Particle Decays and Annihilations

What is a Decay?

The Standard Model explains why some particles decay into other particles.

In nuclear decay, an atomic nucleus can split into smaller nuclei. This makes sense: a bunch of protons and neutrons divide into smaller bunches of protons and neutrons. But the decay of a fundamental particle cannot mean splitting into its constituents, because "fundamental" means it has no constituents. Here, particle decay refers to the transformation of a fundamental particle into other fundamental particles. This type of decay is strange, because the end products are not pieces of the starting particle, but totally new particles.

Nuclear Decay

Particle Decay

In this section we will discuss the types of decay, how they happen, and under what circumstances a decay will or will not happen.

Radioactivity

In the late 1800s the German physicist, Wilhelm Röntgen, discovered a strange new ray produced when an electron beam struck a piece of metal. Since these were rays of an unknown nature, he called them "x rays".

Two months after this discovery, the French physicist, Henri Becquerel, was studying fluorescence, when he found that photographic plates were exposed in the presence of some ores, even when the plates were wrapped in black paper. Becquerel realized that these materials, which included uranium, emitted energetic rays without any energy input.

Becquerel's experiments showed that some natural process must be responsible for certain elements releasing energetic x rays. This suggested that some elements were inherently unstable, because these elements would spontaneously release different forms of energy. This release of energetic particles due to the decay of the unstable nuclei of atoms is called radioactivity.


Radioactive Particles

Scientists eventually identified several distinct types of radiation , the particles resulting from radioactive decays. The three types of radiation were named after the first three letters of the Greek alphabet: (alpha), (beta), and (gamma).

Alpha particles are helium nuclei (2 p, 2 n):

Beta particles are speedy electrons:

Gamma radiation is a high-energy photon:

These three forms of radiation can be distinguished by a magnetic field since

•  the positively-charged alpha particles curve in one direction,

•  the negatively-charged beta particles curve in the opposite direction,

•  and the electrically-neutral gamma radiation doesn't curve at all.

Alpha particles can be stopped by a sheet of paper, beta particles by aluminum, and gamma radiation by a block of lead. Gamma radiation can penetrate very far into a material, and so it is gamma radiation that poses the most danger when working with radioactive materials, although all types of radiation are very dangerous. Sadly, it took scientists many years to realize the perils of radioactivity...  

Confusions about Decays

Many heavy elements decay into simpler things. But a close observation of these decays reveals several confusing problems.

                

Consider uranium-238 decay.

A lump of uranium-238 will decay at a constant rate such that in 4,460,000,000 years -- give or take a few days -- half the uranium will be gone. But there is no way to tell when a specific uranium atom will decay; it could decay five minutes from now, or in ten billion years. Why will an atom decay only according to some probability?

Uranium-238 has a mass of 238.0508 atomic mass units (u). It can decay into thorium (234.0436 u) and an alpha particle (4.0026 u). But uranium's mass minus the mass of its decay products is 0.0046 u. Why is there missing mass?

A Look into the Nucleus

We will answer these questions soon, but first we need to look into the nature of the nucleus and quantum mechanics.

Protons are positive and electrically repel one another. A nucleus would blow apart if it weren't "glued" together by the gluon particles which affect every part of the nucleus. This is called the residual strong force.

Think of a nucleus as a tightly coiled spring which is the electrical repulsion, held in place by a very big rope which is the residual strong force. Even though there is a lot of stored-up energy in the spring, it can't release the energy because the rope is too strong.

 

If It Can Happen, It Will

Subatomic particles do not behave like everyday objects. We can't really say what a particle will do, only what a particle might do. Particles move around like everyday objects and have momentum, but they also have wave properties. Quantum mechanics, the mathematical basis for our theories about particles, explains the behavior of particles in terms of probabilities.

Since particles are wave-like, it is impossible to know both their position and their momenta. While it is easier to think of particles as point-like spheres (which is how we have illustrated them throughout this site) this is misleading since they are better thought of as fuzzy regions in which you are most likely to find the particle.

Protons and neutrons migrate around inside a nucleus. There is a tiny, tiny chance that a conglomeration of two protons and two neutrons (which form an alpha particle) may, at the same instant, actually migrate outside the nucleus. There is a greater chance of this happening in a large nucleus than in a small one.

The alpha particle would then be free of the residual strong force trapping it inside the nucleus, and like a suddenly released spring, the charged alpha particle would fly away from the nucleus.

