Posts Tagged ‘QCD’

The Four-Leafed Clovers of Subatomic Particles: Tetraquarks

Monday, February 29th, 2016

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 Z_c(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 B_s 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.

Tags: Exotic Hadrons, Fermi National Accelerator Laboratory, LHCb, QCD, Quarks, Tetraquark
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Spun out of proportion: The Proton Spin Crisis

Monday, February 1st, 2016

Ricky Nathvani

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.

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.

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.

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.

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.

Tags: polarized protons, proton, proton structure, QCD, Quarks, RHIC, spin
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Drell-Yan, Drell-Yan with Jets, Drell-Yan with all the Jets

Monday, May 18th, 2015

Richard Ruiz

All those super low energy jets that the LHC cannot see? LHC can still see them.

Hi Folks,

Particle colliders like the Large Hadron Collider (LHC) are, in a sense, very powerful microscopes. The higher the collision energy, the smaller distances we can study. Using less than 0.01% of the total LHC energy (13 TeV), we see that the proton is really just a bag of smaller objects called quarks and gluons.

This means that when two protons collide things are sprayed about and get very messy.

One of the most important processes that occurs in proton collisions is the Drell-Yan process. When a quark, e.g., a down quark d, from one proton and an antiquark, e.g., an down antiquark d, from an oncoming proton collide, they can annihilate into a virtual photon (γ) or Z boson if the net electric charge is zero (or a W boson if the net electric charge is one). After briefly propagating, the photon/Z can split into a lepton and its antiparticle partner, for example into a muon and antimuon or electron–positron pair! In pictures, quark-antiquark annihilation into a lepton-antilepton pair (Drell-Yan process) looks like this

feynmanDiagram_DrellYan_Simple

By the conservation of momentum, the sum of the muon and antimuon momenta will add up to the photon/Z boson momentum. In experiments like ATLAS and CMS, this gives a very cool-looking distribution

cms_DY_7TeV

Plotted is the invariant mass distribution for any muon-antimuon pair produced in proton collisions at the 7 TeV LHC. The rightmost peak at about 90 GeV (about 90 times the proton’s mass!) is a peak corresponding to the production Z boson particles. The other peaks represent the production of similarly well-known particles in the particle zoo that have decayed into a muon-antimuon pair. The clarity of each peak and the fact that this plot uses only about 0.2% of the total data collected during the first LHC data collection period (Run I) means that the Drell-Yan process is a very useful for calibrating the experiments. If the experiments are able to see the Z boson, the rho meson, etc., at their correct energies, then we have confidence that the experiments are working well enough to study nature at energies never before explored in a laboratory.

However, in real life, the Drell-Yan process is not as simple as drawn above. Real collisions include the remnants of the scattered protons. Remember: the proton is bag filled with lots of quarks and gluons.

feynmanDiagram_DrellYan_wRad

Gluons are what holds quarks together to make protons; they mediate the strong nuclear force, also known as quantum chromodynamics (QCD). The strong force is accordingly named because it requires a lot of energy and effort to overcome. Before annihilating, the quark and antiquark pair that participate in the Drell-Yan process will have radiated lots of gluons. It is very easy for objects that experience the strong force to radiate gluons. In fact, the antiquark in the Drell-Yan process originates from an energetic gluon that split into a quark-antiquark pair. Though less common, every once in a while two or even three energetic quarks or gluons (collectively called jets) will be produced alongside a Z boson.

feynmanDiagram_DrellYan_3j

Here is a real life Drell-Yan (Z boson) event with three very energetic jets. The blue lines are the muons. The red, orange and green “sprays” of particles are jets.

atlas_158466_4174272_Zmumu3jets

As likely or unlikely it may be for a Drell-Yan process or occur with additional energetic jets, the frequency at which they do occur appear to match very well with our theoretical predictions. The plot below show the likelihood (“Production cross section“) of a W or Z boson with at least 0, 1, 2, 3, or 4(!) very energetic jets. The blue bars are the theoretical predictions and the red circles are data. Producing a W or Z boson with more energetic jets is less likely than having fewer jets. The more jets identified, the smaller the production rate (“cross section”).

cms_StairwayHeaven_2014

How about low energy jets? These are difficult to observe because experiments have high thresholds for any part of a collision to be recorded. The ATLAS and CMS experiments, for example, are insensitive to very low energy objects, so not every piece of an LHC proton collision will be recorded. In short: sometimes a jet or a photon is too “dim” for us to detect it. But unlike high energy jets, it is very, very easy for Drell-Yan processes to be accompanied with low energy jets.

feynmanDiagram_DrellYan_wRadx6

There is a subtlety here. Our standard tools and tricks for calculating the probability of something happening in a proton collision (perturbation theory) assumes that we are studying objects with much higher energies than the proton at rest. Radiation of very low energy gluons is a special situation where our usual calculation methods do not work. The solution is rather cool.

