**About Gluons and QCD**

A gluon is one of a set of eight particles that transmits the strong nuclear force from quark to quark containing two color charges in the Standard Model of Particle Physics, in a manner analogous to the way that photons transmit the electro-magnetic force. Gluons differ from each other only in color, usually expressed as R, G, B, anti-R, anti-G, and anti-B. One would think that three by three possibilities would create nine gluons, but the math of the theory rules on combination out.

Gluons are always confined to color neutral composite particles made up of three quarks (baryons such as the proton and neutron), or two quarks (called mesons), although it is theoretically possible to have larger color neutral composite particles made of quarks and the search is on for them.

Generally gluons are described as having zero mass and no charge, a conclusion theoretically limited by the reality of confinement.

A set of equations called Yang-Mills theory is strongly believed to exactly describe the behavior of quarks and gluons via the strong nuclear force. This area of physics is called quantum chromodynamics (QCD), because it involves color charges, but it is very hard to apply mathematically and experimental results are more precise than any of its predictions. QCD interactions do not appear to interact with leptons (i.e. various flavors of electrons and neutrinos) or with other bosons (i.e. photons and the particles that transmit the weak nuclear force called the W+, the W- (which is the antiparticle of the W+), and the Z.

**The Case For Gluon Mass**

Despite the conventional description of gluons as massless, in the 1980s, research on the Yang-Mills theory suggested that gluons do have an effective mass of 600 MeV/c^2 +/- 25% and that this influences the way that unstable baryons and mesons decay because the high mass of a gluon disfavors decay paths that include "gluon intermediate states."

Two recent investigations that are independent both from each other, and from the original researcher in the 1980s (although, of course, they read each other publications), have proposed a gluon effective mass of 500 MeV/c^2 (which is consistent with the original estimate) by applying Yang-Mills theory in different ways.

Experimental evidence also suggests that "in the low energy limit, glue carries no spin. Rather, true excitations of the Yang-Mills field are some kind of colorless states that makes the spectrum and having the lower state with a massive glueball that can also be seen in labs."

Thus, while gluons are ordinarily thought of as zero mass, spin-1 particles, which accurately summarizes their apparent behavior in the high energy limit, but in the low energy limit gluons decouple from quarks and form glue balls that act like 500 MeV/c^2 mass, spin-0 particles that are colorless.

For comparison's sake, the currently measures values of the other particles in the Standard Model are as approximately as follows (in MeV/c^2 units):

Electron Neutrino: Less than 0.000007

Electron: 0.511

Up Quark: 2-8

Down Quark: 5-15

Muon: 105.7

Muon Neutrino: Less than 0.27

Charm Quark: 1,000-1,600

Strange Quark: 100-300

Tau: 1777

Tau Neutrino: Less than 31

Top Quark: 168,000-192,000

Bottom Quark: 4,100-4,500

W Particles: 80,398

Z Particle: 91,188

Photon: Zero

The predicted mass value for the Higgs Boson tends to hover around 129, with about 114 to 154 being the range where it is not strongly excluded by experimental evidence.

Thus, a low energy state gluon would appear to have more mass than any kind of neutrino, a photon, an electron, a muon, an up quark, a down quark, a strange quark, or a Higgs boson. But, a low energy state gluon has less mass than a charm quark, a top quark, a bottom quark, a W particle, or a Z particle.

Indeed, a low energy state gluon with spin zero and a 500 MeV/c^2 mass, looks quite a bit like one of the electrical charge neutral, colorless Higgs bosons found in supersymmetry theories.

Free gluons appear in the low energy limit decoupled from their quarks. Thus, QCD, and gluons in particular, looks quite different in the low energy limit than in the high energy limit.

For those of you who haven't been paying attention, this is quite remarkable.

It is a rare day when a Standard Model particle mass, let alone eight of them, are determined purely from theory which is different from the pre-existing conventional wisdom. There are, after all, only 37 particles in the Standard Model (including anti-particles, but ignoring chirality and polarization): 12 quarks type particles, 6 electron type particles, 6 neutrino type particles, 1 photon, 3 weak force particles, 8 gluons, and the Higgs boson, and all but the Higgs boson have been experimentally observed for more than a decade.

Note that the six neutrinos has just been confirmed to have mass for less than a year.

Both of these results precede the arrival of any Large Hadron Collider data.

This now leaves the photon as the only massless particle in the Standard Model, which relies on the undiscovered Higgs boson to create mass in the first place.

We now have good reason to believe that there are fourteen more particles that interact with the Higgs field to obtain mass than we did when the Higgs process was originally contemplated, and this is without having discovered any new particles.

The massless photon result is likely to stand, however, as there are deep reasons related to the calculations that determine how photons move in quantum mechanics, and deep reasons in general relativity, for the photon to be massless, and the photon's behavior is understood with more theoretical precision than any other Standard Model particle.

