Quantum Diaries

Posts Tagged ‘Quarks’

Quarks: Yeah, They Exist

Monday, April 16th, 2012

Richard Ruiz

Physics Fact: 58 years ago, quarks were independently proposed by Murray Gell-Mann & George Zweig [1,2]. M.G.M. called them “quarks” and Zweig called them “aces.”

Hi All,

A question I often get, like really often, especially from other physicists, is “How do we know quarks exist?” In particular,

If (light) quarks cannot be directly observed, due to the phenomenon known as color confinement (or infrared slavery as I like calling it), then how do we know quarks exist?

This is a really good question and it has a number of different answers. To a physicist, being able to directly observe an object means being able to isolate it and subsequently measure its properties, for example: electric charge. Due to effects associated with the strong nuclear force, quarks lighter than the top quark will nucleate into other objects (hadrons) in about 3×10^-25 seconds. This is pretty fast, much faster than any piece of modern electronics. Consequentially, light quarks cannot be directly observed with present technology. However, this inability to isolate quarks does not imply we cannot directly measure their properties (like electric charge!).

This brings me to today’s post: How physicists measure quarks’ electric charges!

R

Fig. 1: An electron (e-) and positron (e+) annihilate to produce a virtual photon (γ*) that subsequently decays into a muon (μ-) and anti-muon (μ+). Click for full size.

A very typical calculation done by any student in a course on particle physics (undergraduate or graduate) is to calculate the likelihood (called cross section) of an electron and positron annihilating into a virtual photon, which then decays into a muon and anti-muon. (See the diagram to the right.). Since electrons, muons, and their anti-matter partners all have so little mass, it is pretty reasonable to just pretend they are all massless. The calculation becomes considerably easier, trust me on this. When all is said and done, we find that the cross section is equal to a bunch of constants (which I am just going to collectively call σ₀), times the square of the electron’s electric charge (Q²_e), times the square of the muon’s electric charge (Q²_μ):

Likelihood of e⁺e^- → μ⁺μ^- = σ₀ × Q²_e × Q²_μ

However, the electric charges of electrons and muons are both 1 (in elementary units) so the likelihood reduces to just σ₀. Convenient, right?

Now, if we replace muons with quarks, then he find that the cross section is this:

Likelihood of e⁺e^- → qq = 3 × σ₀ × Q²_q

That’s right: the probability of producing quarks with electrons & positrons is simply three times that for producing muons, scaled by the square of the quarks’ electric charge. This amazing result allows us to then define the quantity “R“, which is just the ratio of the likelihoods:

R = (Likelihood of e⁺e^- → qq) / (Likelihood of e⁺e^- → μ⁺μ^-) = 3 × Q²_q

In other words, by measuring the ratio of how likely it is to produce a particular set of quarks to how likely it is to produce muons, we can directly measure quarks’ electric charge! (BOOYA!)

Measuring R

As far as measuring R goes, it is pretty straightforward. However, there has to be some caveat or complication since this is physics we are talking about. Sure enough there are a few and I am just going to ignore them all, all but one.

In order to determine the probability of producing a particular pair of quarks using electron-positron collisions, experimentalists have to make sure the total energy of the collision is large enough. Simply put, no particle can ever be generated if there is not enough energy to make it. It is an example of the Conservation of Energy. The problem is this: if there is enough energy to make a particular set of quarks, then there is sufficient energy to produce any quark pair lighter than the original set. In addition, it is very difficult to isolate different quark-anti-quark pairs (see the top of this post for why that is).

