Proof of gluon masslessness

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Gluons are supposed to have precisely 0 rest mass.
However, gluons are always colour confined into hadrons with binding energies of hundreds of MeV.
How is gluons´ lack of rest mass proven?
Presumably through some symmetries, or lack of some processes.
Which kinds of asymmetries and processes would be expected if gluons had a rest mass (up to MeV range), equal for all gluons?
Which asymmetries would be visible if gluon rest masses were still under MeV range but different?
 

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  • #2
ohwilleke
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How is gluons´ lack of rest mass proven?

It isn't rigorously proven. The observational evidence isn't inconsistent with a small non-zero gluon mass and it would be relatively straightforward to put such a mass into the relevant equations (although it would make them much more complicated to work with if it were present).

Keep in mind that the upper limit on the precision of ab initio low energy calculations (e.g. determining hadron masses) in QCD is typically between 1% and 0.1% (far less than the corresponding experimental measurements in most cases) and often much worse than that.

This, in turn, is because perturbative methods can't be used at low energies, the magnitude to the strong force coupling constant is very large, and gluons can interact with other gluons. These facts mean that it takes far more terms in a QCD calculation to reach the precision available with far fewer terms in electroweak calculations. Worse yet, the truncated infinite series path integral calculations methods used don't converge and hit their maximum precision at fewer loops than in comparable calculations with the electromagnetic or weak forces.

How cumbersome are these calculations?

To give one example, one of the main groups doing a Standard Model prediction of the QCD part of the recently measured quantity muon g-2 on an ab initio basis (i.e. totally "on paper" as much as possible), whose preprint was published in August 2020 had to take several hundred million "core hours" on seven sets of supercomputers to calculate that (Quanta Magazine has a nice discussion of what this involved with a bit more depth) to only 0.8% precision.

So, using experiments to rigorously test theoretical calculations and to discriminate between fine variations in theoretical calculations, as a generic matter, usually isn't possible in QCD (the Standard Model theory of the strong force).

The Particle Data Group states in its gluon entry:
SU(3) color octet
Mass m = 0.Theoretical value. A mass as large as a few MeV may not be precluded, see YNDURAIN 1995 .

The linked article which is just three pages long is and has the following abstract and citation states:

Upper bounds on the gluon mass, mg , are discussed based on high energy experiments, lack of decay proton-free quarks, and scarcity of isolated quarks in matter. One gets bounds of the order of 1 MeV, 20 MeV or 10−10 MeV, respectively.
F.U. Yndurain, "Limits on the mass of the gluon" 345(4) Phys.Letter.B 524-526 (February 1995) DOI: 10.1016/0370-2693(94)01677-5.

The bound from the scarcity of isolated quarks in matter is, by far, the strongest, at 0.1 meV, and is very close to zero (probably less than or comparable to the lightest neutrino mass in order of magnitude).

Some published physics articles have also argued that gluons acquire mass dynamically, although this rather than using pure QCD is using one of the more common ways of approximating it in a way that makes it possible to do calculations. One such article is this one:

The interpretation of the Landau gauge lattice gluon propagator as a massive-type bosonic propagator is investigated. Three different scenarios are discussed: (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 up to momenta ∼500 MeV, with a constant gluon mass of 723(11) MeV, if one excludes the zero momentum gluon propagator from the analysis, or 648(7) MeV, if the zero momentum gluon propagator is included in the data sets. The ultraviolet lattice data are not compatible with a massive-type propagator with a constant mass. The scenario of a momentum-dependent gluon mass gives a decreasing mass with the momentum, which vanishes in the deep ultraviolet region.
Furthermore, we show that the functional forms used to describe the decoupling-like solution of the Dyson–Schwinger equations are compatible with the lattice data with similar mass scales.
O Oliveira and P Bicudo, "Running gluon mass from a Landau gauge lattice QCD propagator" (2011) J. Phys. G: Nucl. Part. Phys. 38 045003 doi:10.1088/0954-3899/38/4/045003.

