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Posts Tagged ‘Quarks’

Hadrons, the particles made of quarks, are almost unanimously produced in the two or three quark varieties in particle colliders. However, in the last decade or so, a new frontier has opened up in subatomic physics. Four-quark particles have begun to be observed, the most recent being announced last Thursday by a collaboration at Fermilab. These rare, fleetingly lived particles have the potential to shed some light on the Strong nuclear force and how it shapes our world.

The discovery of a new subatomic particle was announced last Thursday by the DØ (DZero) collaboration at Fermilab in Chicago. DØ researchers analysed data from the Tevatron, a proton-antiproton collider based at Fermilab. The new found particle sports the catchy name “X(5568)” (It’s labelled by the observed mass of 5,568 Megaelectron-volts or MeV. That’s about six times heavier than a proton.) X(5568) is a form of “tetraquark”, a rarer variety of the particles known as hadrons. Tetraquarks consist of two quarks and two antiquarks (rather than the usual three quarks or quark-antiquark pairs that make up hadrons particle physicists are familiar with). While similar tetraquark particles have been observed before, the new addition breaks the mould by consisting of four quarks of totally different flavours: bottom, strange, up and down.

[Regular readers and those familiar with the theory of QCD may wish to skip to the section marked ——]

a) An example of a quark-antiquark pair, known as Mesons. b) An example of a three-quark particle, known as Baryons. c) An example of a tetraquark (four quarks) Source: APS/Alan Stonebraker, via Physics Viewpoint, DOI: 10.1103/Physics.6.69

The particle’s decay is best explained Strong force, aptly named since it’s the strongest known force in the universe[1], which also acts to hold quarks together in more stable configurations such as inside the proton. The Strong force is described by a theory known as Quantum Chromodynamics (QCD for short), a crucial part of the Standard Model of particle physics. The properties of X(5568) will provide precision tests of the Standard Model, as well as improving our understanding of the nature of Confinement. This is a dimly understood process by which quarks are bound up together to form the particles (such as protons) that make up most of the visible matter in the universe.

Quarks are defined by the strong force, being the only particles known to physics that interact via QCD. They were originally conceived of in 1964 by two of the early pioneers of particle physics Murray Gell-Mann and George Zweig, who posited the idea of “quarks” to explain the properties of a plethora of particles that were discovered in the mid-twentieth century. After a series of experiments in the late ‘60s and ‘70s, the evidence in favour of the quark hypothesis grew much stronger[2] and it was accepted that many of the particles that interacted and decayed very quickly (due to the magnitude of the strong force) in detectors were in fact made up of these quarks, which are now known to come in six different varieties known as “flavours”. A more precise model of the strong force, which came to be known as QCD, was also verified in such experiments.

QCD is a very difficult theory to draw predictions from because unlike electromagnetism (the force responsible for holding atoms together and transmitting light between objects), the “force carriers” of QCD known as gluons are self-interacting. Whereas light, or photons, simply pass through one another, gluons pull on one another and quarks in complex ways that give rise to the phenomenon of confinement: quarks are never observed in isolation, only as part of a group of other quarks/antiquarks. These groups of quarks and anti-quarks are what we call Hadrons (hence the name Large Hadron Collider). This self interaction arises from the fact that, unlike light which simply couples to positive or negative charges, QCD has a more complicated structure based on three charges labelled as Red, Green and Blue (which confusingly, have nothing to do with real colours, but are instead based on a mathematical symmetry known as SU(3)).

The hadrons discovered in the twentieth century tended to come in pairs of three quarks or quark-antiquark pairs. Although we now know there is nothing in the theory of QCD that suggests you can’t have particles consisting of four, or even five quarks/antiquarks, such particles were never observed, and in fact even some of the finest minds in theoretical physics (Edward Witten and Sidney Coleman) once thought that QCD would not permit such particles to exist. Like clovers, however, although the fourfold or even fivefold variety would be much rarer to come by it turns out such states did, in fact, exist and could be observed.

