Quantum Diaries

Fun post for everyone today. In response to last week’s post on describing KEK Laboratory’s discovery of additional exotic hadrons, I got an absolutely terrific question from a QD reader:

Surprisingly, the answer to “How does an electron-positron collider produce quarks if neither particle contains any?” all begins with the inconspicuous photon.

No Firefox, I Swear “Hadronization” is a Real Word.

As far as the history of quantum physics is concerned, the discovery that all light is fundamentally composed of very small particles called photons is a pretty big deal. The discovery allows us to have a very real and tangible description of how light and electrons actually interact, i.e., through the absorption or emission of photon by electrons.

Figure 1: Feynman diagrams demonstrating how electrons (denoted by e^–) can accelerate (change direction of motion) by (a) absorbing or (b) emitting a photon (denoted by the Greek letter gamma: γ).

The usefulness of recognizing light as being made up many, many photons is kicked up a few notches with the discovery of anti-particles during the 1930s, and in particular the anti-electron, or positron as it is popularly called. In summary, a particle’s anti-particle partner is an identical copy of the particle but all of its charges (like electric, weak, & color!) are the opposite. Consequentially, since positrons (e⁺) are so similar to electrons (e^–) their interactions with light are described just as easily.

Figure 2: Feynman diagrams demonstrating how positrons (e⁺) can accelerate (change direction of motion) by (a) absorbing or (b) emitting a photon (γ). Note: positrons are moving from left to right; the arrow’s direction simply implies that the positron is an anti-particle.

Then came Quantum Electrodynamics, a.k.a. QED, which gives us the rules for flipping, twisting, and combining these diagrams in order to describe all kinds of other real, physical phenomena. Instead of electrons interacting with photons (or positrons with photons), what if we wanted to describe electrons interacting with positrons? Well, one way is if an electron exchanges a photon with a positron.

Figure 3: A Feynman diagram demonstrating the exchange of a photon (γ) between an electrons (e^–)  and a positron (e⁺). Both the electron and positron are traveling from the left to the right. Additionally, not explicitly distinguishing between whether the electron is emitting or absorbing is intentional.

And now for the grand process that is the basis of all particle colliders throughout the entire brief* history of the Universe. According to electrodynamics, there is another way electrons and positrons can both interact with a photon. Namely, an electron and positron can annihilate into a photon and the photon can then pair-produce into a new electron and positron pair!

Figure 4: A Feynman diagram demonstrating  an annihilation of an electrons (e^–)  and a positron (e⁺) into a photon (γ) that then produces an e⁺e^– pair. Note: All particles depicted travel from left to right.

However, electrons and positrons is not the only particle-anti-particle pair that can annihilate into photons, and hence be pair-produced by photons. You also have muons, which are identical to electrons in every way except that it is 200 times heavier than the electron. Given enough energy, a photon can pair-produce a muon and anti-muon just as easily as it can an electron and positron.

Figure 5: A Feynman diagram demonstrating  an annihilation of an electrons (e^–)  and a positron (e⁺) into a photon (γ) that then produces a muon (μ^–) and anti-muon(μ⁺) pair.

But there is no reason why we need to limit ourselves only to particles that have no color charge, i.e., not charged under the Strong nuclear force. Take a bottom-type quark for example. A bottom quark has an electric charge of -1/3 elementary units; a weak (isospin) charge of -1/2; and its color charge can be red, blue, or green. The anti-bottom quark therefore has an electric charge of +1/3 elementary units; a weak (isospin) charge of +1/2; and its color charge can be anti-red, anti-blue, or anti-green. Since the two have non-zero electric charges, it can be pair-produced by a photon, too.

Figure 6: A Feynman diagram demonstrating  an annihilation of an electrons (e^–)  and a positron (e⁺) into a photon (γ) that then produces a bottom quark (b) and anti-bottom quark (b) pair.

On top of that, since the Strong nuclear force is, well, really strong, either the bottom quark or the anti-bottom quark can very easily emit or absorb a gluon!

Figure 7: A Feynman diagram demonstrating  an annihilation of an electrons (e^–)  and a positron (e⁺) into a photon (γ) that produces a bottom quark (b) and anti-bottom quark (b) pair, which then radiate gluons (blue).

In electrodynamics, photons (γ) are emitted or absorbed whenever an electrically charged particle changes it direction of motion. And since the gluon in chromodynamics plays the same role as the photon in electrodynamics, a gluon is emitted or absorbed whenever  a “colorfully” charged particle changes its direction of motion. We can absolutely take this analogy a step further: gluons are able to pair-produce, just like photons.

Figure 8: A Feynman diagram demonstrating  an annihilation of an electrons (e^–)  and a positron (e⁺) into a photon (γ) that produces a bottom quark (b) and anti-bottom quark (b) pair. These quarks then radiate gluons (blue), which finally pair-produce into quarks.

At the end of the day, however, we have to include the effects of the Weak nuclear force. This is because electrons and quarks have what are called “weak (isospin) charges”. Firstly, there is the massive Z boson (Z), which acts and behaves much like the photon; that is to say, an electron and positron can annihilate into a Z boson. Secondly, there is the slightly lighter but still very massive W boson (W), which can be radiated from quarks much like gluons, just to a lesser extent. Phenomenally, both Weak bosons can decay into quarks and form semi-stable, multi-quark systems called hadrons. The formation of hadrons is, unsurprisingly, called hadronization. Two such examples are the the π meson (pronounced: pie mez-on)  or the J/ψ meson (pronounced: jay-sigh mezon). (See this other QD article for more about hadrons.)

Figure 9: A Feynman diagram demonstrating  an annihilation of an electrons (e^–)  and a positron (e⁺) into a photon (γ) or a Z boson (Z) that produces a bottom quark (b) and anti-bottom quark (b) pair. These quarks then radiate gluons (blue) and a W boson (W), both of which finally pair-produce into semi-stable multi-quark systems known as hadrons (J/ψ and π).

In summary, when electrons and positrons annihilate, they will produce a photon or a Z boson. In either case, the resultant particle is allowed to decay into quarks, which can radiate additional gluons and W bosons. The gluons and W boson will then form hadrons. My friend Geoffry, that is how how you can produce quarks and hadrons from electron-positron colliders.

Now go! Discuss and ask questions.

Happy Colliding

– richard (@bravelittlemuon)

* The Universe’s age is measured to be about 13.69 billion years. The mean life of a proton is longer than 2.1 x 10²⁹ years, which is more than 15,000,000,000,000,000,000 times the age of the Universe. Yeah, I know it sounds absurd but it is true.