01 February 2011

Gluons Lose Mass With Momentum

Quantum Chromodynamics (QCD) has been something of the crazy aunt in the closet of quatum mechanics. Quantum electrodynamics produces all sorts of practical and precisely calculable results and illustrates nicely the quirky elements of quantum mechanics that don't apply in "classical" physics. The physics of the weak force is fascinating because it produces such weird events - transmuting one kind of thing into something entirely different.

There is wide consensus that quantum chromodynamics is governed by Yang-Mills Theory, a set of equations that explain how quarks and gluons interact with each other, but these equations produce much more intractable math than other parts of quantum mechanics and has one main prediction that is all you need to know for many practical purposes: quarks are confined into color neutral particles by the strong force as mediated by gluons, but are asymptotically free within those composite particles.

But, Marco Frasca, the author the The Gauge Connection toils away in QCD nonetheless and keeps the world appraised of what is going on in that world.

Despite its obscurity, QCD is vital to distinguishing noise from background in particle accelerator experiments, and in nuclear physics. Until you can solve these equations to get practical results, you can't derive what happens in real life from the math from first principles.

But, after decades of slow going, improved computing power (these calculations push supercomputers to their limits) and some important theoretical insights are shedding light on QCD, particular in low energy systems, which are hard to measure because you can probe them in high energy particle accelerators by smashing them together.

One core observation Frasca makes is that QCD is not a simple matter of quarks exchanging massless, spin one gluons:

At higher energy QCD tends to become a free theory, that is the coupling becomes increasingly small and the gluon propagator one uses at the tree level is that of a free particle. This in turn means that the non-linear contributions from Yang-Mills theory are small and small perturbation theory applies. In this limit we can identify as the excitations of Yang-Mills theory with ordinary gluons carrying spin one.

In the infrared limit, the case of low energies, the behavior of Yang-Mills theory changes radically. The reason is that in this case the non-linear terms in the equations become so strong that ordinary gluons are no more the fundamental excitations of the theory. In this case one has glueballs and the lower end of the spectrum of the glueballs carries spin zero.

Gluons, at least in some circumstances, appear, contrary to the popularized layman's explanation of the theory, to have considerable mass and spin zero (rather like the proposed Higgs boson) rather than being massless and having spin one (rather like photons in QED). It remains a boson in both states, but is a very different animal, really a completely different fundamental particle, at low momentum than at high momentum. A paper by one of his colleagues last year spells out a formula for determining a gluon's mass:

The interpretation of the Landau gauge lattice gluon propagator as a massive type bosonic propagator is investigated for i) an infrared constant gluon mass; ii) an ultraviolet constant gluon mass; iii) a momentum dependent mass. We find that the infrared data can be associated with a massive propagator with a constant gluon mass of 651(12) MeV, but the ultraviolet lattice data is not compatible this type of propagator. The scenario of a momentum dependent gluon mass gives a decreasing mass with the momentum, starting from a value of 630 MeV in the infrared region and suggesting a q^2\ln q^2 dependence for momenta above 1 GeV.

Physics is familiar with the notion of objections whose mass change based upon their motion. An object's rest mass in special relativity, is its minimal mass, but the mass of an object increases with its velocity relative to the observer. In constrast, no other particle in physics has a mass that decreases with momentum with its rest mass being its maximal mass, as appears to be the case for gluons. I am also not aware of any other particle in physics changes its intinsic spin in different circumstances. Yet, this is not "beyond the Standard Model" physics. This is physics being done with the equations of the Standard Model itself!

More generally, new developments in QCD explain a lot about how mass arises. For example, it was used in 1999 to calculate the mass of the proton and neutron to within 2% accuracy from first principles:

More than 99% of the mass of the visible universe is made up of protons and neutrons. Both particles are much heavier than their quark and gluon constituents, and the Standard Model of particle physics should explain this difference. We present a full ab-initio calculation of the masses of protons, neutrons and other light hadrons, using lattice quantum chromodynamics. . . . Our results completely agree with experimental observations and represent a quantitative confirmation of this aspect of the Standard Model with fully controlled uncertainties.

While we have long known that matter and energy are manifestations of the same thing and equivalent for many purposes in physics, QCD appears to be one of the important places where transitions from mass to energy are particularly fluid.

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