——

 

A visualisation of the production and decay of X(5568) to mesons in the Tevatron collider. Source: Fermilab http://news.fnal.gov/

The first hints of the existence of tetraquarks were at the Belle experiment, Japan in 2003, with the observation of a state called X(3872) (again, labelled by its mass of 3872 MeV). One of the most plausible explanations for this anomalous resonance[3] was a tetraquark model, which in 2013, an analysis by the LHCb experiment at CERN found to be a compatible explanation of the same resonance found in their detector. The same year, Belle and the BESIII experiment in China both found a resonance with the same characteristics, labelled Zc(3900), which is now believed to be the first independently, experimentally observed tetraquark. The most recent evidence for the existence of tetraquarks, prior to last Thursday’s announcement, was found by the LHCb experiment in 2014, the Z(4430). This verified an earlier result from Belle in 2007, with an astonishingly high statistical significance of 13.9σ (for comparison, one typically claims a discovery with a significance of 5σ). LHCb would also go on, unexpectedly, to find a pentaquark (four quarks and an antiquark) state in 2015, which could provide a greater understanding of QCD and even a window into the study of neutron stars.

Z(4430) was discovered from the analysis of its decay into mesons (hadrons consisting of quark-antiquark pairs), specifically the ψ’ and π mesons from the decay B0 → K + ψ’  π. In the analysis of the B0 decay, it was found that the Z(4430) was needed as an intermediate particle state to explain the resonant behaviour of the ψ’ and π. The LHCb detector, whose asymmetric design and high resolution makes it particularly well suited for the job, reconstructs these mesons and looks at their kinematic properties to determine the shape and properties of the resonance, which were found to be consistent with a tetraquark model. The recent discovery of X(5568) by the DØ collaboration involved a similar reconstruction from Bs and π mesons, which was used to infer its quark flavour structure (b, s, u, d, though which two are the particles and which two are the antiparticles remains to be determined).

X(5568) is found to have a large width (22 MeV) in the distribution of its decays, implying that it decays very quickly, best explained by QCD. Since quarks cannot change flavours in QCD interactions (while they can do so in weak nuclear interactions), this is what allowed DØ to determine its quark content. The other properties of this anomalous particle, such as its mass and its lack of spin (i.e. S = 0) are measured from the kinematics of the mesons it produces, and can help increase our understanding of how QCD combines the quarks in such an unfamiliar arrangement.

The two models for tetraquarks: Left, a single bound state of four quarks. Right, a pair of mesons bound to one another in orbit, resembing a four quark state. Source: Fermilab http://news.fnal.gov (Particle Physicists have a strange relationship with Comic Sans)

One of the long-standing controversies surrounding tetraquark states is whether the states are truly a joint four particle state or in fact a sort of molecule of two strongly bound mesons, which although they form a bound state of four particles in total, is actually analogous to two separate atoms in a molecule rather than a single, heavy atom. The analysis from DØ, based on X(5568)’s mass seems to imply that it’s the former, a single particle of four quarks tightly bound in an exotic hadron, though the jury is still out on the matter.

DØ’s discovery is based on an analysis of the historic data collected from the Tevatron from the 28 years it was operating, since the collider itself ceased operation 2011. Despite LHCb having found tetraquark candidates in the past and being suited to finding such a particle again, it has not yet independently verified the existence of X(5568). LHCb will now review their own data as well as future data that will recommence being collected later this year, to see if they too observe this unprecedented result and hopefully improve our understanding of its properties and whether they are consistent with the Standard Model. This is definitely a result to look out for later this year and should shed some light on one of the fundamental forces of nature and how it acts to create the particles, such as protons, that make up the world around us.

[1] That is, the dimensionless coupling of the force carrier particle interactions is greater than electromagnetism and the weak nuclear force, both of which in turn are stronger than gravity (consider how a tiny magnet can lift a paper clip against the gravity of the entire Earth). Many theories of Beyond the Standard Model physics predict new forces, and it may turn out that all the forces are unified into a single entity at high energies.

[2] For an excellent summary of the history of quarks and some of the motivations behind the quark model, check out this fantastic documentary featuring none other than the Nobel Prize wining physicists, Richard Feynman and Murray Gell-Mann themselves.