As we said, the Z boson produced in the quark-antiquark annihilation has much more energy than any of the low energy gluons that are radiated, so emitting a low energy gluon should not affect the system much. This is like massive freight train pulling coal and dropping one or two pieces of coal. The train carries so much momentum and the coal is so light that dropping even a dozen pieces of coal will have only a negligible effect on the train’s motion. (Dropping all the coal, on the other hand, would not only drastically change the train’s motion but likely also be a terrible environmental hazard.) We can now make certain approximations in our calculation of a radiating a low energy gluon called “soft gluon factorization“. The result is remarkably simple, so simple we can generalize it to an arbitrary number of gluon emissions. This process is called “soft gluon resummation” and was formulated in 1985 by Collins, Soper, and Sterman.

Low energy gluons, even if they cannot be individually identified, still have an affect. They carry away energy, and by momentum conservation this will slightly push and kick the system in different directions.

feynmanDiagram_DrellYan_wRadx6_Text

If we look at Z bosons with low momentum from the CDF and DZero experiments, we see that the data and theory agree very well! In fact, in the DZero (lower) plot, the “pQCD” (perturbative QCD) prediction curve, which does not include resummation, disagrees with data. Thus, soft gluon resummation, which accounts for the emission of an arbitrary number of low energy radiations, is important and observable.

cdf_pTZ dzero_pTZ

In summary, Drell-Yan processes are a very important at high energy proton colliders like the Large Hadron Collider. They serve as a standard candle for experiments as well as a test of high precision predictions. The LHC Run II program has just begun and you can count on lots of rich physics in need of studying.

Happy Colliding,

Richard (@bravelittlemuon)

Tags: @bravelittlemuon, CERN, Drell-Yan, Jets, LHC, QCD, QCD Corrections
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Excited Quarks and Early Discoveries at LHC Run II

Wednesday, February 4th, 2015

Richard Ruiz

The LHC turns back on this year for Run II. What might we see day 1?

The highest-p_T jet event collected by the end of September 2012 (Event 37979867, Run 208781): the two central high-p_T jets have an invariant mass of 4.47 TeV; the highest-p_T jet has a p_T of 2.34 TeV, and the subleading jet has a p_T of 2.10 TeV. The missing E_T and Sum E_T for this event are respectively 115 GeV and 4.97 TeV. Only tracks with p_T> 0.7 GeV are displayed. The event was collected on August 17th, 2012. Image and caption credit: ATLAS

In seven weeks CERN’s Large Hadron Collider (LHC), the largest and most energetic particle accelerator in history, is scheduled to turn back on. The LHC has been shutdown since December 2012 in order for experimentalists to repair and upgrade the different detector experiments as well as the collider itself. When recommissioning starts, the proton beams will be over 60% more energetic than before and probe a regime of physics we have yet to explore directly. With this in mind, today’s post is about a type of new physics that, if it exists, we can potentially see in the first days of LHC Run II: excited quarks.

Excited Quarks and Composite Quarks

Excited quarks are interesting little beasts and are analogous to excited atoms in atomic physics. When light (a photon) is shined onto an atom, electrons orbiting the nucleus will become energized and are pushed into higher, metastable orbits. This is called an excited atom.

After some estimable and often measurable period of time, an electron will radiate light (photon) and drop down to its original orbit. When this happens, we say that an excited atom has relaxed to its ground state.

In analogy, if quarks were bound states of something smaller, i.e., if they were composite particles, then we can pump energy into a quark, excite it, and then watch the excited quark relax back into its ground state.

Feynman diagram representing heavy excited quark (q*) production from quark (q)-gluon (g) scattering in proton collisions.

Observing an excited quark would tell us that the quark model may not be the whole story after all. Presently, the quark model is the best description of protons and neutrons, and it certainly works very, very well, but this does not have to be the case. Nature may have something special in store for us. However, this is not why I think excited quarks are so odd and interesting. What is not obvious is that excited quarks, if they exist, could show up immediately after turning the LHC back on.

Early Dijet Discoveries at LHC Run II

Excited quarks participate in the strong nuclear force (QCD) just like ordinary quarks, which means they can absorb and radiate gluons with equal strength. This is key because protons at the LHC are just brimming with highly energetic quarks and gluons. Of particles in a proton carrying a small-to-medium fraction of the proton’s total energy, gluons are the most commonly found particle in a proton (red g curve below). Of those particles carrying a large fraction of the proton’s energy, the up and down quarks are the most common particles (blue u and green d curves below). Excited quarks, if they exist, are readily produced because their ingredients are the most commonly found particles in the proton.

