Archive for quarks

R.I.P. Murray Gell-Mann (1929-2019)

Posted in The Universe and Stuff with tags , , , on May 25, 2019 by telescoper

I heard this morning of the death of Murray Gell-Mann who passed away yesterday at the age of 89. Professor Gell-Mann was awarded the Nobel Prize for Physics in 1969 for his work on elementary particle physics, specifically for the development of the quark model. It was Gell-Mann who appropriated the phrase from James Joyce’s Finnegans Wake (‘Three quarks for Muster Mark’) from which the word `quark’ passed into the scientific lexicon.

There will be proper tributes from people who knew the man and his science far better than I do, so I’ll just say here that he was a man who made enormous contributions to physics and who will be greatly missed.

Rest in peace Murray Gell-Mann (1919-2019).

A New Baryon on the Block

Posted in The Universe and Stuff with tags , , , , , on April 29, 2012 by telescoper

I just chanced upon the news that a new particle has been discovered at the Large Hadron Collider. This is probably old hat for people who work at CERN, but for those of us following along in their wake it definitely belongs to the category of things marked Quite Interesting.

The new particle is a baryon, which means that it consists of three quarks. These quarks are held together by the colour force (which I refuse to spell the American way); baryonic states exist by virtue of the colours of constituent quarks being a red-green-blue mixture that is colourless.

Quarks are fermions with spin 1/2. The new particle has spin 3/2 which contrasts with the most familiar baryons, the proton and the neutron, which also consist of three quarks but which have spin 1/2. The difference can be understood from basic quantum mechanics: spins have to be added like vectors, so the three individual quark spins can be added to produce total spin 3/2 or 1/2.

The most familiar spin 3/2 baryons are made from the lightest quarks (the up, down and strange) as shown in the diagram below:

The top row contains no strange quarks, only up and down. In fact the Δ0 and Δ+ contain exactly the same quark compositions as the proton and the neutron (udd and uud respectively), but differ in spin. The next row down contains one strange quark (e.g. uds) , the one below two (e.g uss), and the particle at the bottom is a very famous one called the Ω which is entirely strange (sss). For reasons I’ve never really understood, a strange quark carries a strangeness quantum number S=-1 (why not +1?) and the electrical charge is labelled by q in the diagram.

There are six quark flavours altogether so one can construct further baryonic states by substituting various combinations of heavier quarks (c,b and t) in the basic configurations shown above. There are also excited states with greater orbital energy; all the particles shown above have quarks in the lowest state of orbital angular momentum (L=O). There is then a potential plethora of baryonic particles,  but because all are unstable you need higher and higher energies to bring them into existence. Bring on the LHC.

The new particle is called the Ξb*, and it consists of a combination of up, strange and bottom quarks that required collision energies of 7 TeV to make it. The nomenclature reflects the fact that this chap looks a bit like the particles in the third row of the figure, but with one strange quark replaced by a much more massive bottom quark; this one has zero electrical charge because the charges on the u, s and b are +2/3, -1/3 and -1/3 respectively.

Anyway, here’s the graph that represents the detection of the new baryon on the block:

Only 21 events, mind you, but still pretty convincing. For technical details, see the arXiv preprint here.

Whether you really think of this as a new particle depends on how fundamental you think a particle should be. All six quark species have been experimentally detected and in a sense those are the real particles. Things like the Ξb* are merely combinations of these states. You probably wouldn’t say that an excited state of the hydrogen atom (say with the electron in the 2s energy level) is actually a different particle from the ground state so why do different permutations of the same quarks warrant distinct names?

The answer to this I guess is the fact that the mass of an excited hydrogen atom differs from the ground state by only a tiny amount; electronic energy levels correspond to electron-volt scales compared to the 1000 MeV or so that is the rest-mass energy of the nucleus. It’s all very different when you’re talking about energy levels of quarks in baryonic particles. In such situations the binding energies of the quarks are comparable to, or even larger than, their rest masses because the colour force is very strong and the quarks are whirling around inside baryons  with correspondingly enormous energies. When two creatures have enormously different masses, it’s difficult to force yourself to think of them as different manifestations of the same beast!

