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Archive for 2016

B.o.B.

Rap musician, B.o.B. (Image: Frazer Harrison/Getty Images for BMI)

Is the world flat?

That question was posed by popular rap musician B.o.B. on his Twitter account this past week, prompting angry, but comical video and rap responses by popular science communicator Neil deGrasse Tyson and his musician nephew.

What do we really know?

A few thousand years ago, Greek philosophers and Phoenician explorers began to cast doubt on the flat-earth model. They noted differences in star visibility and the sun’s trajectory that depended on the observer’s location, leading them to propose the earth was a sphere. Convinced by this data, as well as the roundness of earth’s shadow cast on the moon during a lunar eclipse, the Greek astronomer Eratosthenes went a step further to estimate the earth’s circumference in 240 BCE. Using trigonometry and shadows cast during the solstice, he came to within a few percent of the actual value. Not bad.

Eratosthenes method for measuring the size of the earth

Image: National Geodetic Survey NOAA, Public Domain.

Evidence backing the round-earth model grew through time and was sufficient five centuries ago to convince sailors they would not fall off earth’s edges. Magellan was the first we know of to circumnavigate the globe and to live to tell about it. Even more convincing were the famous earthrise photos sent down from lunar orbit a few hundred years later. The evidence is overwhelming. So, what’s up with B.o.B.?

Yesterday evening, I had the privilege to discuss the science of the Large Hadron Collider at CERN with a group of 13 and 14 year-olds from Seward, Alaska, USA. They connected via the ATLAS Virtual Visit system to see the experiment and to ask questions about our research. As usual, there were a lot of excellent questions, and fellow CMS physicist, Dave Barney, and I did our best to answer them all.  Then we got to:

“How do you understand things you can’t see?”

Only youth can ask a question so profound.

This started me thinking about our friend B.o.B., and it occurred to me that his skepticism is not so different from that of the student nor even of the scientists at CERN who hunted for the Higgs boson.

More than fifty years ago, an idea was formed by a group of theorists, including François Englert, Robert Brout, and Peter Higgs, essentially describing how fundamental particles attain mass. The proposed mechanism requires the existence of a pervasive, non-directional (we call it scalar) force field and its associated particle, now known as the Higgs boson. It became central to a new theory, called the Standard Model, used by physicists to describe the fundamental particles that make up matter and the forces that act upon them.

Apollo8-Earthrise

Earthrise from moon, shot by astronauts orbiting in Apollo 8 capsule. Image: NASA

The Standard Model, much like the round-earth model, proved itself over time. Just as sailors bet their lives that the earth was a sphere before seeing photos from space, physicists included the Higgs field in their theory and were able to make accurate predictions of the existence (and even the mass) of new particles before seeing images of the Higgs boson. But, we still asked:

Does the Higgs boson exist?

Yes, the empirical evidence was convincing, but just like Magellan, the astronauts, and B.o.B., we scientists wanted our photos. These finally came in 2012, in the form of high-energy proton collisions in the ATLAS and CMS detectors at CERN. Yes, there is something reassuring in seeing it with our own eyes (or detectors).

So, what’s the problem with B.o.B.? If scientists, explorers, and students have the right to be skeptical, why not a musician?

I don’t think Neil deGrasse Tyson is complaining that B.o.B. posed a question. Skepticism is key to the scientific process and questions should be asked. It is far better to ask questions than it is to blindly believe the authoritative figures who present “facts”. If you have doubts, by all means, ask!

Higgs Boson, ATLAS, Physics Events

Candidate Higgs boson decay to 2 photons. Image: ATLAS Experiment © 2011 CERN, CC-BY-SA-4.0

But, B.o.B. went further. He presented a theory (in this case, a very old one) as fact. And he did this without any serious evidence to back it up. This is irresponsible for anyone, but especially for someone who is seen as an authoritative figure by his fans, and moreover for someone who has the means and ability to know better.

We can take comfort in the fact that science is based on uncovering the truth and that truth ultimately reveals itself. But human progress depends on our ability to build upon well-established bricks of knowledge. Sure, we should check the solidity of those bricks from time to time, but let’s not waste effort trying to break them for no good reason.

As a physicist, I am often challenged by friends and family to explain the relevance of our work. So, when the opportunity came last fall to speak at TEDxTUM in Munich, I happily responded to that very question with a simple answer: We have no choice. Human survival depends on basic research. Without our drive to explore and to understand the world, our species would not still be here. We would have starved, been eaten, or died of disease, a long time ago. Hence the threat of B.o.B.

And B.o.B. is not alone.