Distributions of partons in a proton. The x-axis represents the fraction of the proton’s energy a parton has (x=1 means that the parton has 100% of the proton’s energy). The y-axis represents the likelihood of observing a parton. The left (right) plot corresponds to low (high) energy collisions. Credit: MSTW

When an excited quark decays, it will split back into quark and gluon pair. These two particles will be very energetic (each will have energy equal to half the mass of the excited quark due to energy conservation), will be back-to-back (by linear momentum conservation), and will each form jets (hadronization in QCD). Such collisions are called “dijet” events (pronounced: die-jet) and look like this

Display for the event with the highest dijet mass (5.15 TeV) observed in CMS data. Image and caption credit: CMS

Although gluons and quarks in the Standard Model can mimic the signal, one can add up the energies of the two jets (which would equal the excited quark’s mass due to energy conservation) and expect to see a bump in the data centered about the mass of the excited quark. Unfortunately, the data (below) do not show such a bump, indicating that excited quarks with masses below a couple TeV do not exist.

Inclusive dijet mass spectrum from wide jets (points) compared to a fit (solid curve) and to predictions including detector simulation of multijet events and signal resonances. The predicted multijet shape (QCD MC) has been scaled to the data. The vertical error bars are statistical only and the horizontal error bars are the bin widths. For comparison, the signal distributions for a W resonance of mass 1.9 CMS.TeV and an excited quark of mass 3.6 CMS.TeV are shown. The bin-by-bin fit residuals scaled to the statistical uncertainty of the data are shown at the bottom and compared with the expected signal contributions. Image and caption credit: CMS

However, this does not mean that excited quarks do not or cannot exist at higher masses. If they do, and if their masses are within the energy reach of the LHC, then excited quarks are very much something we might see in just a few months from now.

Happy Colliding,

Richard Ruiz (@BraveLittleMuon)

Appreciation to Ms. Frost and her awesome physics classes at Whitney M. Young High School in Chicago, Illinois for motivating this post. Good luck on your AP exams!

Tags: @bravelittlemuon, Beyond Standard Model, BSM, Confinement, dijet, Excited Quarks, Hadron Collider, LHC, QCD
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A transverse look into the proton

Friday, December 19th, 2014

Andrea Signori

Protons and neutrons (alias, the nucleons) constitute the building blocks of matter, accounting for almost all the mass of our world. Even if we are still far from understanding their physical inner structure, many efforts have been made to deepen our knowledge about them.

Over the past few years, thanks to a fruitful synergy of theoretical and experimental progress, we have started opening the study of new multi-dimensional images of the structure of proton, investigating the behavior of its fundamental constituents, the quarks and gluons.

When we look into nucleons with extremely high resolution, we are in the regime of perturbative QCD (in other words, a regime where we can really work out mathematical calculations) and quarks and gluons appear almost free. With the due caveats, we can compare the situation to observing water at extreme magnifications, and seeing quasi-free water molecules. As we reduce the magnification, we realize that the molecules clump together in heavier, composite droplets. Eventually, at low magnification they form a single object, like the proton.

Pursuing the analogy, when we are looking at a proton at rest (not smashed inside a collider, for example) it is as if we were unable to describe water starting from the dynamics of molecules. This is because confinement, the reason for quarks and gluons being inescapably bound inside a proton, is left without any rigorous mathematical justification. Confinement is the most crucial characteristic of the theory and represents one of the hardest physics problems of today.

What we can do is to just describe this jam of quarks and gluons giving rise to a proton through mathematical objects specifically introduced in order to “parametrize” our ignorance about its structure: these are what are called parton distribution functions (PDFs), which shape the probability of finding quarks and gluons within a proton.

The knowledge of the multi-dimensional structure of protons allows the analysis of properties otherwise inaccessible. The situation may be compared to diagnostic studies: electrocardiography, for example, gives us mono-dimensional information about the hearth activity. It is of fundamental importance, but it does not give detailed information about the multidimensional inner structure. Instead, more important for this purpose are multi-dimensional tomographies of heart activity (MRI, CT and others). The enormous advantages of medical diagnostic imaging literally revolutionized medicine and surgery. In a similar way, the latest “multi-dimensional” pictures of the nucleon obtained with QCD phenomenology can improve the current status of hadronic physics and aim at better understanding particle physics in general.

Although one-dimensional (collinear) parton distribution functions are extremely useful for studying any process involving hadrons (including the proton-proton collisions taking place at the LHC), from the point of view of nucleon tomography they are rather limited, because they describe the distribution of partons in a single dimension.

More informative distributions are the so-called transverse-momentum-dependent distributions (TMDs). They represent pictures of three-dimensional probabilities in momentum space. The distributions change depending on the energy scale at which they are probed (in a way that is calculable using evolution equations from perturbative QCD) and on the value of the longitudinal fractional momentum.

Partons (quarks and gluons) are like fishes confined inside a fishbowl (the proton). Each parton has its own collinear and transverse velocity, indicated by black and colored arrows respectively. Different colors indicate different flavors for quarks and external excitations (like photons) can extract partons from inside the proton. (credit: A. Signori)

There are many nontrivial questions concerning TMDs that do not have an answer yet, like their most truthful mathematical representation. At present, we know that experimental data form proton-proton and electron-proton collisions point towards Gaussian shapes (if the spin of quarks is neglected), but other forms could do the job as well.

