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The Quark-Gluon Plasma Paradox July 9, 2007

Posted by dorigo in physics.

Lazily browsing the web in search of something that could divert my attention from the endless morning talks of the CMS-italy meeting, which is taking place at the 5-star Romano Palace Hotel in Catania, I found myself reading a hep-ph preprint on the “Quark-gluon plasma paradox”, by Dariusz Miskowiec.

The word “paradox” triggers my interest like few other things. The paper in question is a pleasantly easy read, and is very qualitative in style. I have no clue on whether the ideas contained therein are meaningful or crackpotty, but the reasoning is simple enough that it can be summarized here in a simple way. In fact, after a bunch of reports from PASCOS 2007, which I unfortunately wrote in a way hard to understand for whomever lacks a PhD in theoretical particle physics (me included), I made the resolution of keeping the next ten posts in the Physics category at a level simple enough that my 8-years-old son can understand. Explaining a quark-gluon plasma paradox, however, does require some initial pedantic definitions, so bear with me if you will.

A quark-gluon plasma is a state of matter believed to form when the density of hadrons (or their temperature, which is in some sense equivalent: the two quantities are in fact connected by the equation of state of the system) exceeds a certain critical level. Hadrons are particles composed of quarks. Mesons are hadrons composed of quark-antiquark pairs, and baryons are hadrons composed of three quarks. Both have zero net color charge (they are “colorless”), and have integer baryon number B, while quarks and gluons are colored and have fractional (quarks) or zero (gluons) baryon number. To exemplify, you can make a B=0 meson by combining a  B=-1/3  anti-red antiquark with a B=1/3 red quark. Or you can make a B=1 baryon by combining three B=1/3 quarks of the three different “primary” colors red, green, and blue.

These particles, mesons and baryons, may lose their individuality if you bring some of them together at a high enough temperature.  They “melt” in the resulting plasma, composed of quarks and gluons that move around freely, “deconfined”, i.e. not bounded inside an enclosing volume of zero net color and integer baryon number. Quarks and gluons, which are usually sources of the QCD (Quantum ChromoDynamic) color field, are free from the QCD force which usually binds them because they are tightly encircled by other charges, whose effect is to screen their own charge.

A quark-gluon plasma is believed to be present inside neutron stars, and to have constituted the bulk of matter in the initial microsecond after the big bang: two reasons why studying it is of great interest to physicists, astrophysicists, and cosmologists. However, creating a plasma of quarks and gluons is not easy. It is the goal of the highest energy heavy ion collisions that are being produced at the RHIC and that will be studied by the ALICE experiment at the LHC.

By colliding two heavy nuclei at high enough energy, physicists believe that during the brief instants of time when the nuclei overlap, their quark matter will have a temperature high enough to form a plasma. The creation of this funny state of matter can then be detected by observing its decay signatures, which involve a number of peculiar characteristics.

In the paper by Miskowiec these experimental details are not discussed. Instead, one is asked to perform a gedanken experiment by imagining a chunk of  plasma extended into a thin, enormous ring, with a 1000 light years diameter. Let us forget the easy objection that producing such a thing is not a piece of cake, because the paradox obviously requires a good dose of fantasy and just obeying to physical laws.

If you were to cut the ring at one position, Miskowiec argues, the plasma would start to create hadrons – the bound states of the plasma constituents – at the two loose ends, continuing to do so until the ring would completely disappear into a finite number of ordinary particles. But if you were to cut the ring simultaneously at two different ends, separated by light years of distance – “not casually connected”, you might have the plasma hadronize unti the remaining bits have fractional baryon number or non-neutral color charge! (see picture below).

By this reasoning, one is led to believe that baryon number and color charge quantum numbers of hadrons may retain some meaning  even inside a plasma of quarks and gluons – that is to say, that the deconfinement phase is not describable as a sea of independent quarks and gluons uncorrelated and free. Otherwise, one would need to buy into some sort of mechanism a’la Einstein-Podolsen-Rosen, whereby the thousand-light-year ring behaves in some coherent way, such that cutting it at one edge collapses its wavefunction everywhere at once. But that seems to allow for superluminal transfer of information, which is hard to acknowledge. Another possibility involves some restraining assumptions on the way the plasma hadronizes, which appear at odds with the current models of the first instants after the big bang.

