# How many gluons are there in a proton?

1. Aug 16, 2011

### jal

How many gluons are there in a proton?
http://en.wikipedia.org/wiki/Proton

Protons are spin-½ fermions and are composed of three quarks,[3] making them baryons (a sub-type of hadrons). The two up quarks and one down quark of the proton are held together by the strong force, mediated by gluons.[2] The proton has an approximately exponentially decaying positive charge distribution with a mean square radius of about 0.8 fm.[4]
http://en.wikipedia.org/wiki/Gluon

In terms of group theory, the assertion that there are no color singlet gluons is simply the statement that quantum chromodynamics has an SU(3) rather than a U(3) symmetry. There is no known a priori reason for one group to be preferred over the other, but as discussed above, the experimental evidence supports SU(3).

Eight gluon colors

Last edited by a moderator: Apr 26, 2017
2. Aug 16, 2011

### Bill_K

We all know that the gluons inside a proton are virtual. That the number of gluons "fluctuates", i.e. is described by a probability distribution rather than a unique value. And that to really calculate an accurate answer would be a challenging problem in lattice gauge theory.

Nevertheless, in the spirit of the question, here's how I get eight. You said the radius of the proton is 0.8 f. Confine a particle in a box of size 1.6 f and you find its zero-point kinetic energy to be 197/1.6 = 123. Eight times this is about the rest energy of the proton.
Edit: well maybe 123 x 3, since the box is a cube. So the number of gluons is 8/3.

3. Aug 16, 2011

Staff Emeritus
The Lattice people won't be able to calculate this, because a) the proton is not in an eigenstate of the gluon number operator, and b) what you call a gluon and what you call the field of a quark is a matter of choice.

4. Aug 16, 2011

### Dickfore

How so?

5. Aug 16, 2011

### kurros

Renormalisation. Particles which exist as virtual loops in some process at one energy can be redefined as part of the tree level process at another energy. This is why particles masses, charges etc are said to 'run', or change with energy. You don't have to do this redefinition, but as you go to higher energies you will find loop contributions are increasingly important, and you will have to add zillions of loop diagrams to get a good answer. It is much easier to redefine what the tree level field is. And in QCD you are especially screwed because you need zillions of diagrams to get even a crap answer to start with.

6. Aug 16, 2011

### Dickfore

But, renormalization only affects the parameters, such as the mass of the particles or their color charge. It does not change a quark (a fermion) into a gluon (boson).

7. Aug 16, 2011

### kurros

No, but these are all virtual particles we are talking about, so we are trying to count this quark-anti-quark pair or that gluon-gluon pair as contributing to the proton mass, and it is arbitrary whether those gluon pairs are contributing to the quark field which contributes to the proton mass or just straight to the proton mass. The point is it is a huge mess of strongly interacting junk in there and it makes no sense to talk about any of these particles as having distinct identities.

All we can know really, unless there is some huge breakthrough in QCD, are the parton distribution functions, and they are certainly energy dependent. For instance the LHC may be colliding protons, but effectively it is just colliding gluons, because at those energies the proton is dominantly a mass of gluons. The quarks contribute hardly at all.

8. Aug 16, 2011

### jal

Doing a search has given me a lot of theoretical papers but no answers.
Gluon density of a proton does appear to be an important piece of information.

http://www.actaphys.uj.edu.pl/sup1/pdf/s01p0371.pdf [Broken]

RECENT MEASUREMENTS OF THE PROTON
STRUCTURE FUNCTIONS AT HERA

A. Glazov
for H1 and ZEUS Collaborations

A detailed knowledge of the proton structure is mandatory for the physics program at the future pp collider. For example, a measurement of the Higgs boson production at the LHC, for light Higgs boson masses, is determined by the proton structure at x ∼ 0.01.

For this kinematic range, the Higgs boson is produced predominantly via gluon–gluon fusion making precise measurement of the gluon density an extremely important task.

Similarly, quark ﬂavor decomposition is needed for precise estimation of the production of the Z and W bosons as well as other heavy particles, present in theories extending the standard model, with diﬀerent coupling to diﬀerent quark ﬂavors.