An important question concerns the flavor dependence of transverse-momentum-dependent distributions: are up quarks moving in the nucleon with greater velocity than the down ones, or vice versa? What about sea quarks? Are they faster than the other ones? Part of my research activity is devoted to the investigation of this topic, which could be quite relevant both from the theoretical and experimental point of view. After lot of struggling with data analysis, we now know that sea quarks are likely to be faster than up quarks, which are then faster than down ones.

The statistical analysis of the huge amount of data collected at hadron colliders like the Tevatron and the LHC strongly relies on the detailed knowledge of parton distribution functions, both in 1D and 3D (the TMDs!). Before now, data analysis has been carried out assuming that quarks have all the same velocity, but we now know that this is not the case! This means that it will be important to refine the knowledge of quark (and gluons too, in the future) velocities, in order to improve the accuracy and reliability of data analysis. That’s what a PhD student can do during his/her amazing time in scientific research!

Tags: Hadrons, partons, PDFs, physics, QCD, TMDs
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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
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That’s Right, Count Them: 4 Quarks

Friday, January 20th, 2012

Richard Ruiz

Hi All,

Exciting news came out the Japanese physics lab KEK (@KEK_jp, @KEK_en) last week about some pretty exotic combinations of quarks and anti-quarks. And yes, “exotic” is the new “tantalizing.” At any rate, I generally like assuming that people do not know much about hadrons so here is a quick explanation of what they are. On the other hand, click to jump pass “Hadrons 101” and straight to the news.

Hadrons 101: Meeting the Folks: The Baryons & Mesons

Hadrons are pretty cool stuff and are magnitudes more quirky than those quarky quarks. The two most famous hadrons, the name for any stable combination of quarks and anti-quarks, are undoubtedly the proton and the neutron:

According to our best description of hadrons (Quantum Chromodynamics), the proton is effectively* made up two up-type quarks, each with an electric charge of +2/3 elementary charges**; one down-type quark, which has an electric charge of -1/3 elementary charges; and all three quarks are held together by gluons, which are electrically neutral. Similarly, the neutron is effectively composed of two down-type quarks, one up-type quark, and all the quarks are held strongly together by gluons. Specifically, any combination of three quarks or anti-quarks is called a baryon. Now just toss an electron around the proton and you have hydrogen, the most abundant element in the Universe! Bringing together two protons, two neutrons, and two electrons makes helium. As they say, the rest is Chemistry.

However, as the name implies, baryons are not the only type of hadrons in town. There also exists mesons, combinations of exactly one quark and one anti-quark. As an example, we have the pions (pronounced: pie-ons). The π⁺ (pronounced: pie-plus) has an electric charge of +1 elementary charges, and consists of an up-type quark & an anti-down-type quark. Its anti-particle partner, the π^– (pronounced: pie-minus), has a charge of -1, and is made up of an anti-up-type quark & a down-type quark.

If we now include heavier quarks, like strange-type quarks and bottom-type quarks, then we can construct all kinds of baryons, mesons, anti-baryons, and anti-mesons. Interactive lists of all known mesons and all known baryons are available from the Particle Data Group (PDG)***. That is it. There is nothing more to know about hadrons, nor has there been any recent discovery of additional types of hadrons. Thanks for reading and have a great day!

* By “effectively,” I mean to ignore and gloss over the fact that there are tons more things in a proton, like photons and heavier quarks, but their aggregate influences cancel out.

** Here, an elementary charge is the magnitude of an electron’s electron charge. In other words, the electric charge of an electron is (-1) elementary charges (that is, “negative one elementary charges”). Sometimes an elementary charge is defined as the electric charge of a proton, but that is entirely tautological for our present purpose.

*** If you are unfamiliar with the PDG, it is arguably the most useful site to high energy physicists aside from CERN’s ROOT user guides and Wikipedia’s Standard Model articles.

The News: That’s Belle with an e

So KEK operates a super-high intensity electron-positron collider in order to study super-rare physics phenomena. It’s kind of super. Well, guess what. While analyzing collisions with the Belle detector experiment, researchers discovered the existence of two new hadrons, each made of four quarks! That’s right, count them: 1, 2, 3, 4 quarks! In each case, one of the four quarks is a bottom-type quark and another is an anti-bottom quark. (Cool bottom-quark stuff.) The remaining two quarks are believed to be an up-type quark and an anti-down type quark.

The two exotic hadrons have been named Z_b(10610) and Z_b(10650). Here, the “Z” implies that our hadrons are “exotic,” i.e., not a baryon or meson, the subscript “b” indicates that it contains a bottom-quark, and the 10610/10650 tell us that our hadrons weigh 10,610 MeV/c² and 10,650 MeV/c², respectively. A proton’s mass is about 938 MeV/c², so both hadrons are about 11 times heavier than the proton (that is pretty heavy). The Belle Collaboration presser is really great, so I will not add much more.

Other Exotic Hadrons: When Barry met Sally.