One nice feature of the paper is that it makes definite predictions, for a change: quoting from the concluding section,

“… the concept of QGP, state of matter with uncorrelated quarks, antiquarks, and gluons, leads to isolated objects with fractional baryon numbers, unless supernuminal signalling is allowed, or, by some mechanism, the hadronization is restricted to the surface of the QGP volume, meaning that e.g. the hadronization in the Early Universe took at least minutes rather than a couple of microseconds. The third, obvious, way of avoiding the paradox is to declare the uncorrelated QGP as non-existent, and to replace it by a state consisting of quark clusters with integer baryon numbers (resonance matter). Both the surface-hadronization and the resonance matter options result in a liquid- rather than a gas-like structure of the matter. This agrees with the hydrodynamical character of the matter created in nuclear collisions at RHIC and, at the same time, indicates that this character will be preserved at higher temperatures.”

As I noted at the start, I am in no position to decide without further study (which I have no time to embark on) on the soundness of the reasoning illustrated in the paper by Miskowiec.  Anybody here willing to comment ?


1. Andrea Giammanco - July 9, 2007

Sorry for the pedantic correction, but it’s Podolsky, not Podolsen.

I can’t understand (probably because I’m ignorant) why objects with fractional baryon numbers should be such a disaster to have to postulate super-luminal phenomena in order to get rid of them: baryon number conservation, after all, in the SM is an “accidental symmetry” resulting as a by-product of the properties of the gauge symmetries. Can’t we accept a few isolated “almost-hadrons” with fractional B, in the universe? (After all, we tend to accept the theorical possibility of a few sparse topological defects, like magnetic monopoles, for the sake of beautiful unifications.)

2. Andrea Giammanco - July 9, 2007

I realize that in my previous comment I was wrongly mixing baryon number conservation with the color-neutrality. So, please forget the wrong part, but the last question still holds;)

3. Stefan Scherer - July 9, 2007

Hi Tommaso,

that’s a nice “paradox” – it reminds me of “frustration” if you pair up antiferromagnetic spins on triangular lattices, were one guy is always left over. Maybe one can reformulate this “paradox” in that language, or in the language of defects that occur at phase transitions. In a sense, the left-over coloured quark after hadronization is in a false vacuum, so one may make this argument even more formal. That goes in the same direction as Andrea’s comment about things like the magnetic monopoles. I could imaginge that such a discussion (relic single quarks?) has even been done already – there has been a whole lot of literature in the 1980s about the hadronization transition in the early universe, discussed then as a possible seed for structure formation.

Now, my impression is that this paradox may occur because of the much oversimplified vision of the QGP that is used. For example, I did not see a discussion of the backreaction on the colour charges by the strong colour-electric fields one would expect to have at the phase boundaries, and which may mix and homogenize colour charge distributions.

I mean, that the concept of the QGP as a gas of somehow classical particles without any interaction and some triplet bookkeeping charge used in the formation of clusters could go wrong and lead to paradoxes is perhaps not that big a surprise – if confinement was so easy to explain ;-)…

Best, Stefan

4. DB - July 9, 2007

If the hadrons remain in place (in the shape of a ring), I’d suppose they form a sort of “dielectric” between the leftover color charges. After all, if you pull color charges apart, that’s what you expect to get – a dielectric string made from hadrons that you popped out of the vacuum by pulling so hard. No paradox there.

If you try to sweep the hadrons out of the way, then you’ll feel the effects of the color force. That must be true (by locality) even for the single-cut experiment. So the only surprise here is that it takes energy to cut and separate the seemingly neutral QGP ring. In other words, the color field lines would rather span your cut than go all the way around the 1000*pi ly circumference, so it still feels like you’re separating charges.

Maybe that’s equivalent to saying the QGP is more like a liquid than a gas, so I vote for that solution. Bonus points for agreeing with the RHIC results!

5. Guess Who - July 10, 2007

DB, I think I agree. If there happens to be a net charge in one half of the ring, the complementary charge must be in the other half of the ring; if you are able to cut the ring effortlessly, it must mean that no field lines connecting those net charges pass through your cuts, but it does not mean that there are no field lines connecting them at all. For all you (and your assistant) know, there can be a gluon string stretching from anywhere on half-ring A to anywhere on half-ring B – a centimeter from your “scissors”, or 500 light years away.

Or (more likely) when you cut the ring, you happened to push a quark or two out of the way, and they went into the half-ring where they were most wanted.😉

6. Matti Pitkanen - July 10, 2007

Funny coincident, I have just reworked p-adic mass calculations for hadrons: in the resulting model liberation of color is not assumed to occur in RHIC events. The posting Pomeron, valence quarks, and super-canonical dark matter as very dark matter and four postings before it and one after might give some idea about the new picture about hadrons.

In the model hadrons consists of quark space-time sheets glued to hadronic space-time sheets. Hadronic space-time sheets are analogs of hadronic strings and responsible for non-perturbative aspects of hadron physics (jnot reducible to QCD). They carry most of the baryon mass as a matter which has angular momentum and color but no electro-weak charges: ordinary gluons are not in question however. This matter is in a very strong sense dark. Hadron space-time sheet can be visualized as highly tangled string and is rather blackhole like structure and TGD based model of neutron star involves a fusion of the nucleon space-time sheets in the scale of star. Blackhole would be very similar structure but with Scwartschild radius.