In practical approximations of QCD, it is more common to fix a characteristic QCD energy scale (roughly 200 MeV), or to set a pion mass (140 MeV to two significant digits) with reference to experimental data (see, e.g., here), than it is to insert a mass scale via a gluon mass itself. Both of these are more often associated in the minds of the reader and author of an article with the strength of the QCD coupling constant than with mass scale of the gluons themselves.

Among the better reasons to assume that the gluon is massless is that it isn't obviously necessary (using E=mc2 to use the gluon field to contribute mass to hadrons), and that it is not a good fit to the Higgs mechanism that provides the masses of all of the other massive fundamental particles in the Standard Model (with the possible exception of the neutrinos whose mass generation mechanism is the subject of ongoing investigation).

Also, the strength of the gluon field differs from hadron to hadron in systemic ways well explained by Quantum Chromodynamics (QCD), while we can't easily find a way to fit the gluon field sourced mass of hadrons to some particular fixed gluon mass. Counting particles is inherently more difficult with bosons that obey Bose-Einstein relations so that more than one can be in the same place at the same time, than it is for fermions, although as the example of photons and the W and Z bosons illustrates, it isn't impossible. Confinement, that keeps all gluons within either composite hadrons, or at very high temperatures, quark-gluon plasma, is an even more daunting difficulty. And, for what it is worth, there still isn't a rigorous mathematical proof that the empirical reality of confinement of quarks and gluons below the quark-gluon plasma temperature is actually required by the true equations of QCD.

Like so many things in high energy physics that aren't really rigorously established, the fact that the equations of QCD work properly to give you sensible results that correspond to experimental data (over a very broad range of applicability), when you put this particular mass value for gluons into them, suggests that this is the correct value.

Put another way, the theoretical zero rest mass value for gluons satisfies Occam's Razor. It reduces the complexity of the model of QCD (which is deceptively simple as a result, despite the very complex phenomena it can give rise to), while providing no meaningful cost to the model in terms of its predictive accuracy.

I also note that while gluons themselves are theoretically assumed in QCD to have zero rest mass, composite particles bound by the strong force made up entirely of gluons, called "glueballs" are not assumed to have zero mass and indeed have a mass that can be calculated using only the QCD part of the Standard Model Lagrangian and one experimentally measured physical constant (the strong force coupling constant) to good approximation in QCD. On the other hand, we've also yet to observe free glueballs, even though they were the first hadron masses calculated using QCD. This is presumably because they blend and mix with other bosons with the same quantum numbers, in differing proportions for reasons that aren't perfectly well articulated in a way that can reproduce the spectrum of hadrons observed from scratch.

I also observe that all fundamental particles in the Standard Model believed to have rest mass interact via the weak force, which gluons do not. And, as a zero rest mass particle, gluons would not experience time (just like photons) which would be fitting given that the strong force does not have CP symmetry violation (which is equivalent to not showing a dependence upon direction in time). These are both merely observations, however, and shouldn't be taken as actual reasons for the assumption of zero rest mass for gluons.

Basically, while a free gluon has no rest mass, a bound system including gluons does have rest mass attributable in substantial part of the strong force fields mediated by gluons.
 
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  • #3
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It isn't rigorously proven. The observational evidence isn't inconsistent with a small non-zero gluon mass and it would be relatively straightforward to put such a mass into the relevant equations (although it would make them much more complicated to work with if it were present).

The linked article which is just three pages long is and has the following abstract and citation states:


F.U. Yndurain, "Limits on the mass of the gluon" 345(4) Phys.Letter.B 524-526 (February 1995) DOI: 10.1016/0370-2693(94)01677-5.

The bound from the scarcity of isolated quarks in matter is, by far, the strongest, at 0.1 meV, and is very close to zero (probably less than or comparable to the lightest neutrino mass in order of magnitude).
Thanks!
I looked for the article, but could not get it. Could anyone tell what was the reasoning in deriving the numbers of quark abundance from specific gluon mass values?
 