For those keeping track, the Belle Collaboration’s recent finding of two new 4-quark hadrons makes it the twelfth-or-so “tetra-quark” discovery. What makes this so special, however, is that all previous tetra-quarks have been limited to include a charm-type quark and an anti-charm-type quark. This is definitely the first case to include bottom-type quarks, and therefore offer more evidence that the formation of such states is not a unique property of particularly charming quarks but rather a naturally occurring phenomenon affecting all quarks.

Furthermore, it suggests the possibility of 5-quark hadrons, called penta-quarks. Now these things take the cake. They are a sort of grand link between elementary particle physics and nuclear physics. To be exact, we know 6-quark systems exist: it is called deuterium, a ~~radioactive~~ stable isotope of hydrogen (Thanks to @incognitoman for pointing out that deuterium is, in fact, stable.). 9-quark systems definitely exist too, e.g., He-3 and tritium. Etc. You get the idea. Discovering the existence of five-quark hadrons empirically establishes a very elegant and fundamental principle: That in order to produce a new nuclear isotope, so long as all Standard Model symmetries are conserved, one must simply tack on quarks and anti-quarks. Surprisingly straightforward, right? Though sadly, history is not on the side of 5-quark systems.

Now go discuss and ask questions! 🙂

Run-of-the-mill hadrons that are common to everyday interactions involving the Strong Nuclear Force (QCD) are colloquially called “standard hadrons.” They include mesons (quark-anti-quark pairs) and baryons (three-quark/anti-quark combinations). Quark combinations consisting of more than three quarks are called “exotic hadrons.”

Happy Colliding.

– richard (@bravelittlemuon)

PS, I am always happy to write about topics upon request. You know, QED, QCD, OED, etc.

http://en.wikipedia.org/wiki/Neutron

Tags: @bravelittlemuon, Atomic, baryons, Belle, chemistry, coffee, Exotic Hadrons, Hadrons, KEK, mesons, neutron, Nuclear, Penta, Pentaquarks, pion, proton, QCD, Tetra, Tetraquark
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Paper vs. Protons (Pt. 1)

Tuesday, July 19th, 2011

Richard Ruiz

It’s summer conference season! Well actually, it is summer school season for me…. but it is summer nonetheless. Last time, I briefly alluded to the fact that I am attending a 10-day summer school on how exactly physicists turn Feynman diagrams (Fig. 1) into numerical predictions, honest-to-goodness numbers that can be tested with an experiment (Fig. 9). Unfortunately, when I started writing my original post I of course decided to make a few pictures… let’s just say I got a little carried away and I am now dividing my summer school adventures into two parts. It’s also 3 am for me. 🙂

My goal for part 1 of “Paper vs. Protons” is to give an intuitive picture of how we generate electron (e-) & positron (e+) pairs when we physically collide two protons. Hopefully, the images are detailed enough so that you don’t have to read the text to understand what is happening. The words are there mostly for completeness.

Figure 1: A quark (q) & an anti-quark (q-bar) with equal and opposite charges combine and become a photon (γ).
The photon then decays into an electron (e-) & a positron (e+).

My colleague/fellow blogger Flip Tanedo has already done an awesome job describing Feynman diagrams, what they are, how they work, and why physicists love them so much. I do neither him nor Feynman justice when I say that the diagrams are simply ways for anyone (not just physicists!) to intuitively visualize how two or more pieces of matter can interact. The point I want to make with figure 1 (above) is that one way we can produce an electron and a positron pair at the Large Hadron Collider (LHC) is by having a quark from one proton and an anti-quark from another proton smash into each other and become a photon (γ). This photon then travels for a very short amount of time (and I mean very short) before it decays into an electron (e-) and a positron (e+). This process can also happen if we were to replace the photon (γ) with a related particle called the Z boson. You can forget about the Z boson for now, though we will need it for the very end of the post.

At the Large Hadron Collider (LHC), we are colliding protons (left black circle) with other protons (right black circle) in order to look for new physics.

Figure 2. Two protons (black circles) are moments from colliding.

We learned a while back ago that the proton is primarily composed of two up-type quarks and one down-type quark. The proton is also made up of something called “gluons,” they help mediate the Strong nuclear force. Gluons are emitted and absorbed from quarks at such a fantastic rate that the proton is ostensibly made of three quarks tied to one another with rigid rope. The three quarks are represented by the red/blue/green circles and the curly lines are the gluons.

Figure 3: The proton is actually made up quarks (red/green/blue circles), gluons (curly lines),
and virtual particles (black circles).

In the image right above you might have noticed that there are small little black circles, these are virtual particles. Quantum Mechanics and Special Relativity tell us that if we have enough energy, then matter can spontaneously form for a short amount of time. These could be muons (my personal favorite) or even other quarks. So long as matter and antimatter are produced in equal amounts all is well in the universe. Things get interesting when these virtual particles are produced right before two protons collide (below).