Anyway, the naming of this particle isn’t really the important thing. A rose by any other name would smell as sweet. What matters is that existence of this new quark state provides another example of a test of our understanding of quark-quark interactions based on the theory of quantum chromodynamics. You might say that it passed with flying colours…

Get thee behind me, Plato

Posted in The Universe and Stuff with tags , , , , , , , , , , on September 4, 2010 by telescoper

The blogosphere, even the tiny little bit of it that I know anything about, has a habit of summoning up strange coincidences between things so, following EM Forster’s maxim “only connect”, I thought I’d spend a lazy saturday lunchtime trying to draw a couple of them together.

A few days ago I posted what was intended to be a fun little item about the wave-particle duality in quantum mechanics. Basically, what I was trying to say is that there’s no real problem about thinking of an electron as behaving sometimes like a wave and sometimes like a particle because, in reality (whatever that is), it is neither. “Particle” and “wave” are useful abstractions but they are not in an exact one-to-one correspondence with natural phenomena.

Before going on I should point out that the vast majority of physicists are well away of the distinction between, say,  the “theoretical” electron and whatever the “real thing” is. We physicists tend to live in theory space rather than in the real world, so we tend to teach physics by developing the formal mathematical properties of the “electron” (or “electric field”) or whatever, and working out what experimental consequences these entail in certain situations. Generally speaking, the theory works so well in practice that we often talk about the theoretical electron that exists in the realm of mathematics and the electron-in-itself as if they are one and the same thing. As long as this is just a pragmatic shorthand, it’s fine. However, I think we need to be careful to keep this sort of language under control. Pushing theoretical ideas out into the ontological domain is a dangerous game. Physics – especially quantum physics – is best understood as a branch of epistemology. What is known? is safer ground than what is there?

Anyway, my  little  piece sparked a number of interesting comments on Reddit, including a thread that went along the lines “of course an electron is neither a particle nor a wave,  it’s actually  a spin-1/2 projective representation of the Lorentz Group on a Hilbert space”. That description, involving more sophisticated mathematical concepts than those involved in bog-standard quantum mechanics, undoubtedly provides a more complete account of natural phenomena associated with the electrons and electrical fields, but I’ll stick to my guns and maintain that it still introduces a deep confusion to assert that the electron “is” something mathematical, whether that’s a “spin-1/2 projective representation” or a complex function or anything else.  That’s saying something physical is a mathematical. Both entities have some sort of existence, of course, but not the same sort, and the one cannot “be” the other. “Certain aspects of an electron’s behaviour can be described by certain mathematical structures” is as I’m  prepared to go.

Pushing deeper than quantum mechanics, into the realm of quantum field theory, there was the following contribution:

The electron field is a quantum field as described in quantum field theories. A quantum field covers all space time and in each point the quantum field is in some state, it could be the ground state or it could be an excitation above the ground state. The excitations of the electron field are the so-called electrons. The mathematical object that describes the electron field possesses, amongst others, certain properties that deal with transformations of the space-time coordinates. If, when performing a transformation of the space-time coordinates, the mathematical object changes in such a way that is compatible with the physics of the quantum field, then one says that the mathematical object of the field (also called field) is represented by a spin 1/2 (in the electron case) representation of a certain group of transformations (the Poincaré group, in this example).I understand your quibbling, it seems natural to think that “spin 1/2″ is a property of the mathematical tool to describe something, not the something itself. If you press on with that distinction however, you should be utterly puzzled of why physics should follow, step by step, the path led by mathematics.

For example, one speaks about the ¨invariance under the local action of the group SU(3)” as a fundamental property of the fields that feel the nuclear strong force. This has two implications, the mathematical object that represents quarks must have 3 ¨strong¨ degrees of freedom (the so-called color) and there must be 32-1 = 8 carriers of the force (the gluons) because the group of transformations in a SU(N) group has N2-1 generators. And this is precisely what is observed.