**Beyond Gluons**

Research, both theoretical and experimental, also favors a model in which particles made of quarks exchange not just gluons, but also pions, which are two quark mesons (made of up or down flavor quarks) that come in three varieties, have spin zero, and act in a manner similar to a boson that exchanges forces between particles like the photon and the gluon in the low energy limit of the theory. These are called "pseudo-Goldstone bosons."

The experiments involved measure proton spin statistics and attempt to reconcile them with the theory, an effort that has been underway and reached no resolution since Feynman discussed it in his QED lectures in the 1980s, so far without success, although results are now tantalizingly close.

**Millenium Problem in QCD Solved?**

One of the grand prizes in mathematics is the Millenium Prize, which awards $1,000,000 to the first person to solve one of seven very hard unsolved problems in applied mathematics proposed in the year 2000. One was solved in March of this year (the PoincarĂ© conjecture, a problem in topology related to what is necessary to prove that a shape is topologically equivalent to a three dimensional sphere). Six remain unsolved after a decade.

A problem allegedly solved now relates to quantum chromodynamics, but a proposed solution from a Russian physicist at The Ohio State University, has not yet been evaluated to determine if it is correct.

The problem requires proof that:

the quantum field theory underlying the Standard Model of particle physics, called Yang-Mills theory, satisfies the standard of rigor that characterizes contemporary mathematical physics, i.e. constructive quantum field theory. The winner must also prove that the mass of the smallest particle predicted by the theory be strictly positive, i.e., the theory must have a mass gap. . . .

beyond a certain scale, known as the QCD scale (more properly, the confinement scale, as this theory is devoid of quarks), the color charges are connected by chromodynamic flux tubes leading to a linear potential between the charges. (In string theory, this potential is the product of a string's tension with its length.) Hence free color charge and free gluons cannot exist. In the absence of confinement, we would expect to see massless gluons, but since they are confined, all we see are color-neutral bound states of gluons, called glueballs. If glueballs exist, they are massive, which is why we expect a mass gap.

The proposed proof, if true, would establish that the Standard Model is mathematically "well behaved," rather than a mere "dirty trick" of physicists that is conceptually flawed.

This doesn't require proof, however, that Yang-Mills theory actually describes nature, only proof that if it did, that it would be a mathematically consistent way of dong so. In the case of Quantum Electrodynamics (QED) the evidence that the theory describes reality is overwhelming. But, scientific understanding of the strong and weak nuclear forces is still being refined.

**Implications**

For most practical purposes, QCD is little more than a tool for classifying and predicting the properties of vast numbers of odd, unstable composite particles made up of quarks that are exceedingly rarely observed outside of particle accelerators. One can support an exceedingly technologically sophisticated society with a quite simple proton, neutron model of atomic nuclei and empirical data on how those atomic nuclei behave which is systematized in the period table, tables of atomic isotypes and tables of atomic binding energy each kind of atomic nucleus that can be derived from classical physics. The interesting parts of nuclear physics usually relate to the weak force.

But, if you are a scientist, rather than an engineer, these developments are highly relevant.

From an experimenter's perspective, the results permit high energy physicists to do more accurate experiments without new equipment. Typically, high energy physicists looking at phenomena like CP violations must first separate the interesting part of their data from well understood background information explained by the strong force. The most precisely the strong force is understood, the more accurately other results of a high energy physics experiment can be discerned.

And, both experimenters and theoretical physicists now need to be consider the question of whether massive particle effects observed at the Large Hadron Collider are Higgs bosons or glueballs, or whether they are in fact different names for the same things.

From a theoretical physicists perspective, glueballs raise all sorts of questions about how mass arises. Also, many theoretical models require gluons that are always massless, something that has not been a problem until now. Because gluons interact at very short distances from each other, massive gluons could also be influences in a non-negligible way by gravity, which grows in strength relative to the strong nuclear force as quarks get closer together to each other.

**The Mystery of Mass in Physics**

Mass is a really mysterious and confounding problem in modern physics. Almost everything that is ugly or odd about modern physics is deeply connected to mass. Somehow or other, we are all missing some deeply important piece of the puzzle necessary to understand it.

Most of the unexplained fundamental constants in the Standard Model involve particle masses, or appear to be intimately related to mass like the gravitational constant or the propensity of a particle to undergo beta decay by particular paths.

The deepest divide in quantum mechanics scholarship, between string theorists and proponents of loop quantum gravity, involves the question of whether quantum gravity is a force mediated by a graviton or is a product of the geometry of space-time. The only undiscovered particle in the Standard Model exists to impart mass to particles in the theory.

The separation of the mass imparting Higgs boson from the gravity producing graviton in supergravity theories (including Sting Theory) oddly unwinds the equivalence between inertial mass and gravitational mass that is so central to general relativity, making the equivalence seem merely coincidental.