Powerful people who would like to be world leaders are acting similarly or worse, attacking evidence-based science for the sake of political gain. And while a flat-earth conspiracy might be innocuous or even silly, those who deny important measurements, such as those of climate change, threaten our survival much more directly.

So, when scientists react to B.o.B. with words, images, or even song, they are not just defending their turf, they are expressing primal instincts. They are defending our species. And when individuals like B.o.B. threaten human survival, I suggest they watch their back. They might just get pushed off the edge of the earth.

A question of survival: Why we hunted the Higgs. (Video: TEDxTUM)

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Depuis le 15 décembre, j’ai compté 200 nouveaux articles théoriques, chacun offrant une ou plusieurs explications possibles sur la nature d’une nouvelle particule qui n’a pas encore été découverte. Cette frénésie a commencé lorsque les expériences CMS et ATLAS ont toutes deux rapporté avoir trouvé quelques événements qui pourraient révéler la présence d’une nouvelle particule se désintégrant en deux photons. Sa masse serait autour de 750 GeV, soit cinq fois la celle du Higgs boson.

Personne ne sait si un tel engouement est justifié mais cela illustre combien les physiciens et physiciennes espèrent une découverte majeure dans les années à venir. Est-ce que cela se passera comme pour le boson de Higgs, qui fut officiellement découvert en juillet 2012, bien que quelques signes avant-coureurs apparurent un an auparavant ? Il est encore bien trop tôt pour le dire. Et comme je l’avais écrit en juillet 2011, c’est comme si nous essayions de deviner si le train s’en vient en scrutant l’horizon par une morne journée d’hiver. Seule un peu de patience nous dira si la forme indistincte à peine visible au loin est bien le train longuement attendu ou juste une illusion. Il faudra plus de données pour pouvoir trancher, mais en attendant, tout le monde garde les yeux rivés sur cet endroit.
LeTrainDeMidiLe train de midi, Jean-Paul Lemieux, Galerie nationale du Canada

En raison des difficultés inhérentes à la reprise du LHC à plus haute énergie, la quantité de données récoltées à 13 TeV en 2015 par ATLAS et CMS a été très limitée. De tels petits échantillons de données sont toujours sujets à de larges fluctuations statistiques et l’effet observé pourrait bien s’évaporer avec plus de données. C’est pourquoi les deux expériences se sont montrées si réservées lors de la présentation de ces résultats, déclarant clairement qu’il était bien trop tôt pour sauter au plafond.

Mais les théoriciens et théoriciennes, qui cherchent en vain depuis des décennies un signe quelconque de phénomènes nouveaux, ont sauté sur l’occasion. En un seul mois, y compris la période des fêtes de fin d’année”, 170 articles théoriques avaient déjà été publiés pour suggérer autant d’interprétations différentes possibles pour cette nouvelle particule, même si on ne l’a pas encore découverte.

Aucune nouvelle donnée ne viendra avant quelques mois en raison du de la maintenance annuelle. Le Grand Collisionneur de Hadrons repartira le 21 mars et devrait livrer les premières collisions aux expériences le 18 avril. On espère un échantillon de données de 30 fb-1 en 2016, alors qu’en 2015 seuls 4 fb-1 furent produits. Lorsque ces nouvelles données seront disponibles cet été, nous saurons alors si cette nouvelle particule existe ou pas.

Une telle possibilité serait une véritable révolution. Le modèle théorique actuel de la physique des particules, le Modèle Standard, n’en prévoit aucune. Toutes les particules prédites par le modèle ont déjà été trouvées. Mais puisque ce modèle laisse encore plusieurs questions sans réponses, les théoriciennes et théoriciens sont convaincus qu’il doit exister une théorie plus vaste pour expliquer les quelques anomalies observées. La découverte d’une nouvelle particule ou la mesure d’une valeur différente de celle prévue par la théorie révèleraient enfin la nature de cette nouvelle physique allant au-delà du Modèle Standard.

Personne ne connaît encore quelle forme cette nouvelle physique prendra. Voilà pourquoi tant d’explications théoriques différentes pour cette nouvelle particule ont été proposées. J’ai compilé certaines d’entre elles dans le tableau ci-dessous. Plusieurs de ces articles décrivent simplement les propriétés requises par un nouveau boson pour reproduire les données observées. Les solutions proposées sont incroyablement diversifiées, les plus récurrents étant diverses versions de modèles de matière sombre ou supersymétriques, de Vallée Cachée, de Grande Théorie Unifiée, de bosons de Higgs supplémentaire ou composites, ou encore des dimensions cachées. Il y en a pour tous les goûts : des axizillas au dilatons, en passant pas les cousins de pions sombres, les technipions et la trinification.