So an extremely abstract mathematical principle correctly accounts for the dynamics of an inmensely large quantity of phenomena. Why does then physics follow the derivations of mathematics if its true nature is somewhat different?

No doubt this line of reasoning is why so many theoretical physicists seem to adopt a view of the world that regards mathematical theories as being, as it were,  “built into” nature rather than being things we humans invented to describe nature. This is a form of Platonic realism.

I’m no expert on matters philosophical, but I’d say that I find this stance very difficult to understand, although I am prepared to go part of the way. I used to work in a Mathematics department many years ago and one of the questions that came up at coffee time occasionally was “Is mathematics invented or discovered?”. In my experience, pure mathematicians always answered “discovered” while others (especially astronomers, said “invented”). For what it’s worth, I think mathematics is a bit of both. Of course we can invent mathematical objects, endow them with certain attributes and proscribe rules for manipulating them and combining them with other entities. However, once invented anything that is worked out from them is “discovered”. In fact, one could argue that all mathematical theorems etc arising within such a system are simply tautological expressions of the rules you started with.

Of course physicists use mathematics to construct models that describe natural phenomena. Here the process is different from mathematical discovery as what we’re trying to do is work out which, if any, of the possible theories is actually the one that accounts best for whatever empirical data we have. While it’s true that this programme requires us to accept that there are natural phenomena that can be described in mathematical terms, I do not accept that it requires us to accept that nature “is” mathematical. It requires that there be some sort of law governing some  of aspects of nature’s behaviour but not that such laws account for everything.

Of course, mathematical ideas have been extremely successful in helping physicists build new physical descriptions of reality. On the other hand, however, there is a great deal of mathematical formalism that is is not useful in this way.  Physicists have had to select those mathematical object that we can use to represent natural phenomena, like selecting words from a dictionary. The fact that we can assemble a sentence using words from the Oxford English Dictionary that conveys some information about something we see doesn’t not mean that what we see “is” English. A whole load of grammatically correct sentences can be constructed that don’t make any sense in terms of observable reality, just as there is a great deal of mathematics that is internally self-consistent but makes no contact with physics.

Moreover, to the person whose quote I commented on above, I’d agree that the properties of the SU(3) gauge group have indeed accounted for many phenomena associated with the strong interaction, which is why the standard model of particle physics contains 8 gluons and quarks carrying a three-fold colour charge as described by quantum chromodynamics. Leaving aside the fact that QCD is such a terribly difficult theory to work with – in practice it involves  nightmarish lattice calculations on a scale to make even the most diehard enthusiast cringe –  what I would ask is whether this  description in any case sufficient for us to assert that it describes “true nature”?  Many physicists will no doubt disagree with me, but I don’t think so. It’s a map, not the territory.

So why am I boring you all with this rambling dissertation? Well, it  brings me to my other post – about Stephen Hawking’s comments about God. I don’t want to go over that issue again – frankly, I was bored with it before I’d finished writing my own blog post  – but it does relate to the bee that I often find in my bonnet about the tendency of many modern theoretical physicists to assign the wrong category of existence to their mathematical ideas. The prime example that springs to my mind is the multiverse. I can tolerate  certain versions of the multiverse idea, in fact. What I can’t swallow, however is the identification of the possible landscape of string theory vacua – essentially a huge set of possible solutions of a complicated set of mathematical equations – with a realised set of “parallel universes”. That particular ontological step just seems absurd to me.

I’m just about done, but one more thing I’d say to finish with is concerns the (admittedly overused) metaphor of maps and territories. Maps are undoubtedly useful in helping us find our way around, but we have to remember that there are always things that aren’t on the map at all. If we rely too heavily on one, we might miss something of great interest that the cartographer didn’t think important. Likewise if we fool ourselves into thinking our descriptions of nature are so complete that they “are” all that nature is, then we might miss the road to a better understanding.