This idea that "if it can happen, it will happen!" is fundamental to quantum mechanics. For some atoms there is a certain probability that it will undergo radioactive decay due to the possibility that the nucleus may --for the shortest of instants-- exist in a state that allows it to blow apart. You cannot predict when a particular atom will decay, but you can determine the chance that it will decay in a certain period of time.

Half-Life

A lump of uranium left to itself will gradually decay, one nucleus at a time. The rate of decay is measured by how long it would take for half of a given bunch of uranium atoms to decay (the half-life ). The decay of an individual uranium nucleus is completely unpredictable, but we can accurately predict the way a large lump of uranium will decay.

It is upsetting to think that chance can rule physical properties. In response to this theory Einstein proclaimed "God doesn't play dice!" (Einstein was wrong.)

 

Missing Mass

We still need to answer the question, where does the missing mass in a radioactive decay go? Recall that we said that when uranium decays into thorium and an alpha particle, 0.0046 u of mass appears to have been lost.

As Einstein said,

When uranium nuclei undergo radioactive decay, some of their mass is converted into kinetic energy (the energy of the moving particles). This conversion of energy is observed as a loss of mass.

Particle Decay Mediators

While the nucleus of an atom can decay into a less massive nucleus by splitting apart, how does a fundamental particle decay into other fundamental particles? Fundamental particles cannot split apart, because they have no constituents, but rather they somehow turn into other particles.

It turns out that when a fundamental particle decays, it changes into a less massive particle and a force-carrier particle (always a W boson for fundamental particle decays). These force carriers may then re-emerge as other particles. So, a particle does not just change into another particle type; there is an intermediate force-carrier particle which mediates particle decays

In many cases, these temporary force-carrier particles seem to violate the conservation of energy because their mass is greater than the available energy in the reaction. However, these particles exist so briefly that, because of Heisenberg's Uncertainty Principle, no rules are broken. These are called virtual particles. For example, a charm quark (c) decays into a less massive particle (strange quark, s) and a force carrier particle (W boson) which then decays to u and d quarks.

Virtual Particles

Particles decay via force carrier particles. But in some cases a particle may decay via a force-carrier particle with more mass then the initial particle. The intermediate particle is immediately transformed into lower-mass particles. These short-lived high-mass force-carrier particles seem to violate the laws of conservation of energy and mass -- their mass just can't come out of nowhere!

A result of the Heisenberg Uncertainty principle is that these high-mass particles may come into being if they are incredibly short-lived. In a sense, they escape reality's notice. Such particles are called virtual particles .

In 1927, Werner Heisenberg determined that it is impossible to measure both a particle's position and its momentum exactly. The more precisely we determine one, the less we know about the other. This is called the Heisenberg Uncertainty Principle, and it is a fundamental property of quantum mechanics.

The precise relation is:

This constant is Planck's constant divided by two; Planck's constant is represented by the symbol , or "h-bar," and equals 1.05 x 10^-34 joule-seconds, or 6.58 x 10^-22 MeV-seconds.

The act of measuring a particle's position will affect your knowledge of its momentum, and vice-versa. We can also express this principle in terms of energy and time:

This means that if a particle exists for a very brief time, you cannot precisely determine its energy. A short-lived particle could have a tremendously uncertain energy, which leads to the idea of virtual particles .

Virtual particles do not violate the conservation of energy. The kinetic energy plus mass of the initial decaying particle and the final decay products is equal. The virtual particles exist for such a short time that they can never be observed.

Most particle processes are mediated by virtual-carrier particles. Examples include neutron beta decay, the production of charm particles, and the decay of an eta-c particle, all of which we will explore in depth soon.

Different Interactions

Strong, electromagnetic, and weak interactions all cause particle decays. However, only weak interactions can cause the decay of fundamental particles.

Weak Decays:

Only weak interactions can change a fundamental particle into another type of particle. Physicists call particle types "flavors." The weak interaction can change a charm quark into a strange quark while emitting a virtual W boson (charm and strange are flavors). Only the weak interaction (via the W boson) can change flavor and allow the decay of a truly fundamental particle.

Electromagnetic Decays:

The 0 (neutral pion) is a meson. The quark and antiquark can annihilate; from the annihilation come two photons. This is an example of an electromagnetic decay.

Strong Decays:

The particle is a meson. It can undergo a strong decay into two gluons (which emerge as hadrons).

The strong force-carrier particle, the gluon, mediates decays involving color changes. The weak force-carrier particles, W + and W - , mediate decays in which particles change flavor (and electric charge).

