent asymmetry is not there. This raises a deeper question: why does the observable universe contain so much more matter than antimatter? The origin of this imbalance remains an open problem in physics, beyond the scope of this textbook.

Particles can also be revealingly grouped according to what forces they feel between them. All particles (even those that are massless) are affected by gravity, since gravity affects the space and time in which particles exist. All charged particles are affected by the electromagnetic force, as are neutral particles that have an internal distribution of charge (such as the neutron with its magnetic moment). Hadrons are composite particles whose constituents are bound by the strong interaction. Protons, neutrons, and pions are examples. Leptons are elementary particles that do not participate in the strong interaction; examples include electrons, muons, neutrinos, and their antiparticles. Both hadrons and leptons participate in weak interactions, so the weak interaction does not distinguish these two groups.

Table 14.13.1 lists the characteristics of some of the most important subatomic particles, including the directly observed carrier particles for the electromagnetic and weak nuclear forces, all leptons, and some hadrons. Several hints related to an underlying substructure emerge from an examination of these particle characteristics. The photon, gluons, and W and Z bosons are gauge bosons: the particles associated with the electromagnetic, strong, and weak interactions in the Standard Model. The hypothetical graviton is discussed separately as a proposed carrier of gravity. A boson is a particle with an integer value of intrinsic spin (such as $s=\mathrm{0,\; 1,\; 2,\; ...}$), whereas a fermion is a particle with a half-integer value of intrinsic spin ($s=1/\mathrm{2,}3/\mathrm{2,}\text{.}\text{.}\text{.}$). Fermions obey the Pauli exclusion principle whereas bosons do not. All the known and conjectured carrier particles are bosons.

All known leptons are listed in the table given above. There are only six leptons (and their antiparticles), and they seem to be fundamental in that they have no apparent underlying structure. Leptons have no discernible size other than their wavelength, so that we know they are pointlike down to about ${10}^{-18}\text{m}$. Leptons occur in electron, muon, and tau families. For each family, assign +1 to its charged lepton and neutrino, −1 to their antiparticles, and zero to other particles. Adding these values gives the corresponding family number, $L_e$, $L_{\mu }$, or $L_{\tau }$. The decay reactions considered here conserve each family number: the total before the reaction equals the total afterward. One of these was known from $\beta$ decay, where the existence of the electron neutrino implied that a new quantum number, called the electron family number $L_e$ is conserved in these beta-decay reactions. Thus, in $\beta$ decay, an electron antineutrino ${\overline{\nu }}_e$ must be created with $L_e=-1$ when an electron with $L_e=+1$ is created, so that the total remains zero as it was before decay.

Once the muon was discovered in cosmic rays, its decay mode was found to be

which illustrates the muon family and its associated muon family number $L_{\mu }$. The muon neutrino in this decay balances the muon family number carried by the initial muon, so the total is the same before and after the decay.

More recently, a third lepton family was discovered when $\tau$ particles were created and observed to decay in a manner similar to muons. One principal decay mode is

These family numbers are useful for analyzing the decay reactions shown here. However, they are not universally conserved: neutrino oscillations change the flavor composition of a neutrino as it propagates.

Now, note that the hadrons in the table given above are divided into two subgroups, called mesons (originally for medium mass) and baryons (the name derives from the Greek for “heavy”). The distinction between these groups reflects their internal structure, which we will discuss later in this section, rather than their masses. Their observed decay patterns helped physicists recognize the distinction. Mesons can decay entirely into particles that are not hadrons, so the number of mesons need not be conserved. In observed decays of unstable baryons, the products include another baryon. These patterns illustrate the conservation rule introduced below. A new physical quantity called baryon number $B$ seems to always be conserved in nature and is listed for the various particles in the table given above. Mesons and leptons have $B=0$ so that they can decay to other particles with $B=0$. But baryons have $B=+1$ if they are matter, and $B=-1$ if they are antimatter. The conservation of total baryon number is a more general rule than first noted in nuclear physics, where it was observed that the total number of nucleons was always conserved in nuclear reactions and decays. That rule in nuclear physics is just one consequence of the conservation of the total baryon number.