[3] Particles are discovered by the bumps or resonances they leave in the statistical distributions of particle decays/scattering events. See for example, one of the excesses of events that led to the discovery of the Higgs Boson.

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In the late 1980s, as particle colliders probed deeper into the building blocks of nature, there were hints of a strange and paradoxical behaviour in the heart of atoms. Fundamental particles have a curious quantum mechanical property known as “spin”, which the electron carries in magnitude ½. While the description of electron’s spin is fairly simple, protons are made up of many particles whose “spins” can add together in complicated ways and yet remarkably, its total spin turns out to be the same as the electron: ½. This led to one of the great mysteries of modern physics: how do all the particles inside the proton conspire together to give it a ½ spin? And what might this mean for our understanding of hadrons, the particles that make up most of the visible universe?

[This article is largely intended for a lay-audience and contains an introduction to foundational ideas such as spin. If you’ve had a basic introduction to Quantum Mechanics before, you may wish to skip to section marked —— ]

We’ve known about the proton’s existence for nearly a hundred years, so you’d be forgiven for thinking that we knew all there was to know about it. For many of us, our last exposure to the word “proton” was in high school chemistry, where they were described as a little sphere of positive charge that clumps with neutrons to make atomic nuclei, around which negatively charged electrons orbit to create all the atoms, which make up Life, the Universe and Everything1.

2000px-Proton.svg

The simple, three-quark model of a proton (each coloured circle is a type of “quark”).

Like many ideas in science, this is a simplified model that serves as a good introduction to a topic, but skips over the gory details and the bizarre, underlying reality of nature. In this article, we’ll focus on one particular aspect, the quantum mechanical “spin” of the proton. The quest to measure its origin has sparked discovery, controversy and speculation that has lasted 30 years, the answer to which is currently being sought at a unique particle collider in New York.

The first thing to note is that protons, unlike electrons2, are composite particles, made up from lots of other particles. The usual description is that the proton is made up of three smaller “quarks” which, as far as we know, can’t be broken down any further. This picture works remarkably well at low energies but it turns out at very high energies, like those being reached at the at the LHC, this description turns out to be inadequate. At that point, we have to get into the nitty-gritty and consider things like quark-antiquark pairs that live inside the proton interacting dynamically with other quarks without changing its overall charge. Furthermore, there are particles called gluons that are exchanged between quarks, making them “stick” together in the proton and playing a crucial role in providing an accurate description for particle physics experiments.

So on closer inspection, our little sphere of positive charge turns out to be a buzzing hive of activity, with quarks and gluons all shuffling about, conspiring to create what we call the proton. It is by inferring the nature of these particles within the proton that a successful model of the strong nuclear force, known as Quantum Chromodynamics (QCD), was developed. The gluons were predicted and verfied to be the carriers of this force between quarks. More on them later.

Proton structure

A more detailed model of the proton. The golden chains between the quarks (the coloured spheres) are representations of gluons, transferred between them. Quark anti-quark pairs are also visible with arrows representing spins.

That’s the proton, but what exactly is spin? It’s often compared to angular momentum, like the objects in our everyday experience might have. Everyone who’s ever messed around on an office chair knows that once you get spun around in one, it often takes you a bit of effort to stop because the angular momentum you’ve built up keeps you going. If you did this a lot, you might have noticed that if you started spinning with your legs/arms outstretched and brought them inwards while you were spinning, you’d begin to spin faster! This is because angular momentum (L) is proportional to the radial (r) distribution of matter (i.e. how far out things are from the axis of rotation) multiplied by the speed of rotation3 (v). To put it mathematically L = m × v × r where m is just your constant mass. Since L is constant, as you decrease r (by bringing your arms/legs inwards), v (the speed at which you’re spinning) increases to compensate. All fairly simple stuff.

So clearly, for something to have angular momentum it needs to be distributed radially. Surely r has to be greater than 0 for L to be greater than 0. This is true, but it turns out that’s not all there is to the story. A full description of angular momentum at the quantum (atomic) level is given by something we denote as “J”. I’ll skip the details, but it turns out J = L + S, where L is orbital angular momentum, in a fashion similar to what we’ve discussed, and S? S is a slightly different beast.