La situation est donc tout ce qu’il y a de plus clair : tout est possible, y compris rien du tout. Mais n’oublions pas qu’à chaque fois qu’un accélérateur est monté en énergie, on a eu droit à de nouvelles découvertes. L’été pourrait donc être très chaud.

Pauline Gagnon

Pour en savoir plus sur la physique des particules et les enjeux du LHC, consultez mon livre : « Qu’est-ce que le boson de Higgs mange en hiver et autres détails essentiels».

Pour recevoir un avis lors de la parution de nouveaux blogs, suivez-moi sur Twitter: @GagnonPauline ou par e-mail en ajoutant votre nom à cette liste de distribution.

tableau

Un résumé partiel du nombre d’articles publiés jusqu’à maintenant et le type de solutions proposées pour expliquer la nature de la nouvelle particule, si nouvelle particule il y a. Pratiquement tous les modèles théoriques connus peuvent être adaptés pour accommoder une nouvelle particule compatible avec les quelques événements observés. Ce tableau est juste indicatif et en aucun cas, strictement exact puisque plusieurs articles étaient plutôt difficiles à classer. Une de ces idées s’avèrera-t-elle être juste ?

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Frenzy among theorists

Thursday, February 4th, 2016

Since December 15, I have counted 200 new theoretical papers, each one suggesting one or several possible explanations for a new particle not yet discovered. This flurry of activity started when the CMS and ATLAS Collaborations both reported having found a few events that could possibly reveal the presence of a new particle decaying to two photons. Its mass would be around 750 GeV, that is, five times the mass of the Higgs boson.

No one knows yet if all this excitement is granted but it clearly illustrates how much physicists are hoping for a huge discovery in the coming years. Will it be like with the Higgs boson, which was officially discovered in July 2012 but had already given some faint signs of its presence a year earlier? Right now, there is not enough data. And just as I wrote in July 2011, it is as if we were trying to guess if the train is coming by looking in the far distance on a grey winter day. Only time will tell if the indistinct shape barely visible above the horizon is the long awaited train or just an illusion. But until more data become available, everybody will keep their eyes on that spot.

LeTrainDeMidi

The noon train, Jean-Paul Lemieux, National Gallery of Canada

Due to the difficulties inherent to the restart of the LHC at higher energy, the amount of data collected at 13 TeV in 2015 by ATLAS and CMS was very limited. Given that small data samples are always prone to large statistical fluctuations, the experimentalists exerted much caution when they presented these results, clearly stating that any claim was premature.

But theorists, who have been craving for signs of something new for decades, jumped on it. Within a single month, including the end-of-the-year holiday period, 170 theoretical papers were published to suggest just as many possible different interpretations for this yet undiscovered new particle.

No new data will come for a few more months due to annual maintenance. The Large Hadron Collider is due to restart on March 21 and should deliver the first collisions to the experiments around April 18. The hope is to collect a data sample of 30 fb-1 in 2016, to be compared with about 4 fb-1 in 2015. Later this summer, when more data will be available, we will know if this new particle exists or not.

This possibility is however extremely exciting since the Standard Model of particle physics is now complete. All expected particles have been found. But since this model leaves many open questions, theorists are convinced that there ought to be a more encompassing theory. Hence, discovering a new particle or measuring anything with a value different from its predicted value would reveal at long last what the new physics beyond the Standard Model could be.

No one knows yet what form this new physics will take. This is why so many different theoretical explanations have been proposed for this possible new particle. I have compiled some of them in the table below. Many of these papers described the properties needed by a new boson to fit the actual data. The solutions proposed are incredibly diversified, the most recurrent ones being various versions of dark matter or supersymmetric, new gauge symmetries, Hidden Valley, Grand Unified Theory, extra or composite Higgs bosons and extra dimensions. There enough to suit every taste: axizillas, dilatons, dark pion cousins of a G-parity odd WIMP, one-family walking technipion or trinification.

It is therefore crystal clear: it could be anything or nothing at all… But every time accelerators have gone up in energy, new discoveries have been made. So we could be in for a hot summer.

Pauline Gagnon

Learn more on particle physics, don’t miss my book, which will come out in English in July.

To be alerted of new postings, follow me on Twitter: @GagnonPauline  or sign-up on this mailing list to receive an e-mail notification.

table

A partial summary of the number of papers published so far with the type of solutions they proposed to explain the nature of the new particle, if new particle there is. Just about all known theoretical models can be adapted to produce a new particle with characteristics compatible with the few events observed. This is just indicative and by no means, strictly exact since many proposals were rather hard to categorize. Will one of these ideas be the right one?

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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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