Figure 4: Two protons are about to collide right after an anti-quark (magenta circle) and its quark partner (not shown) were produced.

If, for instance, an anti-up quark (the magenta dot in the left circle, above… I did not come up with the color convention but I do like it.) were to form, it could then collide with a u-type quark from an oncoming proton (green circle in right circle, above) and become an photon. Jumping now to the image below, we can imagine the photon being that little black dot in center of the two incoming protons.

Figure 5: Two protons (gray circles) are about to collide resulting in an up quark (green circle, right) & an anti-up quark (magenta dot, left) becoming a photon (black dot, center), and decay into an electron & positron (two outgoing arrows).

If we now zoomed in on the collision (below), we would see the two protons physically overlap when they collide and it is at this moment the quark and its anti-partner combine to become a photon. I have removed the gluons just for clarity. Trust me, they are still there.

Figure 6: Two protons (gray circles) are about to collide resulting in an up quark (green circle, right) & an anti-up quark (magenta dot, left) becoming a photon (black dot, center), and decay into an electron & positron (two outgoing arrows).

Here is where things get messy. Imagine a firework exploding and fragmenting into a bunch of small pieces. Well, that is not too different from when two protons collide; they just kind of explode when they smash into each other while traveling at 99.99999% the speed of light. In the image below I left the q q-bar → e+ e- diagram in order to give you an idea how the protons, or what were formerly known as protons, fragment and decay. The dashed arrows should give you an idea of how they fan out.

Figure 7: Post collisions, the remnants of the two protons begin to fragment and decay.

Okay, let’s zoom all the way out because this is all happening in one of the LHC detectors!

Figure 8: How the q q-bar → e+ e- + fragmenting protons might look in a particle detector. The different colors represent the different layers in a collider detector. The beam travels horizontally through the center of the white region.

So one proton enters from the far left and the other proton comes from the far right. Again, the q q → e+ e- diagram has been left as a reference. After the two protons collide, an electron travels one way (long back arrow) and gets stopped pretty early. In a similar fashion, the positron heads out in the opposite direction from the electron in order to conserve momentum (the other long black arrow). The remaining proton fragments continue to decay and just start spewing out particles. The neatest thing about everything above is that we observe this stuff all the time at the LHC. Sadly, I could not find an event that matched our process perfectly. I did, however, find an real life event (below), seen with the ATLAS detector, where a quark and an anti-quark become a Z boson (Remember? Like a photon but heavier.) which then decays into an electron and positron (yellow lines). The remnants of the protons can be seen in teal.

Figure 9: A real q q-bar → Z → e+ e- from proton collisions at the LHC, seen with the ATLAS detector. Click on image for high-res version. The e- and e+ can be seen in yellow and proton fragments in teal.

I had a blast writing this post, even though I had a few WordPress issues. So what do you think? Cool right?

– richard (@bravelittlemuon)

PS Happy Colliding.

Tags: ATLAS, Feynman Diagrams, Gamee, LHC, Phenomenology, QCD, Summer 2011, Zee
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In a World Without Color, Why do I believe in Gluons?

Saturday, July 9th, 2011

Brian Dorney

I’m often asked as a high energy physicist how do we know that the elementary particles exist. One might think such questions are absurd. But, if the scientific method is to stand for anything, then these questions must have merit (and be taken seriously). After all, it is our duty as scientists to take an unbiased skeptical viewpoint; and to report on what is actually observed in nature.

Trust me, I would find a world were Hogwarts Castle actually existed as a school of magic far more interesting. But alas, nature has no room for such things as wands or Horcruxes.

But I thought I’d try to discuss this week how the gluon was “discovered” decades ago. The gluon is represented by the “g” in our “periodic table” of elementary particles:

Experimentally observed members of the Standard Model (Ref. 1)

The gluon is what’s called a “vector boson,” meaning it has spin 1 (in units of planck’s fundamental constant, ℏ). And it is the mediator of the strong nuclear force. The force which is responsible for binding quarks into hadrons and keeping atomic nuclei together. When I say the gluon is a mediator, I mean that when a quark interacts with another quark or anti-quark, it does so by exchanging gluons with the other quark/anti-quark. In fact gluons themselves interact with other gluons by exchanging gluons!!!

But how exactly do the quarks/anti-quarks and gluons interact? Well quarks & gluons (whenever I say quarks, my statement also applies to anti-quarks) carry something called Color Charge. Color is a type of charge (similar to electric charge) in physics. It comes in three types labelled as red, green & blue. Now where as electric charge has a postive and a negtive, color charge has a “color” (i.e. red charge) and an “anti-color” (i.e. anti-red charge). It is this color charge that gives rise to the strong nuclear force, and is what is responsible for the interaction of quarks and gluons with each other. The quantum theory associated with the interactions of quarks and gluons is known as Quantum Chromodynamics (QCD, “Chromo-“ for color!).