The weak nuclear force transforms fermions (i.e. quarks, neutrinos and electron-like particles) into identical particles of higher or lower mass. These flavor (a.k.a. generation) transformations were totally unexpected when they are first discovered. Higher mass versions of quarks, neutrinos and electrons are exceedingly unstable. Generally speaking, the heavier a fundamental particle is, the less stable it is. Sixteen of the twenty four fermions in the Standard Model are unstable higher generation versions of their stable cousins.

All observed charge parity symmetry violations (CP violations) involve decays of at least one higher generation particle. Why does the weak interaction so intertwined with mass (e.g. in decay rates), maximally violate parity of all things, despite the fact that parity symmetry appears to be valid for all reactions involving electromagnetism and strong interactions (despite a theoretical possibility of CP violation in strong interactions with the existing equations)? Why are the probabilities of electrons and neutrinos behaving in certain ways in weak interactions so deeply intertwined with the probability that corresponding quarks will do the same and the the mass ratios of the respective particles?

We know that mass and energy are related in a strictly observed conservation relationship, but conservation of mass itself is apparently grossly disregarded in both strong and weak nuclear interactions. Beta decay, and now apparently, the low energy limit of QCD, routinely produce particles that weigh much more than the particles from which they arose. As the mass of different flavors of quarks show, even the relative relationships of one kind of quark of a given flavor to another kind of quark of the same flavor in terms of relative mass is not stable.

There is nothing inconsistent or theoretically improper about systems having changing masses. The E=mc^2 relationship neatly converts energy into matter and visa versa. But, that doesn't make these systems any less maddening. Conservation of matter is deeply ingrained in human intuition and the fact that it isn't observed in certain circumstances outside our normal perception and experience is as a result jarring.

Our intuition yearns to find some sort of intermediate structure, preons or strings excitations, for example, between raw mass-energy and the particles of the Standard Model. There could very well be some. But, modern quantum mechanics and general relativity provide this to us without sugar coating or explanation. It tells us precisely the likelihood that a muon will all of the sudden become an electron, but it doesn't very little to illuminate why this happens.

Electromagnetism doesn't generally change a particle's rest mass by itself. An electron remains an electron. Photons have differing energies, but remain massless at all times. Rarely, an electron and positron condense out of a high energy electron, but these instances are brief and the conditions that produce them are exceptional.

The strong nuclear force is at least discrete about it. It hides its massive glueballs in low energy states within confined systems where they can only be observed indirectly.

The weak nuclear force, in contrast, flaunts itself, spitting out impossibly large products from impossibly small packages. The weak force is also a tease. One can be forgiven for thinking that a down quark is simply a composite particle made up of the up quark, electron and electron neutrino which provide its most common channel of beta decay. The combined masses on both sides of the reaction are very similar. Yet, nothing in quantum mechanics comes out and says that particles are composite, and the intuition that down type quarks are composite is far less solid when at the next flavor, a strange quark decays into a charm quark, a muon and a muon neutrino, with combined masses far in excess of that of the strange quark.

While weak force branching ratio grids strongly suggest that there are precisely three generations of fermions, the reasons that the universe comes in precisely three flavors of four kinds of particles, one of which, the neutrino, appears to come only left handed varieties, is obscure.

All hypothetical particles with spins other than 1/2 or 1 are deeply connected with gravity and mass in their respective theories.

We know that a particle's speed relative to the speed of light affects its relativistic linear momentum, which looks very similar to its mass, because in Newtonian circumstances and in the low speed limit of special relativity, linear momentum is simply mass times velocity. The analog to Newtonian mass in general relativity that induces gravity, called the stress-energy tensor, in addition to rest mass-energy density, also includes linear momentum, linear momentum flux, energy flux, sheer stress, and pressure.

Missing mass, called dark matter, whose apparent effects are observed, but whose nature is not known, appears to make up about 30% of the stuff in the universe and may act differently than ordinary matter. At galactic scales, dark matter effects and "dark energy" effects (which also can be found in the mass driven equations of gravity as the "cosmological constant" and in quantum theory as the vacuum effective value of the Higgs field estimated to be about 256 MeV/c^2) totally overwhelm the Newtonian gravitational simplification of general relativity that we expect to see in most circumstances.

The key parameter of loop quantum gravity is deduced primarily from the physics of supermassive black holes. While we normally experience gravity as the simplest of fundamental forces, behaving in its Newtonian form GMm/r^2 in almost all circumstances we encounter, the experimentally well established General Relativity expressions of gravity are more complex than those of any of the other fundamental forces of physics.

## 1 comment:

The words "discrete" and "discreet", while pronounced identically, mean different (one might even say "discrete") things.

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