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In short, the answer is: because gluons behave in a way that makes them useless for this purpose. To understand why, let's back up a little and look at how photons are useful, and then see how gluons behave differently. We (animals pretty broadly) evolved to see photons because they allow us to move around in and respond to our environment more efficiently....

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The problem In case you were not aware of this, finding a proof for confinement is one of the Millenium Problems by the Clay Mathematics Institute. You can find the (detailed) answer to your question in the official problem description by Arthur Jaffe and Edward Witten. In short: proving confinement is essentially equivalent to showing that a quantum Yang-...

27

in the late 1960s, the strongly interacting particles were a jungle. Protons, neutrons, pions, kaons, lambda hyperons, other hyperons, additional resonances, and so on. It seemed like dozens of elementary particles that strongly interacted. There was no order. People thought that quantum field theory had to die. However, they noticed regularities such as ...

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Let me begin with QED. I will subsequently connect with QCD. There are 4 kinds of divergence in QED: Ultraviolet divergences. Naive calculations depend on the cut-off in such a way that they go to infinity as the cut-off do. However, QED is a perturbatively renormalizable theory so that non-naive, well-done computations (see regularization and ...

23

From the study of the spectrum of quarkonium (bound system of quark and antiquark) and the comparison with positronium one finds as potential for the strong force $$V(r) = - \dfrac{4}{3} \dfrac{\alpha_s(r) \hbar c}{r} + kr$$ where the constant $k$ determines the field energy per unit length and is called string tension. For short distances this resembles ...

23

This is covered by a few existing answers (see for example About free quarks and confinement) though surprisingly it doesn't appear that anyone has asked this exact question before. Anyhow, the answer is that the colour force is mediated by particles called gluons just as the electromagnetic force is mediated by photons. The difference is that while photons ...

21

Dear qftme, I agree that your question deserves a more expansive answer. The answer, "pions" or "gluons", depends on the accuracy with which you want to describe the strong force. Historically, people didn't know about quarks and gluons in the 1930s when they began to study the forces in the nuclei for the first time. In 1935, Hideki Yukawa made the most ...

17

No, there is none such equation. Reason is that these equations are highly classical and invalid in both relativistic (there is an action at a distance, incompatible with finite speed of light) and quantum mechanical regime (distances strong force is important at are quite microscopic). Also, strong force is confining, meaning you can't ever observe ...

12

At the level of quantum hadron dynamics (i.e. the level of nuclear physics, not the level of particle physics where the real strong force lives) one can talk about a Yukawa potential of the form $$V(r) = - \frac{g^2}{4 \pi c^2} \frac{e^{-mr}}{r}$$ where $m$ is roughly the pion mass and $g$ is an effective coupling constant. To get the force related to ...

12

From lattice calculations (see String Tension of Quark-Anti-Quark Pairs in Lattice QCD) it has been found that the string tension of the quarks, in the case of pions, is given by $$\sqrt{\sigma}\sim460\ \mathrm{MeV}$$ which is equivalent to a length of $\sim 2.7\ \mathrm{fermi}$. In the case of the charmonium ($\bar c c$), the tension (see Charmonium ...

11

The utility of using branes to realize gauge theories in string theory, compared to using heterotic, lies in the ease with which we can decouple bulk gravity. Basically you can zoom in to the branes to isolate the degrees of freedom on them, forgetting the gravity. In contrast, in heterotic compactificarions, both gauge fields and gravity live in the same ...

11

Suppose that $\text{U}(3)$ was the gauge group. We can decompose this as $$\text{U}(3)=\text{U}(1)\times\text{SU}(3),$$ which implies that in addition to the $\text{SU}(3)$ that has eight generators corresponding to eight gluons, there would be an additional generator for $\text{U}(1)$. The latter in principle corresponds to an additional gauge boson, but ...

10

Dear dbrane, $\Lambda_{\rm QCD}$ is the only dimensionful parameter of pure QCD (pure means without extra matter). It is dimensionful and replaces the dimensionless parameter $g_{\rm QCD}$, the QCD coupling constant. The process in which a dimensionless constant such as $g$ is replaced by a dimensionful one such as $\Lambda$ is called the dimensional ...

10

Texts on QCD don't divide the generators of $SU(3)$ – and therefore "bicolors of gluons" – into two groups because this separation is completely unphysical and mathematically artificial (basis-dependent). Moreover, the number of "bicolors of gluons" i.e. generators of $SU(3)$, the gauge group of QCD, isn't nine as you seem to think but only eight. The group ...