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Nicola Cabibbo (1935-2010)

Posted in The Universe and Stuff with tags , , , , on August 16, 2010 by telescoper

Just a short post to convey the very sad news that the great Italian physicist Nicola Cabibbo passed away today at the age of 75. I know I’m not alone in thinking that he should have received a share of the Nobel prize in 2008, which was awarded to Yoichiro Nambu (half the prize) and the other half was split between Makoto Kobayashi and Toshihide Maskawa.

As I wrote in 2008:

All three are extremely distinguished physicists and their contributions certainly deserve to be rewarded. But, in the case of Kobayashi and Maskawa, the Nobel Foundation has made a startling omission that I really can’t understand at all and which even threatens to undermine the prestige of the prize itself.The work for which these two were given half the Nobel Prize this year relates to the broken symmetry displayed by weak interactions between quarks. We now know that there are three generations of quarks, each containing quarks of two different flavours. The first generation contains the up (u) and the down (d), the second the strange (s) and the charmed (c), and the third has the bottom (b) and the top (t). OK, so the names are daft, but physicists have never been good at names.

The world of quarks is different to penetrate becauses quarks interact via the strong force which binds them close together into hadrons which are either baryons (three quarks) or mesons (a quark and an anti-quark).

But there are other kinds of particles too, the leptons. These are also arranged in three generations but each of these families contains a charged particle and a neutrino. The first generation is an electron and a neutrino, the second a muon and its neutrino, and the third has the tau and another neutrino. One might think that the three quark generations and the three lepton generations might have some deep equivalence between them, but leptons aren’t quarks so can’t interact at all by the strong interaction. Quarks and leptons can both interact via the weak interaction (the force responsible for radioactive beta-decay).

Weak interactions between leptons conserve generation, so the total number of particles of electron type is never changed (ignoring neutrino oscillations, which have only relatively recently been discovered). It seemed natural to assume that weak interactions between quarks should do the same thing, forbidding processes that hop between generations. Unfortunately, however, this is not the case. There are weak interactions that appear to convert u and/or d quarks into c and/or s quarks, but these seem to be relatively feeble compared to interactions within a generation, which seem to happen with about the same strength for quarks as they do for leptons. This all suggests that there is some sort of symmetry lurking somewhere in there, but it’s not quite what one might have anticipated.

The explanation of this was proposed by Nicola Cabibbo who, using a model in which there are only two quark generations, developed the idea that states of pure quark flavour (“u” or “d”, say) are not really what the weak interaction “sees”. In other words, the quark flavour states are not proper eigenstates of the weak interaction. All that is needed is to imagine that the required eigenstates are a linear combination of the flavour states and, Bob’s your uncle, quark generation needn’t be conserved. This phenomenon is called Quark Mixing. What makes it simple for only two generations is that it can be described entirely by one number: the Cabibbo angle, which measures how much the quark flavour basis is misaligned with the weak interaction basis. The angle is small so the symmetry is only slightly broken.

Kobayashi and Maskawa generalized the work of Cabibbo to the case of three quark generations. That’s actually quite a substantial task as the description of mixing in this case requires not just a single number but a 3×3 matrix each of whose entries is complex. This matrix is universally called the Cabibbo-Kobayashi-Maskawa (CKM) matrix and it now crops up all over the standard model of particle physics.

And there’s the rub. Why on Earth was Cabibbo not awarded a share of this year’s prize? I was shocked and saddened to find out that he’d been passed over despite the fact that his work so obviously led the way. I can think of no reason why he was omitted. It’s outrageous. I even feel sorry for Kobayashi and Maskawa, because there is certain to be such an outcry about this gaffe that it may detract from their success.

But really

I hope, however,  that controversy doesn’t intrude too much on what I hope will be the forthcoming celebration of Cabibbo’s immense contributions to particle physics. I’ll leave it to the experts to write more detailed appreciations that do better justice to his achievements. I’ll just say that I only met him once in real life, but found him charmingly modest and altogether quite delightful company. He will be greatly missed.


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