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 [link]. 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 π0 size 12{π rSup { size 8{0} } } {} is its own antiparticle and has a half-life about 10−8 size 12{"10" rSup { size 8{ - 8} } } {} shorter than π+ size 12{π rSup { size 8{+{}} } } {} and π− size 12{π rSup { size 8{ - {}} } } {}, 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.

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.

[link] 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=0, 1, 2, ... size 12{s=0,`1,`2,` "." "." "." } {}), whereas a fermion is a particle with a half-integer value of intrinsic spin (s=1/2,3/2,... size 12{s=1/2,`3/2,` "." "." "." } {}). Fermions obey the Pauli exclusion principle whereas bosons do not. All the known and conjectured carrier particles are bosons.

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.Selected Particle Characteristics

The lower of the ∓ size 12{ -+ {}} {} or ± size 12{ +- {}} {} symbols are the values for antiparticles.

Category	Particle name	Symbol	Antiparticle	Rest mass ( MeV / c 2 )	B	L e	L μ	L τ size 12{L rSub { size 8{τ} } } {}	S size 12{S} {}	Lifetime Lifetimes are traditionally given as t1/2/0.693 (which is 1/λ size 12{ {1} slash {λ} } {}, the inverse of the decay constant). (s)
Gauge	Photon	γ size 12{γ} {}	Self	0	0	0	0	0	0	Stable
Bosons	W size 12{W} {}	W + size 12{W rSup { size 8{+{}} } } {}	W − size 12{W rSup { size 8{ - {}} } } {}	80 . 39 × 10 3 size 12{"80" "." "22" times "10" rSup { size 8{3} } } {}	0	0	0	0	0	1.6 × 10 − 25 size 12{3 times "10" rSup { size 8{ - "25"} } } {}
Z size 12{Z} {}	Z 0 size 12{Z rSup { size 8{0} } } {}	Self	91 . 19 × 10 3 size 12{"91" "." "19" times "10" rSup { size 8{3} } } {}	0	0	0	0	0	1.32 × 10 − 25 size 12{3 times "10" rSup { size 8{ - "25"} } } {}
Leptons	Electron	e − size 12{e rSup { size 8{ - {}} } } {}	e + size 12{e rSup { size 8{ - {}} } } {}	0.511	0	± 1 size 12{ +- 1} {}	0	0	0	Stable
Neutrino (e)	ν e size 12{e rSup { size 8{ - {}} } } {}	v ¯ e size 12{ { bar {v}} rSub { size 8{e} } } {}	0 7 . 0 eV size 12{0` left (<7 "." 0`"eV" right )} {} Neutrino masses may be zero. Experimental upper limits are given in parentheses.	0	± 1 size 12{ +- 1} {}	0	0	0	Stable
Muon	μ − size 12{μ rSup { size 8{ - {}} } } {}	μ + size 12{μ rSup { size 8{+{}} } } {}	105.7	0	0	± 1 size 12{ +- 1} {}	0	0	2 . 20 × 10 − 6 size 12{2 "." "20" times "10" rSup { size 8{ - 6} } } {}
Neutrino (μ size 12{μ} {})	v μ size 12{v rSub { size 8{μ} } } {}	v - μ size 12{v rSub { size 8{μ} } } {}	0 ( < 0.27 )	0	0	± 1 size 12{ +- 1} {}	0	0	Stable
Tau	τ − size 12{τ rSup { size 8{ - {}} } } {}	τ + size 12{τ rSup { size 8{+{}} } } {}	1777	0	0	0	± 1 size 12{ +- 1} {}	0	2 . 91 × 10 − 13 size 12{2 "." "29" times "10" rSup { size 8{ - "13"} } } {}
Neutrino (τ size 12{τ} {})	v τ size 12{v rSub { size 8{τ} } } {}	v - τ size 12{ { bar {v}} rSub { size 8{τ} } } {}	0 ( < 31 )	0	0	0	± 1 size 12{ +- 1} {}	0	Stable
Hadrons (selected)
Mesons	Pion	π + size 12{π rSup { size 8{+{}} } } {}	π − size 12{π rSup { size 8{ - {}} } } {}	139.6	0	0	0	0	0	2.60 × 10 −8
π 0 size 12{π rSup { size 8{0} } } {}	Self	135.0	0	0	0	0	0	8.4 × 10 −17
Kaon	K + size 12{K rSup { size 8{+{}} } } {}	K − size 12{K rSup { size 8{ - {}} } } {}	493.7	0	0	0	0	± 1 size 12{ +- 1} {}	1.24 × 10 −8
K 0 size 12{K rSup { size 8{0} } } {}	K - 0 size 12{ { bar {K}} rSup { size 8{0} } } {}	497.6	0	0	0	0	± 1 size 12{ +- 1} {}	0.90 × 10 −10
Eta	η 0 size 12{η rSup { size 8{0} } } {}	Self	547.9	0	0	0	0	0	2.53 × 10 −19
(many other mesons known)
Baryons	Proton	p size 12{p} {}	p - size 12{ { bar {p}}} {}	938.3	± 1	0	0	0	0	Stable Experimental lower limit is >5×1032 size 12{>5 times "10" rSup { size 8{"32"} } } {} for proposed mode of decay.
Neutron	n size 12{n} {}	n - size 12{ { bar {n}}} {}	939.6	± 1	0	0	0	0	882
Lambda	Λ 0 size 12{Λ rSup { size 8{0} } } {}	Λ - 0 size 12{ { bar {Λ}} rSup { size 8{0} } } {}	1115.7	± 1	0	0	0	∓ 1 size 12{ -+ 1} {}	2.63 × 10 −10
Sigma	Σ + size 12{Σ rSup { size 8{+{}} } } {}	Σ - − size 12{ { bar {Σ}} rSup { size 8{ - {}} } } {}	1189.4	± 1	0	0	0	∓ 1 size 12{ -+ 1} {}	0.80 × 10 −10
Σ 0 size 12{Σ rSup { size 8{0} } } {}	Σ - 0 size 12{ { bar {Σ}} rSup { size 8{0} } } {}	1192.6	± 1	0	0	0	∓ 1 size 12{ -+ 1} {}	7.4 × 10 −20
Σ − size 12{Σ rSup { size 8{ - {}} } } {}	Σ - + size 12{ { bar {Σ}} rSup { size 8{+{}} } } {}	1197.4	± 1	0	0	0	∓ 1 size 12{ -+ 1} {}	1.48 × 10 −10
Xi	Ξ 0 size 12{Ξ rSup { size 8{0} } } {}	Ξ - 0 size 12{ { bar {Ξ}} rSup { size 8{0} } } {}	1314.9	± 1	0	0	0	∓ 2 size 12{ -+ 2} {}	2.90 × 10 −10
Ξ − size 12{Ξ rSup { size 8{ - {}} } } {}	Ξ + size 12{Ξ rSup { size 8{+{}} } } {}	1321.7	± 1	0	0	0	∓ 2 size 12{ -+ 2} {}	1.64 × 10 −10
Omega	Ω − size 12{ %OMEGA rSup { size 8{ - {}} } } {}	Ω + size 12{ %OMEGA rSup { size 8{+{}} } } {}	1672.5	± 1	0	0	0	∓ 3 size 12{ -+ 3} {}	0.82 × 10 −10
(many other baryons known)