Both L and S can only take on discrete values at the microscopic level, that is, they have quantised values. But whereas a point-like particle cannot have L > 0 in its rest frame (since if it isn’t moving around and v = 0, then L = 0), S will have a non-zero value even when the particle isn’t moving. S is what we call Spin. For the electron and quarks, it takes on the value of ½ in natural units.

Spin has a lot of very strange properties. You can think of it like a little arrow pointing in a direction in space but it’s not something we can truly visualise. One is tempted to think of the electron like the Earth, a sphere spinning about some kind of axis, but the electron is not a sphere, it’s a point-like particle with no “structure” in space. While an electron can have many different values of L depending on its energy (and atomic structure depends on these values), it only has one intrinsic magnitude of spin: ½. However, since spin can be thought of as an arrow, we have some flexibility. Loosely speaking, spin can point in many different directions but we’ll consider it as pointing “up” (+½) or “down” (- ½). If we try to measure it along a particular axis, we’re bound to find it in one of these states relative to our direction of measurement.

Spin250

Focus on one of the red faces. When the cube rotates every 360 degrees, the red ribbon appears to go above and below the cube alternatively! Because the cube is coupled to its environment, it takes 720 degrees to return it to it’s original orientation.


One of the peculiar things about spin-½ is that it causes the wave-function of the electron to exhibit some mind bending properties. For example, you’d think rotating any object by 360 degrees would put it back into exactly the same state as it was, but it turns out that doesn’t hold true for electrons. For electrons, rotating them by 360 degrees introduces a negative sign into their wave-function! You have to spin it another 360 degrees to get it back into the same state! There are ways to visualise systems with similar behaviour (see right) but that’s just a sort of “metaphor” for what really happens to the electron. This links into the famous conclusion of Pauli’s that no two identical particles with spin-½ (or any other half-integer spin) can share the same quantum mechanical state.

——

Spin is an important property of matter that only really manifests on the quantum scale, and while we can’t visualise it, it ends up being important for the structure of atoms and how all solid objects obtain the properties they do. The other important property it has is that the spin of a free particle likes to align with magnetic fields4 (and the bigger the spin, the greater the magnetic coupling to the field). By using this property, it was discovered that the proton also had angular momentum J = ½. Since the proton is a stable particle, it was modelled to be in a low energy state with L = 0 and hence J = S = ½ (that is to say, the orbital angular momentum is assumed to be zero and hence we may simply call J, the “spin”). The fact the proton has spin and that spin aligns with magnetic fields, is a crucial element to what makes MRI machines work.

Once we got a firm handle on quarks in the late 1960s, the spin structure of the proton was thought to be fairly simple. The proton has spin-½. Quarks, from scattering experiments and symmetry considerations, were also inferred to have spin-½. Therefore, if the three quarks that make up the proton were in an “up-down-up” configuration, the spin of the proton naturally comes out as ½ – ½ + ½ = ½. Not only does this add up to the measured spin, but it also gives a pleasant symmetry to the quantum description of the proton, consistent with the Pauli exclusion principle (it doesn’t matter which of the three quarks is the “down” quark). But hang on, didn’t I say that the three-quarks story was incomplete? At high energies, there should be a lot more quark-antiquark pairs (sea quarks) involved, messing everything up! Even so, theorists predicted that these quark-antiquark pairs would tend not to be polarised, that is, have a preferred direction, and hence would not contribute to the total spin of the proton.

If you can get the entirety of the proton spinning in a particular direction (i.e. polarising it), it turns out the scattering of an electron against its constituent quarks should be sensitive to their spin! Thus, by scattering electrons at high energy, one could check the predictions of theorists about how the quarks’ spin contributes to the proton.

In a series of perfectly conducted experiments, the theory was found to be absolutely spot on with no discrepancy whatsoever. Several Nobel prizes were handed out and the entire incident was considered resolved, now just a footnote in history. OK, not really.