The solution to this issue is to simply measure the likelihood of producing ALL types of quarks for a particular energy. To do so, all we need is to add up all the individual cross sections for each set of quarks. The total cross section simplifies to this:

Likelihood of e⁺e^- → ALL qq = 3 × σ₀ × Q²_e × Sum Q²_q

That is to say, the probability of producing ALL quark-anti-quark pairs in electron-positron collisions is equal to a bunch of constants (σ₀) times the square of the electron’s electric charge (Q²_e), times the sum of the square of each quark’s electric charge (Q²_q). Consequently, R becomes

R = (Likelihood of e⁺e^- → ALL qq) / (Likelihood of e⁺e^- → μ⁺μ^-) = 3 × Sum of all Q²_q

R may no longer be a direct measurement of a single quark’s electric charge, but it is still a direct measurement of the electric charge of all the quarks. Without further ado, here are the predictions:

Table 1: R-values for energies below 200 MeV (0.1 GeV) and above 9 GeV. Click for full size.

Here are the data. This plot is taken from my favorite particle physics books, Quarks & Leptons:

Fig. 2: The R value of light quarks versus energy of quark-anti-quark pair. Click for full size. Credit: F. Halzen and D. Martin, "Quarks and Leptons: An Introductory Course in Modern Particle Physics", Wiley 1984.

That Disagreement Near 5-8 GeV is Not Really a Disagreement

Time for a little extra credit. If you look closely at figure 2, you may notice that between 5 GeV and 8 GeV all the data points are uniformly above the R=10/3 line. This feature is actual the result of two things: the first is that quarks really do have masses and cannot be ignored at these energies; the second is that the strong nuclear force surprisingly contributes to this process. I will not say much about the first point other than mention that, in our quick calculation above, we pretended to ignore all masses because electrons and muons were so light. The mass (in natural units) of the charm quark is about 1.3 GeV, and that is hardly small compared to 5 GeV.

Taking a closer look at where the virtual photon produces a quark and anti-quar k pair, we realize that quark and anti-quark are pretty close together. They are actually close enough to emit and absorb gluons, the particle that mediates the strong nuclear force. This has a very important consequence. Previously, the quark and anti-quark pair could only be produced in such a way that the total momentum of the system was conserved. However, if we consider the fact that the quarks can exchange gluons, and hence exchange momenta, then the quark and anti-quark pair can be produced an infinite number of different ways that violate the conservation of total momentum, so long as at least one gluon is exchanged between the two in order to restore total momentum. This amplification in likelihood is highly sensitive to energy but it causes about a 20% increase in R between 5 and 8 GeV. This 20% increase in R is precisely the difference between all the data points and the R = 10/3 line.

Fig. 3: A Feynman diagram representing the annihilation of an electron (e-) and positron (e+) into a virtual photon (γ*) that decays into a quark (q) and anti-quark (q) pair. The photon-quark-quark vertex is enlarged to highlight the ability for nearby quarks to exchange gluons. Click for full size.

Happy Colliding.

- richard (@bravelittlemuon)

P.S. #PhysicsFact should totally be a trend today. Go! Make it trend!

Tags: @bravelittlemuon, Color Confinement, Electric Charge, Infrared Slavery, QED, Quarks, R Value
Posted in Latest Posts | 2 Comments »

Everytime a Belle Rings, A Hadron Gets Its Wings

Friday, January 27th, 2012

Richard Ruiz

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.

Tags: @bravelittlemuon, annihilation, b quark, Belle, electron, ewk, Feynman Diagrams, Hadrons, photons, positron, QCD, QED, Quarks, Twitter, w boson, Z boson
Posted in Latest Posts | 12 Comments »

Grab Your Computer, Grab Your Headphones, and Pop the Popcorn

Sunday, October 2nd, 2011

Richard Ruiz

Update I: Included Medicine Award (Oct 03)

Update II: Included Physics Award (Oct 04)

… it’s Nobel Week! October means three things: Halloween (duh), Fall, and Nobel Week, the week during which the famed prizes are awarded to those who have “conferred the greatest benefit on mankind” [1]. Okay, before I get comments about the subjectivity of those who award the prizes, I gladly admit that the history of the prize is not without controversy relating to those who have & have not won, in both the science and non-science categories.

I am just going to ignore all of that and talk about why everyone should be excited about this week. Though before I talk about this week’s Nobels, I feel I should probably give the SparkNotes version of the prizes’ history.

