# B Since gluons are massless, shouldn't glueballs also be massl

1. Aug 20, 2016

### kodama

since gluons are massless, shouldn't glueballs also be massless?

is there any possibility gluons acquire mas by interacting with other gluons, not higgs?

2. Aug 20, 2016

### Staff: Mentor

Is the mass of a proton the sum of three quark masses?

Same for the glueball. It has energy, therefore it has mass.

3. Aug 20, 2016

### kodama

gluons also carry energy. they also couple to other gluons

4. Aug 20, 2016

### Staff: Mentor

Yes. So where is the problem?

5. Aug 20, 2016

### kodama

i understand that the mainstream particle physics is that elementary particles have mass due to yukawa interaction of a scalar field, the higgs, and dirac field, fermions.

since gluons carry energy, and they carry color charge, and they experience confinement, isn't that a form of inertial mass, independent of the higgs field?

gluons carry energy and gluon's interaction with gluon field causes a resistance to a change in motion, so therefore it also has an inertial mass independent of the higgs. gluons are short ranged not infinite range so they have an effective mass.

6. Aug 20, 2016

### Staff: Mentor

Glueballs are not elementary particles.
They don't exist as free particles, but in terms of propagation they are massless: they don't have a mass term from any source.

7. Aug 20, 2016

### kodama

in terms of propagation they are massless, so they should have unlimited range. something restricts their range.
given that gluons don't exist as free particles, they experience color confinement, isn't color confinement a form of "mass"?

i understand mass term is a technical requirement in qft that involves interactions between a higgs field and a dirac field.
i think that color confinement of a massless gluon gives it a form of mass that is independent of a mass term.

8. Aug 20, 2016

### ChrisVer

not necessarily... most of the SM fermions (since you talk about dirac fields) needed the Higgs field to have a mass because their chirality mixing terms $\psi_L \psi_R$ violated the Electroweak Symmetry. The Yukawa terms allowed for the leading order mass terms (bare masses) to appear in the Lagrangian after the non-zero vev is acquired by the Higgs field. How are glueballs connected to this?
The EW gauge bosons (not gluons!) don't have Yukawa terms; they got a mass because they got mixed in such a way that led to a mass term (sometimes the whole procedure is described as the goldstone bosons of the Higgs being eaten by the gauge bosons to become heavy). A particular combination of those gauge bosons remained massless after the EWSB and they are called photons.

Last edited: Aug 20, 2016
9. Aug 20, 2016

### Staff: Mentor

Light in a box of mirrors doesn't propagate infinitely far either. Does that mean light has mass? No.

10. Aug 21, 2016

### vanhees71

How do you come to this conclusion? Mainstream particle physics tells us that only 2% of the mass of the matter surrounding us is due to the Higgs mechanism used to describe the electroweak interaction in a consistent model (the Glashow-Salam-Weinberg Model, which is part of the Standard Model, which in addition also describes the strong interaction in terms of QCD). The remaining 98% are due to the strong interaction. One must admit that a full understanding of this phenomenon has not been reached yet. However, evaluating QCD on a space-time lattice ("lattice QCD") shows that the correct mass pattern of the known hadrons come out of this picture. So we are pretty confident that it is correct.

11. Aug 31, 2016

### ohwilleke

While gluons have zero rest mass, their usual propagator function does act as if the gluons acquire mass dynamically as a function of their momentum. A discussion of the topic can be found for example at 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 whose abstract states:

Glueball mass calculations are in principle some of the easiest composite particle mass calculations to make because they depend entirely on only one of the experimentally determined constants of the Standard Model (the strong force coupling constant which is known to an accuracy of about 0.5%) and the rest of the inputs are known exactly. As a result, some of the earliest mass calculations done in QCD were done for glueballs. But, the trouble is that no glueballs have been observed at the masses that they are predicted to have.

The conventional explanation for this is that glueballs, because they are bosons with many trivial quantum numbers, almost always exist only in linear combinations with other bosons rather than in free states, and can't be found in near pure states. A lengthier discussion is found at a blog post I did on the subject in 2013: http://dispatchesfromturtleisland.blogspot.com/2013/10/glueball-found.html The main current experimental effort to find glueballs is the GlueX experiment at Jefferson Labs.

It is also possible that while the Standard Model's QCD explains almost everything about the strong force interaction, that it is missing a minor rule whose sole effect is to rule out the trivial case of the glueball, or that the non-existence of glueballs is a subtle corollary of existing QCD rules for some subtle reason that has yet to be identified.