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Richard Ruiz | Univ. of Pittsburgh | U.S.A.

View Blog | Read Bio

Everytime a Belle Rings, A Hadron Gets Its Wings

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.

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12 Responses to “Everytime a Belle Rings, A Hadron Gets Its Wings”

  1. Navneeth says:

    Thank you so much for the article, and the previous ones as well. (I just love the care that the people at QD take in formatting their posts, especially the ones with so many diagrams.)

    In what sense do you use the word [i]phenomenally[/i] in [i]Phenomenally, both Weak bosons can decay into quarks…[/i]?

  2. Navneeth says:

    Oops… those were meant to be HTML tags. (Oh, and don’t bother to publish this comment. :-))

  3. Wonderful post – thanks! The colored Feynman diagrams are lovely. How does the energy of the incident electrons relate the outgoing products (aside from balance required)?

    • Richard Ruiz says:

      Hi Binkley,

      Aside from requiring that total energy and total momentum are conserved, one neat phenomenon that occurs at higher energies is that the outgoing products are unevenly distributed about a particle detector, which is not the case at low energies.

      My favorite example is if the total energy of the incoming electron and positron is *VERY* close to the mass of the Z boson. A fun fact about the Z boson (and the Weak nuclear force in general) is that the Z boson interacts with particles that are spinning with a clockwise orientation slightly more than particles that are spinning with a counter-clockwise orientation. If, for example, the Z boson decayed into a muon and anti-muon, then this slight preference for clockwise muons causes a small (but very measurable!) asymmetry in the distribution of muons a detector. Imagine having 100 Z bosons that decay into 100 muons & anti-muons pairs, and always finding that 55 pairs on one side of a particle detector and 45 on the other side. In the case of photons, there is always be a 50-50 split. This effect is very prominent when the energy of the incoming electron and positron are very close to the mass of the Z boson but is virtually negligible at much lower energies.

  4. John Carter says:

    I thought the statement, “a gluon is emitted or absorbed whenever a “colorfully” charged particle changes its direction of motion” was very insightful. Although not indicated on the feynmen diagrams, each REAL gluon emission/absorption is associated with a change in the quarks momentum! Given the “strong” nature of the force, the nucleus of the atom must be “chaotic” place! Is the ease of gluon interaction (and as a result momentum change of the quark) related to the asymmetric freedom of the quark? Seems they would be intimately linked.

    • Richard Ruiz says:

      Hi John, I am really happy to hear you liked that bit about momenta changes.

      You are absolutely right about the chaotic/crazy nature of a nucleus’ interior. Since quarks so readily emit/absorb gluons, attempting to calculate anything about a nucleus gets very complicated, very easily. Fortunately at high energies (at the LHC for example), calculating things does indeed get easier. A property of the Strong nuclear force is that it gets weaker at higher energies (weird, I know). According to our predictions, at sufficiently high energy, the Strong force is practically negligible and quarks will not radiate gluons. No gluon emission means that gluons travel freely and unimpeded. In other words: at *asymptotically* high energies, quarks act as free particles. Hence the term “asymptotic freedom.” ;)

      As a bonus, at very low energies the Strong force becomes…. STRONG, to say the least. When this happens, quarks immediately combine with other quarks to form hadrons. For physicists, the low energy regime is often called the “infrared regime” and therefore we call this phenomenon “infrared slavery.”

  5. Chris Greenley says:

    Thanks for the good explanation! I particularly enjoyed it since I have been learning about Feynman diagrams this last week in my particle physics class.

  6. Mike Bertenshaw says:

    As a very interested dunce – how does a photn produce a particle with mass eg electron is it a consequence of e=m csquared ?

    • Richard Ruiz says:

      Hi Mike,

      Judging by your question’s time stamp, I think I owe you an apology for my slowness in replying. When the electron an positron annihilate, they form a virtual photon, which can have mass. The mass of this virtual object is actually given by the equation:
      mass^2 = Total Energy^2 – Total momentum^2;

      this is a more general (and much more preferred) form of Einstein’s famous Energy = mass * speed of light^2. The virtual particle produced by the annihilation is never directly observed (hence the term “virtual”), and possesses all the same quantum mechanical properties as a photon, just not its mass.

      I hope that made sense.

  7. Kevin says:

    Wow. Love this article. Thank you!

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