Annihilations

Annihilations are of course not decays, but they too occur via virtual particles. In an annihilation a matter and an antimatter particle completely annihilate into energy.

That is, they interact with each other, converting the energy of their previous existence into a very energetic force carrier particle (a gluon, W/Z, or photon). These force carriers, in turn, are transformed into other particles.

Quite often, physicists will annihilate two particles at tremendous energies in order to create new, massive particles.

Bubble Chamber and Decays

This is an actual bubble chamber photograph of an antiproton (entering from the bottom of the picture), colliding with a proton (at rest), and annihilating. Eight pions were produced in this annihilation. One decayed into a + and a . The paths of positive and negative pions curve opposite ways in the magnetic field, and the neutral  leaves no track.

Bubble chambers are an older type of detector. As charged particles pass through a bubble chamber, they leave a trail of tiny bubbles that make it easy to track the particles.

We have talked a lot about decays and annihilations, so let's now look at some examples of these processes.

Neutron Beta Decay

A neutron (udd) decays to a proton (uud), an electron, and an antineutrino. This is called neutron beta decay. (The term beta ray was used for electrons in nuclear decays because they didn't know they were electrons!)

•  Frame 1: The neutron (charge = 0) made of up, down, down quarks.

•  Frame 2: One of the the down quarks is transformed into an up quark. Since the down quark has a charge of -1/3 and and the up quark has a charge of 2/3, it follows that this process is mediated by a virtual W- particle, which carries away a (-1) charge (thus charge is conserved!)

•  Frame 3: The new up quark rebounds away from the emitted W-. The neutron now has become a proton.

•  Frame 4: An electron and antineutrino emerge from the virtual W- boson.

•  Frame 5: The proton, electron, and the antineutrino move away from one another.

The intermediate stages of this process occur in about a billionth of a billionth of a billionth of a second, and are not observable.

Electron/Positron Annihilation

When an electron and positron (antielectron) collide at high energy, they can annihilate to produce charm quarks which then produce D + and D - mesons.

•  Frame 1: The electron and positron zoom towards their certain doom.

•  Frame 2: They collide and annihilate, releasing tremendous amounts of energy.

•  Frame 3: The electron and positron have annihilated into a photon, or a Z particle, both of which may be virtual force carrier particles .

•  Frame 4: A charm quark and a charm antiquark emerge from the virtual force carrier particle.

•  Frame 5: They begin moving apart, stretching the color force field (gluon field) between them.

•  Frame 6: The quarks move apart, further spreading their force field.

•  Frame 7: The energy in the force field increases with the separation between the quarks. When there is sufficient energy in the force field, the energy is converted into a quark and an anti-quark (remember ).

•  Frames 8-10: The quarks separate into distinct, color-neutral particles: the D + (a charm and anti-down quark) and D - (an anti-charm and down quark) mesons.

The intermediate stages of this process occur in about a billionth of a billionth of a billionth of a second, and are not observable.

Top Production

A quark (from within a proton) and an antiquark (from an antiproton) colliding at high energy can annihilate to produce a top quark and a top antiquark, which then decay into other particles.

•  Frame 1: One of the proton's quarks and one of the antiproton's antiquarks are heading toward a collision.

•  Frame 2: The quark and antiquark collide and annihilate....

•  Frame 3: ...into virtual gluons.

•  Frame 4: A top and antitop quark emerge from the gluon cloud.

•  Frame 5: These quarks begin moving apart, stretching the color force field (gluon field) between them.

•  Frame 6: Before the top quark and antiquark have moved very far, they decay into a bottom and antibottom quark (respectively) with the emission of W force carrier particles.

•  Frame 7: The new bottom quark and antibottom quark rebound away from the emitted W force carrier particles.

•  Frame 8: An electron and neutrino emerge from the virtual W - boson, and an up quark and down antiquark emerge from the virtual W + boson.

•  Frame 9: The bottom quark and bottom antiquark, electron, neutrino, up quark, and down antiquark all move away from one another.

What is wrong with this picture?
We ignored the color force field that develops as the b quark and b antiquark move apart. This energy is converted into another quark/antiquark pair; eventually only distinct, color-neutral particles emerge (B mesons). The same is true for the u quark and d antiquark. To see what really happens look at an analogous process in the picture of e+ and e- --> D+ and D-.

The intermediate stages of this process occur in about a billionth of a billionth of a billionth of a second, and are not observable.