33.4 Particles, Patterns, and Conservation Laws

Matter and Antimatter

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 33.13. 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 created in accelerator experiments in 1956 and the antiproton is negative. Antihydrogen atoms, consisting of an antiproton and antielectron, were observed in 1995 at CERN, too. It is possible to contain large-scale antimatter particles such as antiprotons by using electromagnetic traps that confine the particles within a magnetic field so that they don't annihilate with other particles. However, particles of the same charge repel each other, so the more particles that are contained in a trap, the more energy is needed to power the magnetic field that contains them. It is not currently possible to store a significant quantity of antiprotons. 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. But this knowledge does raise another question—why is there such a predominance of matter and so little antimatter? Possible explanations emerge later in this and the next chapter.

Hadrons and Leptons

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). Special names are given to particles that feel the strong and weak nuclear forces. Hadrons are particles that feel the strong nuclear force, whereas leptons are particles that do not. The proton, neutron, and the pions are examples of hadrons. The electron, positron, muons, and neutrinos are examples of leptons, the name meaning low mass. Leptons feel the weak nuclear force. In fact, all particles feel the weak nuclear force. This means that hadrons are distinguished by being able to feel both the strong and weak nuclear forces.

Table 33.2 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. Note that the carrier particles are called gauge bosons. First mentioned in Patterns in Spectra Reveal More Quantization, a boson is a particle with zero or 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.

Figure 33.13 When a particle encounters its antiparticle, they annihilate, often producing pure energy in the form of photons. In this case, an electron and a positron convert all their mass into two identical energy rays, which move away in opposite directions to keep total momentum zero as it was before. Similar annihilations occur for other combinations of a particle with its antiparticle, sometimes producing more particles while obeying all conservation laws.

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 ${\text{10}}^{-\text{18}}\text{m}$. The leptons fall into three families, implying three conservation laws for three quantum numbers. One of these was known from $\beta$ decay, where the existence of the electron’s neutrino implied that a new quantum number, called the electron family number $L_e$ is conserved. Thus, in $\beta$ decay, an antielectron’s neutrino ${\stackrel{-}{v}}_e$ must be created with $L_e=-1$ when an electron with $L_e\text{=+}1$ is created, so that the total remains 0 as it was before decay.

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

which implied another “family” and associated conservation principle. The particle $v_{\mu }$ is a muon’s neutrino, and it is created to conserve muon family number$L_{\mu }$. So muons are leptons with a family of their own, and conservation of total $L_{\mu }$ also seems to be obeyed in many experiments.

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

Conservation of total $L_{\tau }$ seems to be another law obeyed in many experiments. In fact, particle experiments have found that lepton family number is not universally conserved, due to neutrino “oscillations,” or transformations of neutrinos from one family type to another.

Mesons and Baryons

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 originally meaning large mass). The division between mesons and baryons is actually based on their observed decay modes and is not strictly associated with their masses. Mesons are hadrons that can decay to leptons and leave no hadrons, which implies that mesons are not conserved in number. Baryons are hadrons that always decay to another baryon. 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 $B\text{=+}1$ 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.

Forces, Reactions, and Reaction Rates

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 ${\text{10}}^{-\text{16}}\text{s}$. The neutron is a good example of decay via the weak force. The process $n\to p+e^{-}+{\stackrel{-}{v}}_e$ 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 ${\stackrel{-}{v}}_e$. 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 ${\text{10}}^{-\text{16}}$ to ${\text{10}}^{-\text{12}}$ s, whereas those that decay via the strong force have lifetimes mostly in the range of ${\text{10}}^{-\text{16}}$ to ${\text{10}}^{-\text{23}}$ s. Turning this around, if we measure the lifetime of a particle, we can tell if it decays via the weak or strong force.

Yet another quantum number emerges from decay lifetimes and patterns. Note that the particles $\text{Λ}\text{,}\text{Σ}\text{,}\text{Ξ}$, and $\Omega$ decay with lifetimes on the order of ${\text{10}}^{-\text{10}}$ s (the exception is ${\text{Σ}}^0$, whose short lifetime is explained by its particular quark substructure.), implying that their decay is caused by the weak force alone, although they are hadrons and feel the strong force. The decay modes of these particles also show patterns—in particular, certain decays that should be possible within all the known conservation laws do not occur. Whenever something is possible in physics, it will happen. If something does not happen, it is forbidden by a rule. All this seemed strange to those studying these particles when they were first discovered, so they named a new quantum number strangeness, given the symbol $S$ in the table given above. The values of strangeness assigned to various particles are based on the decay systematics. It is found that strangeness is conserved by the strong force, which governs the production of most of these particles in accelerator experiments. However, strangeness is not conserved by the weak force. This conclusion is reached from the fact that particles that have long lifetimes decay via the weak force and do not conserve strangeness. All of this also has implications for the carrier particles, since they transmit forces and are thus involved in these decays.

There are hundreds of particles, all hadrons, not listed in Table 33.2, 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. Quarks: Is That All There Is? explores the basics of the underlying quark building blocks.

Figure 33.14 Murray Gell-Mann (b. 1929) proposed quarks as a substructure of hadrons in 1963 and was already known for his work on the concept of strangeness. Although quarks have never been directly observed, several predictions of the quark model were quickly confirmed, and their properties explain all known hadron characteristics. Gell-Mann was awarded the Nobel Prize in 1969. (credit: Luboš Motl)