The forces that act between particles regulate how they interact with other particles. For example, pions feel the strong force and do not penetrate as far in matter as do muons, which do not feel the strong force. (This was the way those who discovered the muon knew it could not be the particle that carries the strong force—its penetration or range was too great for it to be feeling the strong force.) Similarly, reactions that create other particles, like cosmic rays interacting with nuclei in the atmosphere, have greater probability if they are caused by the strong force than if they are caused by the weak force. Such knowledge has been useful to physicists while analyzing the particles produced by various accelerators.

The forces experienced by particles also govern how particles interact with themselves if they are unstable and decay. For example, the stronger the force, the faster they decay and the shorter is their lifetime. An example of a nuclear decay via the strong force is ${}^8\text{Be}\to \alpha +\alpha$ with a lifetime of about ${10}^{-16}\text{s}$. The neutron is a good example of decay via the weak force. The process $n\to p+e^{-}+{\overline{\nu }}_e$ has a longer lifetime of 882 s. The weak force causes this decay, as it does all $\beta$ decay. An important clue that the weak force is responsible for $\beta$ decay is the creation of leptons, such as $e^{-}$ and ${\overline{\nu }}_e$. None would be created if the strong force was responsible, just as no leptons are created in the decay of ${}^8\text{Be}$. The systematics of particle lifetimes is a little simpler than nuclear lifetimes when hundreds of particles are examined (not just the ones in the table given above). Particles that decay via the weak force have lifetimes mostly in the range of ${10}^{-16}$ to ${10}^{-12}$ s, whereas those that decay via the strong force have lifetimes mostly in the range of ${10}^{-16}$ to ${10}^{-23}$ s. Turning this around, if we measure the lifetime of a particle, we can tell if it decays via the weak or strong force.

Some hadrons are readily produced through strong interactions but decay much more slowly through the weak interaction. This unexpected behavior led physicists to introduce a quantum number called strangeness, denoted by $S$. Total strangeness is conserved in strong and electromagnetic interactions but can change in weak interactions. Consequently, a decay that changes strangeness must proceed through the weak interaction. These conservation rules helped explain the observed patterns of particle production and decay.

A memorable maxim associated with Murray Gell-Mann captures the search for such rules: “Everything not forbidden is compulsory.” In particle physics, this is a useful guide: a process permitted by the relevant conservation laws may occur, although its probability can be extremely small. A process that has not been observed might therefore be forbidden—or simply too rare for experiments to have detected it.

There are hundreds of particles, all hadrons, not listed in Table 14.13.1, most of which have shorter lifetimes. The systematics of those particle lifetimes, their production probabilities, and decay products are completely consistent with the conservation laws noted for lepton families, baryon number, and strangeness, but they also imply other quantum numbers and conservation laws. There are a finite, and in fact relatively small, number of these conserved quantities, however, implying a finite set of substructures. Additionally, some of these short-lived particles resemble the excited states of other particles, implying an internal structure. All of this jigsaw puzzle can be tied together and explained relatively simply by the existence of fundamental substructures. Leptons seem to be fundamental structures. Hadrons seem to have a substructure called quarks. We have so far discovered six quarks in three generations: up and down quarks, charm and strange quarks, and top and bottom quarks.

The quark model explains the distinction between the two groups of hadrons introduced earlier. In the simplest quark model, mesons are bound states of a quark and an antiquark, while baryons are bound states of three quarks. Antibaryons consist of three antiquarks. Pions and kaons are examples of mesons; protons and neutrons are examples of baryons.

In the quark model, each quark has baryon number +1/3 and each antiquark has baryon number −1/3. A three-quark baryon therefore has baryon number +1, an antibaryon has −1, and a quark–antiquark meson has zero.

The quark model gives strangeness a simple interpretation: each strange quark contributes −1, and each strange antiquark contributes +1. Other quarks contribute zero. Thus, a particle’s strangeness is the number of strange antiquarks minus the number of strange quarks it contains.