Valence quarks space-time sheets are connected by color flux tubes to form connected structures. Their contribution to baryon mass is small: 170 MeV in the case of nucleon. In high energy collisions the structure formed by valence quark space-time sheets separates from the hadronic space-time sheets (“ionization energy” is 170 MeV) and can be identified as “Pomeron”, the anomalous object of Regge model having no Regge trajectory. The separation of this space-time sheet from proton space-time sheet explains the observations made in Hera for some years ago and implying re-incarnation of Pomeron.

Color glass condensate observed in RHIC would mean separation of “Pomerons” from hadronic space-time sheets of colliding nucleons which fuse to form a single larger blackhole like structure. The collision energy would materialize to the colored matter at hadronic space-time sheets. The evaporation of this blackhole would produce final state hadrons.

Coming to the topic of posting: there is no need to assume the separation of quark color above nucleon length scale. Instead of liberation of color valence quarks separation of hadronic blackholes and Pomerons would occur. Similar process would occurs also in strange cosmic ray events like Centauro. The mass of hadronic space-time sheet in the case of nucleon is very nearly equal to that of nucleon and one can wonder how large fraction of dark matter consists of nucleons which have lost their Pomerons!;-)

Cheers, Matti

7. dorigo - July 10, 2007

Hi all,

Andrea – yes, Podolsky-Rosen became Podolsen-Rosen – it would have been funnier if it was Podolsen-Rosky. As for fractional baryon number, I have to agree. I think that abandoning the idea of baryon number conservation – i.e. the locality of it – is inherent in the idea of a quark-gluon plasma: the very concept of a well-defined integer B is at odds with the idea of a non-localized gas of quarks and gluons.

Stefan, that’s right – the “paradox” is just a misnomer for our inability to describe successfully such a complicated phase of matter. Confinement and deconfinement are just two words, behind which lies the deepest secrets of QCD. We have not gotten to the point of saying we know those…

DB, GW – I agree. In particular, the very concept of “cutting the ring” may be in accordance to physical laws but certainly hides the details of how color strings extend and how we cut them.

Matti – thank you for your description of your ideas and TGD. I admit I understand too little of it to be able to comment meaningfully, but I am happy to host your comment here.

Cheers to all,

8. carlbrannen - July 10, 2007

Dorigo, Lovely post and paradox. Quark confinement is yet another piece of nonsense that learners must accept in order to understand the standard model. The early version of quark confinement, heavy quarks, made more sense but had its own problems.

My version of the mass interaction uses preons that do not conserve color charge. So my solution to the paradox is that the two bare color charges will decay to singlets. The decay is slow because the mass interaction is very weak. To a good approximation, color is conserved. So I expect the Higgs to be associated with color non conservation. This is a heavy quark model.

9. island - July 11, 2007

I’m not sure that I understand how hadronization that is restricted to the surface of the QGP volume, and, therefore, occurring over an extended period of time, resolve the paradox?

10. Arun - July 13, 2007

Dealing with paired objects (and not triplets) for simplicity, we imagine the ordinary pairing to be accomplished by strings, connecting pairs of objects, which when cut produces objects at the cut ends and thereby preserves the pairing. One can imagine the plasma to be that the string from each object goes to the point at infinity or else that the string becomes very fat. But string remains nonetheless, and the process of cutting it always produces objects at the cut ends. (If the plasma was by fat strings then we produce diffuse objects as we cut the fat strings). But the objects **always** remain paired no matter how large the plasma, even in rings 1000 lightyears across.

Then being in a quantum coherent state doesn’t matter. I do not know if physically what I wrote makes sense, but anyway it shows that the paradox is really physical, not logical.

11. Arun - July 13, 2007

Sorry, I should say objects **always** remain paired no matter how large the plasma (provided the plasma was created from paired objects in the first place).

12. island - July 13, 2007

provided the plasma was created from paired objects in the first place.

Inherent asymmetry… We have a winner here, folks.

Somebody give that man a cigar…😉

13. dorigo - July 13, 2007

Hi Carl,

your theory is interesting, and I would love to have more time to learn about it – but until the SM is disproven, if you want others to take you seriously you should take the current wisdom seriously – meant as opposed to ironically.


14. dorigo - July 13, 2007

Hi Island,

I think the issue has to do with the topology of strings in space rather than with the time coordinate.

Arun, what you write makes sense to me – indeed, the weakest point of the “paradox” is the fact that one gives for granted that a plasma can be “cut” in arbitrary ways.


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