  • #4
ohwilleke
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Thanks!
I looked for the article, but could not get it. Could anyone tell what was the reasoning in deriving the numbers of quark abundance from specific gluon mass values?
FWIW, I am only aware of pay per view access to that article and as I don't have an academic affiliation to can provide a subscription to look at it, so I can't look at the body text without paying $40ish to read a three page article. Perhaps someone who here who has an academic affiliation can access it and provide a summary of the analysis used or references cited with a bit more depth.

Given its brevity, and that fact that three different approaches are used despite this brevity, it has to be a pretty straightforward back of napkin calculation.

You might also find the following analysis interesting as it used an approach along the lines of what was suggested in your original post:

Retaining only the `timelike' component A0 of the vector potential a skelet model with explicit global center symmetry is constructed for SU(2) Yang-Mills theory. It is shown that the A0 gluon vacuum is equivalent with the 4-dimensional Coulomb-gas. In 1--loop approximation, the effective theory of the skelet model exhibits non-local self-interaction. A coupling constant λ is found that governs the loop expansion. For λ<1 the effective theory does not confine (the string tension vanishes), whereas for λ=1 confinement (with non-vanishing string tension) takes place. In the deconfined phase the A0 gluons exhibit non-zero rest mass and global center symmetry is broken by the vacuum state. Confinement sets on for λ=1 when the rest mass of A0 gluons vanishes and the global center symmetry of the vacuum is restored.

K. Sailer, "Phase structure of SU(2) Yang-Mills theory with global center symmetry" arXiv:hep-ph/9403367 (1994). KLTE-DTP/1994/1

Another theoretical analysis (full pdf linked) suggests that the gluon mass is not zero in the general case with an arbitrary number of types of color charges, but vanishes trivially in the case of one, two or three color charges.
 
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Thanks!
I see a key argument at the shift of pages 1 and 2:
"An interesting property of the potential in Fig. I is
that the barrier with height E,,i, = Km,; ’ acts in bo?h
directions. Not only makes it difficult for quarks inside
to become liberated, but, if a quark stays outside, the
barrier precludes its being captured &ain: liberated
quarks stay liberated. "

I am NOT convinced that the qq potential depicted on Figure 1, and the key argument, is actually what follows from gluon mass. And if it does not, the following arguments do not follow. Like the argument from proton stability.
 
  • #7
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Thanks!
I see a key argument at the shift of pages 1 and 2:
"An interesting property of the potential in Fig. I is
that the barrier with height E,,i, = Km,; ’ acts in bo?h
directions. Not only makes it difficult for quarks inside
to become liberated, but, if a quark stays outside, the
barrier precludes its being captured &ain: liberated
quarks stay liberated. "

I am NOT convinced that the qq potential depicted on Figure 1, and the key argument, is actually what follows from gluon mass. And if it does not, the following arguments do not follow. Like the argument from proton stability.
Nussinov and Shrock have a 2010 paper on this topic:
https://arxiv.org/pdf/1005.0850.pdf

This paper cites Yndurain [11] and other, more-recent papers:
Particle Data Group [10], Bethke [18], etcetera.

There is a good discussion of the upper limit of gluon mass,
beginning in Section III on page 4. Using Equation (14) on
the following page, 0.5 MeV is calculated. This seems
reasonable to me, being the same mass as an electron;
I do not believe in "coincidence".
Using a different approach (Schwinger mechanism, see below)
Equation (21) gives the result 35 MeV, using ε = 0.01 as an
"illustrative value", which seems reasonable. My own calculation
gives ε = 2.2*10-6 when 0.5 MeV is substituted for gluon mass
in Equation (21), indicating the two approaches are not mutually
compatible, within two orders of magnitude.

Cohen and McGady have details of the Schwinger mechanism
in a 2008 paper:
https://arxiv.org/abs/0807.1117
 
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