Figure 1: The 2008 Chemistry Prize was awarded for the discovery and development of green fluorescent protein (GFP), which when inserted into a soon-to-be parent is passed onto an offspring who can then glow green. Glowing cat!
(Image: The Nobel Foundation)

[1] http://www.nobelprize.org/alfred_nobel/will/will-full.html

A Brief History of Alfred Nobel

Figure 2: Alfred Nobel. (Image: The Nobel Foundation)

The year is 1866, the Second Industrial Revolution is raging, innovation is surging, and the US Civil War over.

Insert Alfred Nobel: A son of a successful engineer who developed controlled explosives for the demolition and mining industries. The younger Nobel, unsurprisingly, decided be a chemist after playing with nitroglycerin in a French laboratory. As a public service announcement, I should probably mention that nitroglycerin is very dangerous and is a principle ingredient in dynamite. In fact, Nobel was so convinced that nitroglycerine had useful application in construction that he decided to invent dynamite. Needless to say, dynamite made Nobel a very, very, very rich man. At the end of his life, he decided to endow, with the bulk of his fortune, a set of prizes to recognize those who have contributed greatest in the Fields of Medicine, Physics, Chemistry, Literature, and Peace. Economics, though not stipulated in the original will, was added later and is funded separately.

Figure 2: The chemical structure of nitroglycerin. This stuff is wicked; the physical chemistry behind its structure worth a gander. Consider this an advertisement to go earn a chemistry degree. (Image: Wikipedia)

What Makes a Prize

The Nobels has come a long way since they were first instituted. Most notably, they no longer are awarded for the greatest discovery or invention from the past year; the prizes now award those results with the most lasting influence and impact. Take last year for example. The 2011 award for Physiology or Medicine went solely to Sir Robert Edwards for having developed in vitro fertilization. You would think something that is, in every sense of the word, responsible for the existence of millions of people would have been awarded long, long ago. I mean, that is what went through my mind last October. Therein lies the novelty of the Nobel Prizes: These days, the awards are given to what seem like common knowledge, because in some sense they are. What one has to realize though is that prior a laureate’s discovery or invention, these ideas and concepts just did not exist. Imagine a world in which no one knew of insulin (Nobel 1923). Weird, no?

This brings me to why Nobel Week is so much fun. Sometimes you know quite a bit about the award-winning discovery and so you get to spend the day reading news articles and science blogs learning all about the topic’s history. Werner Forssmann’s invention of the cardiac catheter (Nobel 1953) has a hysterical history that is well worth a read. At other times, you have no idea what the award citation even means, but you just know it is worth spending a few minutes or even a few hours learning. I mean, why else would a Nobel be awarded? Take, as another example, 2008′s Physics prize. The award citation reads:

“… for the discovery of the mechanism of spontaneous broken symmetry in subatomic physics,” [2]

and

“for the discovery of the origin of the broken symmetry
which predicts the existence of at least three families of quarks in nature.” [2]

Yup, it is a mouthful and probably seems a bit obtuse. That is, until you start looking up Wikipedia or news articles (or Quantum Diaries!), and realize how amazingly awesome these discoveries are. I mean, sure discovering spontaneous symmetry breaking (SSB) sounds nice and fancy but did you know that is why the bosons in the Standard Model of Physics have the masses they do?!? SSB, when applied specifically to the Electroweak bosons (photon, W, & Z) is the Higgs Mechanism, and when applied to fermions, is what generates the higgs boson. SSB is an established scientific fact and is also the driving force behind superconductivity (Nobel 1972) Whether or not the higgs boson exists, however, is completely different story.

Figure 3: The quark sector of the Standard Model of Particle Physics and their discovery dates. (Image: Nobel Foundation)

So back in 1977 a Fermilab team, led by Leon Lederman, discovered the bottom quark (Nobel 1988), and in 1995, the CDF & DZero Tevatron experiments discovered the top quark. Ever wonder how we knew to look for them in the first place? It was because of something called the CKM matrix. It was introduced as a way of organizing the the different ways particles in the Standard Model could interact and decay. However, as gorgeous as this new organization was, in order to work the CKM matrix required the existence of two new quarks. Well guess what, Fermilab found those two quarks and set the Standard Model in stone.

