Wednesday, December 14, 2011

Musings On Gluon Speed, Mass and Charge

We assume, for some very good reasons, that gluons have no mass and move at a uniform speed equal to the speed of light. But, we've never directly measured a gluon's speed or mass.

Confinement, the principle of quantum chromodynamics that particles with strong force color charge do not persist in non-color neutral systems more than momentarily, prevents us from observing free gluons and free quarks with very few exceptions - top quarks can come into being only to immediately decay via a W boson before forming a color neutral hadron, and in theory, multiple gluons could combine into a color neutral "glueball." Otherwise, quarks and gluons remain confined in hadrons - three quark varieties called baryons and two quark varieties called mesons. One could imagine four or five or more quark hadrons, but they are not observed. The only composite structures with more than three quarks which have been observed have subcomponents which are mesons or baryons.

The strong force interactions we see in mesons and baryons, with protons and neutrons constituting the only two varieties of hadrons that are ever stable, take place overwhelmingly at very short distances. A hadron is on the order of a femtometer. Strong force interactions sometime extend beyond an individual hadron, but I'm not aware of any circumstance where the strong force has ever been observed to act at a distance greater than that of several nuceli, something that follows from the nature of the strong force itself that peaks at a short, characteristic distance, but is vanishingly weak at shorter distances or distances even as large as the diameter of a large atom.

At the tiny distances involved, it would be impossible to distinguish experimentally between gluons that move at the speed of light and gluons that move, for example, at (1+1*10^-5) times the speed of light (the OPERA estimate of the speed of high energy neutrinos). Definitively ruling out a mass for gluons is even more fraught and theory dependent, because on one hand, gluons are conceptualized in the relevant equations as having a "rest mass" of zero, but on the other hand, QCD attributes very little of the mass of hadrons (on the order of 1%) to the rest mass of the constituent quarks and almost all of the mass to the gluonic color force fields that bind them, in effect, to the glue which is embodied in gluons. The mass of a hadron is vastly greater than the sum of the rest masses of its parts, and the equations of QCD impart considerable dynamical masses to gluons. Moreover, given that gluons are never actually at rest, the concept of a "rest mass" of a gluon is as much a parameter in an equation as it is something that is "real" in the sense that it could be directly measured, at least in principle.

We can make some rough boundary estimates on the speed of a gluon based upon the size of the proton and neutron, our knowledge from experiment and lattice simulations about the internal structure of protons and neutrons (the gluon field is strongest in the middle and the three light quarks basically orbit around the edges) and the characteristic time period in which strong force interactions take place (which is shorter than the time frame of bottom quark decay, but longer than the time frame of top quark, W boson or Z boson decay). But, there is far too much uncertainty in these estimates to make a very precise estimate and a naive diameter of the nucleon divided by hadronization time estimate could easily be too fast because it would omit information about indirect paths from one quark to another and the frequency with which gluons are emitted by quarks. We have models that can fill in some of these blanks (although the theory doesn't necessary break down the components of the process that add up to the overall hadronization time one by one), but the estimates that would be made are theory dependent, including the assumption that massless gluons travel at the speed of light, which isn't helpful when that is the parameter of the equation that you are interested in testing at great precision.

The OPERA experiment reopens this line of inquiry. Quarks and charged leptons whose speeds have been directly measured (in the case of quarks indirectly in hadrons), couple to photons which, by definition, move at the speed of light. Neutrinos, whose Lorentz speed limit might conceivably be slightly different, at least in the vicinity of Earth, don't couple to photons. Neither do gluons. Neither do Z bosons or Higgs bosons. Z bosons and Higgs bosons, unlike gluons and photons have mass, so they must always travel at some speed less than their Lorentz speed limit related to their kinetic energy.

The Z boson has the shortest lifetime of any of the fundamental particle, even shorter than a top quark, so it is virtually impossible to simultaneous measure their speed and energy with sufficient precision to distinguish its Lorentz speed limit from the speed of light.

We just barely received a non-conclusive determination that the Higgs boson exists. It appears to be extremely unstable, just like the other massive bosons, the W boson and the Z boson. So, there is no way that we can directly measure the Lorentz speed limit of the Higgs boson any time soon.

The way that we first derived the speed of light in a rigorous scientific way was from Maxwell's equation, which set the speed of light, "c", equal to the inverse of the square root of the product of the permittivity of free space and the permeability of free space, which are measures related to the properties of electric and magnetic fields respectively in a vacuum. The current formulation of special and general relativity insists that the Lorentz speed limit for all kinds of particles is the same, but it wouldn't be inconceivable that the speed of a photon and Lorentz speed limit of charged particles, might be different from the Lorentz speed limit for particles that don't interact with photons.

We can get pretty precise relative speed estimates for neutrinos v. photons from a few supernova that we have caught in the act allowing us to measure the arrival time of a wave of neutrinos relative to the photons, and can make a pretty decent one or two significant digit estimate of how far away the source supernova was in that event based on red shift (and perhaps other methods). But, this method cannot measure absolute distances to five significant digits, and we don't have a perfect understanding of the underlying supernova dynamics so we can't be sure, for example, in what sequence the neutrinos and photons were emitted in that event.

Because the strong nuclear force and weak nuclear force operate only at short range, it isn't obvious to me that a revised theory of special relativity and general relativity in which there was one "c" for particles that couple to photons or are photons, and another slightly different "c'" for particles that don't couple to photons and aren't photons, would have any phenomenological impact that would be observable apart from neutrinos travelling a little bit faster than photons.

A theory with more than one Lorentz speed limit for different kinds of particles would be an ugly theory, but so far as I can tell, not one that would necessarily lead to any paradoxes or theoretical inconsistencies.

As a related aside, I don't think that we have found any way to confirm that gluons don't have a magnetic dipole that would be sufficient to indicate that they were composite, rather than being truly fundamental particles with no inherent electromagnetic charge at all. The determination that there are eight different kinds of gluons itself and the way that Feynman diagrams for QCD interactions are handled is almost itself a preon theory, further complicated by linear combinations, as is, for that matter, the derivation of the weak force bosons in electroweak unification theory. We don't call gluons or quarks composite, but the way they exchange color charges comes very close to that kind of description.

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