Last edited by a moderator: May 5, 2017
9. Aug 16, 2011

### kurros

Yes, the point is that when a collision between protons and something else happens, you can say probabilistically what sub-component of the proton is going to be involved in the collision. As you go up in energy, it becomes more probable that it will be a gluon, not a quark, that dominates the collision. This only works for high-energy collisions though, proton sub-structure is not very meaningful at low energy, except for the valence quarks which give you the charge and spin. The mass you just have to measure.

10. Aug 17, 2011

### jal

I want to put in some links so that this discussion might be easier to follow by the amateurs.

http://en.wikipedia.org/wiki/Parton_(particle_physics [Broken])
The term parton is often used to mean "a quark or a gluon"

Generalized parton distributions (GPDs) are a more recent approach to better understand hadron structure by representing the parton distributions as functions of more variables, such as the transverse momentum and spin of the parton. Early names included "non-forward", "non-diagonal" or "skewed" parton distributions. They are accessed through exclusive processes for which all particles are detected in the final state. Ordinary parton distribution functions are recovered by setting to zero (forward limit) the extra variables in the generalized parton distributions. Other rules show that the electric form factor, the magnetic form factor, or even the form factors associated to the energy-momentum tensor are also included in the GPDs. A full 3-dimensional image of partons inside hadrons can also be obtained from GPDs.

http://arxiv.org/abs/hep-ph/0504030

Unraveling hadron structure with generalized parton distributions
(Submitted on 5 Apr 2005 (v1), last revised 27 Jun 2005 (this version, v3))
The generalized parton distributions, introduced nearly a decade ago, have emerged as a universal tool to describe hadrons in terms of quark and gluonic degrees of freedom. They combine the features of form factors, parton densities and distribution amplitudes--the functions used for a long time in studies of hadronic structure. Generalized parton distributions are analogous to the phase-space Wigner quasi-probability function of non-relativistic quantum mechanics which encodes full information on a quantum-mechanical system. We give an extensive review of main achievements in the development of this formalism. We discuss physical interpretation and basic properties of generalized parton distributions, their modeling and QCD evolution in the leading and next-to-leading orders. We describe how these functions enter a wide class of exclusive reactions, such as electro- and photo-production of photons, lepton pairs, or mesons. The theory of these processes requires and implies full control over diverse corrections and thus we outline the progress in handling higher-order and higher-twist effects. We catalogue corresponding results and present diverse techniques for their derivations. Subsequently, we address observables that are sensitive to different characteristics of the nucleon structure in terms of generalized parton distributions. The ultimate goal of the GPD, (generalized parton distributions), approach is to provide a three-dimensional spatial picture of the nucleon, direct measurement of the quark orbital angular momentum, and various inter- and multi-parton correlations.
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parton distribution functions (PDF)
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Coming back to my nave question, do we know how many gluons are in a proton?

Last edited by a moderator: May 5, 2017
11. Aug 17, 2011

### kurros

After all that how can you still be asking that? The question doesn't make sense. It is like say, asking how many photons there are in an atom. Yes, photons mediate the force binding electrons to the nucleus, but there is not a definite number of them there that you can count.

12. Aug 17, 2011

### jal

Contrary to your statement, there are an awful lot of people trying to find out what is in a proton.
jal

13. Aug 18, 2011

### kurros

Of course, but they are not asking how many gluons there are in there.

14. Aug 18, 2011

### PAllen

How many photons are in a proton? (quarks have electric charge and interact with photons as well as gluons). How many W and Z are in a proton (quarks interact weakly as well)? Such questions are ridiculous.

15. Aug 18, 2011

### jal

I can think of one or maybe up to 4 gluons that are in the make up of protons.
The most influential is the one that gives the mass to the proton. The others 3 gluons are inside and give mass to the quarks.
hint .. hint ... They call it the Higgs. The search is ongoing to identify the gluons.

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Since I’m learning I reserve the right to change my mind.

jal

16. Aug 18, 2011