However, no particle with a color charge can be directly observed in the universe today. This is due to something called “Color Confinement,” which causes colored particles to form bind together into “white” (all colors present in equal parts), or “colorless” (net color is zero) states. We sometimes call these states “color neutral” or “color singlet” states. Flip Tanedo has written this nice post about Color Confinement if you’d like to know more.

So if an experimentalist cannot directly observe a gluon, how were they discovered? One of the best answers to this question comes from electron-positron colliders, such as the LHC’s predecessor: the Large Electron-Positron Collider (LEP), and this is where our story takes us.

Jet’s in Electron-Positron Collisions

While electrons & positrons do not carry color charge, they can produce colored particles in a collision. The Feynman Diagram for such a process is shown here:

Here an electron and a positron annihilate, emit a virtual photon, which then pair produces a quark and an anti-quark (Image courtesy of Wikipedia, Ref. 2)

Since the quark & anti-quark produced carry color; they must hadronize, or bind together, to form color neutral states. This hadronization process then gives rise to the formation of jets.

If the momentum of the colliding electron and the positron are equal but opposite (the angle between them is 180 degrees), the two jets produced would appear to be “back-to-back.” Meaning that the angle between them is also 180 degrees (For those of you counting, you must look in the center-of-momentum frame).

The reason for this is that momentum must be conserved. If the electron comes in with Y momentum, and the positron comes in from the opposite direction with -Y momentum, then the total momentum of the collision is zero. Then if I sum over all the momentum of all the particles produced in the collision (termed “outgoing” particles), this sum must also equal zero. In this case there are only two outgoing particles, and the angle between them must be 180 degrees!

We call such a collision event a “di-jet event,” because two jets are created. Here’s an example of a Di-Jet Event as seen by the CMS Detector, and would look identical to what is observed in an electron-positron collider.

Di-Jet Event within the CMS Detector, as seen in looking down the beam-pipe in the xy-plane.

The two protrusions of rectangles together with the solid and dotted purple lines represent the two jets in the above image. The black lines represent each jet’s direction. Notice how the angle between them is almost exactly 180 degrees.

Now suppose either the quark or the anti-quark in the above Feynman Diagram was very energetic, and radiated off another particle. QCD tells us that this particle that is radiated is a gluon. The Feynman Diagram for this “gluon radiation” would look like the above diagram, but with one additional “line,” as shown here:

Gluon radiation from an anti-quark in an electron-positron collision (Image courtesy of Wikiepdia, Ref. 2)

We say this Feynman Diagram describes the process e⁺e^– →qqg. Here the anti-quark is shown as radiating a gluon, but the quark could have just as easily radiated a gluon. If the radiated gluon is very energetic, the theory tells us it would have a different direction from the quark and the anti-quark. Thus the gluon would make its own jet!

Now an experimentalist has something to look for! If gluons exist, we should see events in which we have not two, but three jets created in electron-positron collisions. Due to momentum conservation, these three jets should also all lie in the same plane (called “the event plane”); and if the gluon has enough energy, the three jets should be “well separated,” or the angles between the jets are large.

Such electron-positron collision events were observed in the late 1970s/early 1980s at the Positron Electron Tandem Ring Accelerator (PETRA) at the Deutsches Elektronen Synchrotron (DESY). Here are two examples of three jet events observed by the JADE detector (one of the four detectors on PETRA):

A Tri-Jet event observed in the JADE Detector, again looking down the beampipe (Ref. 3)

Another Tri-Jet event observed in the JADE detector (Ref. 4)

From these event displays you can see the grouping of charged & neutral tracks (the solid & dotted lines in the images) in three regions of the JADE detector. Notice how the tracks are clustered, we say they are “collinear.” The reason they are appear collinear is because when a quark/gluon hadronizes, the hardonization process must conserve momentum. The particles produced from hadronization must travel in the same direction as the original quark/gluon. Then because of this collinear behavior the tracks group together to form jets. Notice also how the jets are no longer back-to-back, but are well separated from each other (as expected).

While these images were first reported decades ago, we still observe three jet events today at the LHC and other colliders. Here is an example of a three jet event as recorded by the CMS Detector:

A Tri-Jet event in CMS

But now let’s actually compare some theoretical predictions of QCD to the experimental data seen at PETRA and see if we can come up with a reason to believe in the gluon.

QCD Wins the Day

The MARK-J Collaboration (also one of the detectors at PETRA) decided to investigate three jet events based on two models of the day, the first of which was QCD [4], now a fully formalized theory, which interpreted three jet events as:

e⁺e^– →qqg

In which a gluon is produced in the collision, in addition to the quark and anti-quark. The second model they used was what was called the quark/anti-quark model, or phase-space model [4]. Which interpreted three jet events as simply:

e⁺e^– →qq

In which only a quark and an anti-quark are produced.

To compare their theoretical predictions to the experimental data they looked at how energy was distributed in the detector. They looked to see how well the two predictions matched what was observed by using something called a “normalized chi-squared test” (a test which is still widely used today across all areas of research).