In truth, the total opposite happened. Although the experiments had a reasonable amount of uncertainty due to the inherent difficulty of polarising protons, a landmark paper by the European Muon Collaboration found results consistent with the quarks contributing absolutely no overall spin to the proton whatsoever! The measurements could be interpreted with the overall spin from the quarks being zero5. This was a complete shock to most physicists who were expecting verification from what was supposed to be a fairly straightforward measurement. Credit where it is due, there were theorists who had predicted that the assumption about orbital angular momentum (L = 0) had been rather ad-hoc and that L > 0 could account for some of the missing spin. Scarcely anyone would have expected, however, that the quarks would carry so little of the spin. Although the nuclear strong force, which governs how quarks and gluons combine to form the proton, has been tested to remarkable accuracy, the nature of its self-interaction makes it incredibly difficult to draw predictions from.

The feynman diagram for Deep Inelastic Scattering (electron line at the top, proton on the bottom). This type of scattering is sensitive to quark spin.

The Feynman diagram for Deep Inelastic Scattering (electron line at the top, proton on the bottom, with a photon exchanged between them). This type of scattering is sensitive to quark spin.

Future experiments (led by father and son rivals, Vernon and Emlyn Hughes6 of CERN and SLAC respectively) managed to bring this to a marginally less shocking proposal. The greater accuracy of the measurements from these collaborations had found that the total spin contributions from the quarks was actually closer to ~30%. An important discovery was that the sea quarks, thought not to be important, were actually found to have measurable polarisation. Although it cleared up some of the discrepancy, it still left 60-70% of spin unaccounted for. Today, following much more experimental activity in Deep Inelastic Scattering and precision low-energy elastic scattering, the situation has not changed in terms of the raw numbers. The best estimates still peg the quarks’ spin as constituting only about 30% of the total.

Remarkably, there are theoretical proposals to resolve the problem that were hinted at long before experiments were even conducted. As mentioned previously, although currently impossible to test experimentally, the quarks may carry orbital angular momentum (L) that could compensate for some of the missing spin. Furthermore, we have failed to mention the contribution of gluons to the proton spin. Gluons are spin-1 particles, and were thought to arrange themselves such that their total contribution to the proton spin was nearly non-existent.

BNL AERIALS

The Brookhaven National Laboratory where RHIC is based (seen as the circle, top right).


The Relativistic Heavy Ion Collider (RHIC) in New York is currently the only spin-polarised proton collider in the world. This gives it a unique sensitivity to the spin structure of the proton. In 2014, an analysis of the data collected at RHIC indicated that the gluons (whose spin contribution can be inferred from polarised proton-proton collisions) could potentially account for up to 30 of the missing 70% of proton spin! About the same as the quarks. This would bring the “missing” amount down to about 40%, which could be accounted for by the unmeasurable orbital angular momentum of both quarks and gluons.

As 2016 kicks into gear, RHIC will be collecting data at a much faster rate than ever after a recent technical upgrade that should double it’s luminosity (loosely speaking, the rate at which proton collisions occur). With the increased statistics, we should be able to get an even greater handle on the exact origin of proton spin. 


The astute reader, provided they have not already wandered off, dizzy from all this talk of spinning protons, may be tempted to ask “Why on earth does it matter where the total spin comes from? Isn’t this just abstract accountancy?” This is a fair question and I think the answer is a good one. Protons, like all other hadrons (similar, composite particles made of quarks and gluons) are not very well understood at all. A peculiar feature of QCD called confinement binds individual quarks together so that they are never observed in isolation, only bound up in particles such as the proton. Understanding the spin structure of the proton can inform our theoretical models for understanding this phenomenon.

This has important implications, one being that 98% of the mass of all visible matter does not come from the Higgs Boson. It comes from the binding energy of protons! And the exact nature of confinement and precise properties of QCD have implications for the cosmology of the early universe. Finally, scattering experiments with protons have already revealed so much to fundamental physics, such as the comprehension of one of the fundamental forces of nature. As one of our most reliable probes of nature, currently in use at the LHC, understanding them better will almost certainly aid our attempts to unearth future discoveries.

Kind regards to Sebastian Bending (UCL) for several suggestions (all mistakes are unreservedly my own).