The 2009 Nobel Prizes are equally impressive. Half the prize was awarded for the development of fiber optics, which is the foundation of modern telecommunications, and something called Charged-Coupled Devices (CCD). What took me a few hours to learn is that if you take this sensor, attach a flashbulb, a battery, and maybe a memory card, you get a digital camera. In other words, half the 2009 prize was awarded for inventing the digital camera. The prize winners were simply trying to develop a better way of storing data and inadvertently created an entire industry. A fun fact: the first transistor (Nobel 1967) was made of paperclips. If you are curious about what makes transistors so important, take apart your computer and take a peek. (Please, make sure the computer is unplugged before opening it.)

[2] http://www.nobelprize.org/nobel_prizes/physics/laureates/2008/

Does Every Major Discovery/Invention Get a Prize?

No. First off, Nobel Prizes are no longer awarded posthumously. Secondly, from my discussions about this issue, there seems to be a consensus there may be a limit to what is & is not awarded when it comes to the sciences. Now the Swedish Academies always reserve the right to set a new precedent, however, it is unlikely that any organizations will be awarded a Nobel in science categories anytime soon. (This is the complete opposite for the Peace Prize, of course.) What does this all mean? Well, the top quark was a pretty heavy discovery and is well worth its weight in gold, at least in my opinion. However, to whom would you award the prize? No single person at the CDF experiment can justly say she or he discovered the quark; it was a team effort and all CDF personnel can proudly state she or he helped discover the quark.

“Which of the Gang of Six, if the higgs boson is discovered, should get the Nobel, if at all?” is an honest, open question and is well above my pay grade. A similar statement could be made about Supersymmetry.

Turning Nobel Week into Fun-bel Week

Now for the fun part. So during this week, pick your favorite subject, which of course is physics, and go figure out what the whole big hubbub is. Depending on your timezone, this may either be with your morning coffee or afternoon tea. In any case, it is an excuse to learn something new!

Alternatively, you can check back here Tuesday afternoon (Madison/Chicago time) because I am sure many of us will be commenting on the latest news.

This Week’s Schedule

Live Video Player here.

Physiology or Medicine – Awarded for the discovery of the innate and adaptive immune systems! Okay, really this is great. The human body has evolved to be inherently immune to certain pathogens. The human body, in its resourcefulness, can also adapt and become immune to pathogens. The end result is that when the two are combined and wait a few hundred thousand years, you get us!

Physics – Awarded for discovering that expansion rate of the universe, is itself increasing. The universe expands, Edwin Hubble discovered that decades ago. Today’s award winners discovered that the universe expands at an accelerating rate! Bravo!

Chemistry – The prize will be announced on Wednesday 5 October, 11:45 a.m. CET [5:45 am CDT/Chicago].

Peace – The prize will be announced on Friday 7 October, 11:00 a.m. CET [5:00 am CDT/Chicago].

Economics – The prize will be announced on Monday 10 October, 1:00 p.m. CET [7:00 am CDT/Chicago].

Literature – To Be Announced

Regardless of the outcome, I would love to read everyone’s thoughts and speculations before and after the awards!

Happy Colliding

- richard (@bravelittlemuon)

Tags: @bravelittlemuon, Alfred Nobel, chemistry, CKM, Economics, Fermilab, Higgs, Literature, Medicine, Nitroglycerin, nobel, October, physics, Physiology, Quarks, SSB, TooManyTags, top quark, Transistor
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Posts Tagged ‘Quarks’

R

Measuring R

That Disagreement Near 5-8 GeV is Not Really a Disagreement

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

A Brief History of Alfred Nobel

What Makes a Prize

Does Every Major Discovery/Invention Get a Prize?

Turning Nobel Week into Fun-bel Week

This Week’s Schedule

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