In a normalized chi-squared test, you perform a statistical test between the two “data sets” (in this case one set is the experimental data, the other is the theoretical prediction), from this test you get a “chi-squared” value. If the “chi-squared” value divided by the “number of degrees of freedom” (usually the number of data points available) is equal to one, then we say that the two data sets are well matched. Or, the theoretical prediction has matched the experimental observation. So if one of the two above models (QCD, and the “Phase-Space” model) has a normalized chi-squared value of one or near one when compared with the data, then that is the model that matches nature!

So to make their energy distributions, the MARK-J Collaboration decided to work in a coordinate system defined by three axes [4,5]. The first of which was called the “Thrust” axis, defined as the direction for which the “energy flow” is maximum [4,5]. This basically means the Thrust axis is taken as the direction of the most energetic jet in the event.

The second axis, the “Major” axis, is taken to be perpendicular to the Thrust axis; but with the requirement that the projected energy of the most energetic jet onto the Major axis in is maximized [4,5]. Meaning if I took the dot product between the Major axis and the direction of the most energetic jet, this dot product would always be maximum (but still keep the Major axis and the Thrust axis perpendicular). This additional requirement needs to be specified so that the Major axis is unique (there are an infinite number of perpendicular directions to a given direction).

The third axis, called the “Minor” axis, is then perpendicular to these two. However, it turns out that energy flow along this direction is very close to the minimum energy flow along any axis [4,5].

But let’s not get bogged down in these definitions. All this is doing is setting up a way for us to compare different events all at once; since no two events will have jets oriented in exactly the same way. In addition, these definitions also identify the event plane for each collision event.

So here’s what the energy distributions turned out looking like for all events considered:

Energy distributions in selected three jet events recorded by the MARK-J Collaboration. The black dots are the data points, the dotted line is the theoretical prediction, more details below (Ref. 5).

The angles in the above plots correspond to the where in the energy was deposited within the MARK-J Detector. The distance from the black dots to the center of each graph is proportional to the amount of energy deposited in the detector in this direction [4,5].

Forty events in total were used to make the above distributions [4]. Each event’s jet topologies where re-oriented so they matched the definitions of the Thrust, Major & Minor axes outlined above. From the top diagram labeled as “Thrust-Major” plane we see three “lobes” or clustering of data points. This indicates that the three jet structure, or topology, of these forty events.

By rotating the entire picture along the thrust axis by 90 degrees we end up looking at the “Thrust-Minor” plane, the bottom diagram. Notice how we now only have two clusterings of data points or lobes. This is because we are looking at the event plane edge on. Imagine looking at the Mercedes-Benz symbol. The plane that the three spokes in it is the “Thrust-Major” Plane. Then if I turn it so I can see only the metal rim of the Mercedes symbol, I’m looking in the “Thrust-Minor” plane. So the bottom diagram then illustrates that these events have the jets all lying in a plane, as expected due to momentum conservation.

Now how well did the two theoretical predictions mentioned above match up to the experimental observations?

The “phase space” model (no gluons) was not plotted in the above diagrams. However, the normalized chi-squared value between the experimental data and the “phase space” model was reported as 222/70 [4]; which is nowhere near one! Researchers took this to mean that this theoretical model does not do a good job at describing the observed behavior in nature (and is thus wrong, or missing something).

Now the QCD prediction (with gluons!) is shown as the dotted line in the above diagrams. See how well it matches the experimental data? In fact the normalized chi-squared value between the data and the predictions of QCD was 67/70 [4,5]; now this is close to one! So the predictions of QCD with three jet events being caused by the radiation of an energetic gluon has matched the experimental observation, and given us the proof we needed to believe in gluons!

However, the story of the gluon did not end there. Much more was needed to be done, for example QCD predicts the gluon to have spin 1. These measurements which I have outlined in this post did not measure the spin of the gluon. More work was needed for that; but safe to say by the mid 1980s the gluon was well established as an elementary particle, and we have lived with this knowledge ever since.

Until next time,

-Brian

References

[1] Wikipedia, The Free Encyclopedia, “The Standard Model of Elementary Particles,” http://en.wikipedia.org/wiki/File:Standard_Model_of_Elementary_Particles.svg, July 5^th, 2011.

[2] Wikipedia, The Free Encyclopedia, “Feynmann Diagram Gluon Radiation,” http://en.wikipedia.org/wiki/File:Feynmann_Diagram_Gluon_Radiation.svg, July 5th, 2011.

[3] P. Söding, “On the discovery of the gluon,” The European Physical Journal H, 35 (1), 3-28 (2010).

[4] P. Duinker, “Review of e+e- physics at PETRA,” Rev. Mod. Phys. 54 (2), 325-387 (1982).

[5] D.P. Barber, et. al., “Discovery of Three-Jet Events and a Test of Quantum Chromodynamics at PETRA,” Phys. Rev. Letters, 43 (12), 830-833 (1979).

Tags: DESY, discoveries, event displays, gluons, PETRA, QCD
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