 

[1] …excluding dark matter and dark energy which constitute the dark ~95% of the universe.

[2] To the best of our knowledge.

[3] Strictly speaking the component of velocity perpendicular to the radial direction.

[4] Sometimes, spins in a medium like water like to align against magnetic fields, causing an opposite magnetic moment (known as diamagnetism). Since frogs are mostly water, this effect can and has been used to levitate frogs.

[5] A lot of the information here has been summarised from this excellent article by Robert Jaffe, whose collaboration with John Ellis on the Ellis-Jaffe rule led to many of the predictions discussed here.

[6] Emlyn was actually the spokesperson for SLAC, though he is listed as one of the primary authors on the SLAC papers regarding the spin structure of the proton.

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J/ψ

Wednesday, August 6th, 2014

The particle with two names: The J/ψ Vector Meson. Again, under 500 words.

jpsi_NOVA

Trident decay of J/Psi Credit: SLAC/NOVA

Hi All,

The J/ψ (or J/psi) is a very special particle. Its discovery was announced in 1974 independently by two groups: one lead by Samuel Ting at Brookhaven National Laboratory (BNL) in New York and the second lead by Burton Richter at Standford Linear Accelerator Center (SLAC) in California. J/ψ is special because it established the quark model as a credible description of nature. Having been invented by Gell-Man and Zweig as a bookkeeping tool, it was not until Glashow, Iliopoulos and Maiani (GIM) that the concept of quarks as real particles was taken seriously. GIM predicted that if quarks were real, then they should come in pairs, like the  up and down quarks. Candidates for the up, down, and strange were identified, but there was no partner for the strange quark. J/ψ was the key.

ting-group-335px_BNL

Samuel Ting and his BNL team. Credit: BNL

Like the proton or an atom, the J/ψ is a composite particle. This means that J/ψ is made of smaller, more elementary particles. Specifically, it is a bound state of  one charm quark and one anticharm quark. Since it is made of quarks, it is a “hadron“. But since it is made of exactly one quark and one antiquark, it is specifically a “meson.” Experimentally, we have learned that the  J/ψ has an intrinsic angular momentum (spin) of 1ħ (same as the photon), and call it a “vector meson.” We infer that the charm and anticharm, which are both spin ½ħ, are aligned in the same direction (½ħ + ½ħ = 1ħ). The J/ψ must also be electrically neutral because charm and anticharm quarks have equal but opposite electric charges.

richter_SLAC

Burton Richter following the announcement of co-winning the 1976 Nobel Prize. Credit: SLAC

At 3.1 GeV/c², the J/ψ is a about three times heavier than the proton and about three-quarters the mass of the bottom quark. However, because so few hadrons are lighter than it, the J/ψ possesses a remarkable feature: it decays 10% of the time to charged leptons, like an electron-positron pair. By conservation of energy, it is forbidden to decay to heavier hadrons. Because there are so few  J/ψ decay modes, it is appears as a very narrow peak in experiments. In fact, the particle’s mass and width are so well-known that experiments like ATLAS and CMS use them as calibration markers.

Credit: CMS

Drell-Yan spectrum data at 7 TeV LHC Credit: CMS

The J/ψ meson is one of the coolest things in the particle zoo. It is a hadronic bound state that decays into charged leptons. It shares the same quantum numbers as the photon and Z boson, so it appears as a Drell-Yan processes. It established the quark model, and is critical to new discoveries because of its use as a calibration tool. In my opinion, not too shabby.

Happy colliding.

Richard (@BraveLittleMuon)

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Quarks: Yeah, They Exist

Monday, April 16th, 2012

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 (Q2e), times the square of the muon’s electric charge (Q2μ):

Likelihood of e+e → μ+μ = σ0 × Q2e × Q2μ

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 × Q2q

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 × Q2q

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 × Q2e × Sum Q2q

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 (Q2e), times the sum of the square of each quark’s electric charge (Q2q). Consequently, R becomes

R = (Likelihood of e+e → ALL qq) / (Likelihood of e+e → μ+μ) = 3 × Sum of all Q2q

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!

<sub>μ</sub>
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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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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)

 

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