10

Part b) is a big mathematical physics topic in its own right. The divergent tail of an asymptotic series is not garbage, rather it contains a lot of information that together with some additional information can be used to compute non-perturbative effects. A general introduction to this topic is given here. There are different approaches possible, some ...

9

As you say, "$G(x,Q^2)$ is the probability of finding a gluon with momentum fraction $x$ inside the hadron if the transmitted four-momentum is $Q^2$." In other words, $G(x,Q^2)$ is a probability density function. As you can see from the article, in this case the expectation value of the variable is $E[X] = \int_{0} ^{1} x\cdot G(x,Q^2) dx$ The plot of $x\... 9 There is no known reason that you can't have bound states like$qq\bar{q}\bar{q}$or$qqqq\bar{q}$or higher number excitations, but none have been observed to date. You do have to make a color-neutral state, of course. In the mid-2000 some folks thought that they had of pentaquark states (that the$qqqq\bar{q}$) for a while, but it was eventually ... 9 One of the candidate explanations of the QCD color confinement involves the distinction between the Yang-Mills field electric and magnetic components. This model of confinement was qualitatively proposed in the 70s, and according to which, the quark confinement is explained by assuming the QCD vacuum to be composed of a magnetic monopole condensate in a ... 9 The "resources" linked in the post are bad. But there was a time when serious people were interested in the possibility that quarks have integer charges. Han and Nambu introduced the idea, Pati and Salam made a gauge theory of it, Witten suggested how to test it, and this was done at CERN in the 1980s (see page 11). There would be several ways in which the ... 9 It is known that for an element$U$of the group, in matrix sence: $$Ad_Ux=UxU^{-1}.\,\,(1)$$ Now, we note that the target space of the adjoint rep is spanned by$N^2-1$traceless matrices$t_a$. So, if we add the unity matrix, we get a full basis in$\mathrm{Mat}_N(\mathbb{C})$. We now note that that the adjoint action is trivially extended to this space, ... 9 It's not a sufficient explanation. There are asymptotically free theories which are not strongly coupled in the IR. The rate at which the coupling gets strong is important. In QCD, it seems to get strong very quickly near the confinement scale, so that beyond a certain scale, you only see hadrons. It is not really understood how this works. The ... 8 Once upon a time, I asked an experienced phenomenologist who worked on particle physics in the 60s why even and odd signatured trajectories lie on top of each other. He said the phenomenon was called 'exchange degeneracy' and that so far no one has an explanation. I'm looking back at my notes on Dual Resonance Models, and it looks like by introducing ... 8 If by large density you mean large baryon density, then I believe one of the fundamental large$N_c$results is that at densities of order nuclear densities, but below the density where the baryons have dissolved into quarks, baryonic matter forms a crystalline structure. This has been analyzed in the Skyrme model. I think this paper by Klebanov was one of ... 8 From the beginning of the wikipedia page on Yang-Mills theory (have you read it?): "Yang–Mills theory is a gauge theory based on the SU(N) group ... ... In early 1954, Chen Ning Yang and Robert Mills extended the concept of gauge theory for abelian groups, e.g. quantum electrodynamics, to nonabelian groups to provide ... ... This prompted a significant ... 8 I asked this question a few weeks ago and was dissatisfied with most of the answers I found on the internet, so I eventually managed to procure a copy of Griffiths' excellent text on elementary particles (really, all of his texts are excellent) which includes a section exactly answering my question with what I was looking for. I decided then to answer it ... 8 Global invariance under$SU(N)$is equivalent to the conservation of$N^2-1$charges – these charges are nothing else than the generators of the Lie algebra${\mathfrak su}(N)$that mix some components of$SU(N)$multiplets with other components of the same multiplets. These charges don't commute with each other in general. Instead, their commutators are ... 8 There are two different kinds of symmetry breaking involved in your question. The first would be spontaneous symmetry breaking, in which case we are dealing with a theory that is invariant under a certain symmetry group, but its vacuum is not. The breaking of the symmetry corresponds to a specific choice of the vacuum, the freedom of choosing a vacuum ... 8 Pure QED, unlike Pure Yang Mills ('pure' in the sense that there is only an$F^2\$ term in the lagrangian, and it doesn't couple to matter) is a free theory. That means that it's boring, there's no need for renormalization or perturbation theory or anything. So the coupling constant (in this case the wave function renormalization of the photon) doesn't run ...

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