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 10−18m size 12{"10" rSup { size 8{ - "18"} } m} {}. The leptons fall into three families, implying three conservation laws for three quantum numbers. One of these was known from β size 12{β} {} decay, where the existence of the electron’s neutrino implied that a new quantum number, called the electron family number Le size 12{L rSub { size 8{e} } } {} is conserved. Thus, in β size 12{β} {} decay, an antielectron’s neutrino v-e size 12{ { bar {v}} rSub { size 8{e} } } {} must be created with Le=−1 size 12{L rSub { size 8{e} } = - 1} {} when an electron with Le=+1 size 12{L rSub { size 8{e} } "=+"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 vμ size 12{L rSub { size 8{μ} } } {} is a muon’s neutrino, and it is created to conserve muon family numberLμ size 12{L rSub { size 8{μ} } } {}. So muons are leptons with a family of their own, and conservation of total Lμ size 12{L rSub { size 8{μ} } } {} also seems to be obeyed in many experiments.

More recently, a third lepton family was discovered when τ size 12{τ} {} particles were created and observed to decay in a manner similar to muons. One principal decay mode is

Conservation of total Lτ size 12{L rSub { size 8{μ} } } {} 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.

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 size 12{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 size 12{B=0} {} so that they can decay to other particles with B=0 size 12{B=0} {}. But baryons have B=+1 size 12{B"=+"1} {} if they are matter, and B=−1 size 12{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 Be→α+α size 12{"" lSup { size 8{8} } "Be" rightarrow α+α} {} with a lifetime of about 10−16s size 12{"10" rSup { size 8{ - "16"} } `s} {}. The neutron is a good example of decay via the weak force. The process n→p+e−+v-e size 12{n rightarrow p+e rSup { size 8{ - {}} } + { bar {v}} rSub { size 8{e} } } {} has a longer lifetime of 882 s. The weak force causes this decay, as it does all β size 12{β} {} decay. An important clue that the weak force is responsible for β size 12{β} {} decay is the creation of leptons, such as e− size 12{e rSup { size 8{ - {}} } } {} and v-e size 12{ { bar {v}} rSub { size 8{e} } } {}. None would be created if the strong force was responsible, just as no leptons are created in the decay of 8Be size 12{"" lSup { size 8{8} } "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 size 12{"10" rSup { size 8{ - "16"} } } {} to 10−12 size 12{"10" rSup { size 8{ - "12"} } } {} s, whereas those that decay via the strong force have lifetimes mostly in the range of 10−16 size 12{"10" rSup { size 8{ - "16"} } } {} to 10−23 size 12{"10" rSup { size 8{ - "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 Λ,Σ,Ξ size 12{Λ,`Σ,`Ξ} {}, and Ω size 12{ %OMEGA } {} decay with lifetimes on the order of 10−10 size 12{"10" rSup { size 8{ - "10"} } } {} s (the exception is Σ0 size 12{Σ rSup { size 8{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 size 12{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.