# Tag Info

16

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 ...

12

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 $V(r) = - \frac{4}{3} \frac{\alpha_s(r) \hbar c}{r} + kr$ where the constant $k$ determines the field energy per unit length and is called string tension. For short distances this resembles the ...

11

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 ...

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

A mass-gap means that aside from the vacuum (totally empty space), the next higher energy state has an energy which is bigger than zero by a finite amount, not by an arbitrarily small amount. This usually means no massless particles, since massless particles can have arbitrarily low energy. Another way of saying mass-gap which is somewhat more mathematical ...

10

Color charge is the representation of the SU(3) gauge group. The representation theory of SU(3) is described below: The basic representation is called the "3" or the fundamental, or defining, representation. It is a triplet of complex numbers $V^i$, which transform under a 3 by 3 SU(3) matrix by getting multiplied by the matrix. The value of "i" is ...

8

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 ...

8

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 ...

7

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 ...

7

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 ...

7

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 ...

6

As usual with these things, the presence of QFT and a non-Abelian gauge theory makes life hard, so let's take the prototypical theory that we can actually calculate with easily: Maxwell's equations. The question is then something like "what happens if I put a single electron in a (classical) lattice simulation?". Immediately, one realises that this question ...

6

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 ...

6

Such a process is forbidden by energy conservation: the proton is the lightest baryon (that is the lightest bound state of three quarks). hawking radiation finds it's energy by reducing the energy of the black hole, but there is not lighter baryon state for the proton to go to. Baryon number violating proton decay processes are theorized, but have not been ...

5

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 ...

5

Color forces are not like electromagnetic ones. There exist no unbound color carrying particles analogous to the electron, because the forces increase with the distance rather than decrease and collective effects appear only within nuclei through residuals of the colored forces which attract the nucleons and hold them in the nuclei. Collective effects ...

5

Hydrogen-1 (i.e. hydrogen with no neutrons) has a mass of 1.007825 AMU. To get energy from fusing it you have to preserve baryon number. So you look for the atom that has the lowest mass per nucleon (i.e. lowest mass average over the protons and neutrons that make it up). This lowest (most stable) atom turns out to be iron-56, which has a mass of ...

5

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 ...

5

The two most well-known parton distribution function tables are CTEQ from the US and MSTW from Europe. Some people claim that the European one is of higher quality, but I don't know enough to judge.

5

The asymptotic states of QCD are gauge invariant. They can include mesons which are quark-anti quark bound states and glueballs (which are roughly speaking bound states of gluons) but not gluons themselves. It doesn't really make any sense to say that the gluon propagator has a dynamically generated mass as this is a very gauge dependent statement and gluons ...

5

The situation is well represented in the following very pictorial picture but this is a very active field of study. It is interesting to note that a real proof of existence for the critical endpoint (CEP, indicated as a critical point in the figure), both from a theoretical and numerical point of view, does not exist yet. The reason, at least for the ...

5

Well, I was kindly thanked on the very page 31 so it should be fair for me to try to offer an answer, however imperfect: Construction of the Lagrangian I feel that the Lagrangian in components is clearly described in appendix A, especially equation (A.4), but the fact that the structure of the terms looks laborious isn't an illusion; it is a complicated ...

5

As a quick explanation: all bound states are color-neutral. The intuitive reason is that the strong interaction is so strong that it would pull any color-charged particles together. (Because the strong force increases with distance, you can't get around this by spreading out the charged particles, as you can with the EM interaction.) Since there are 3 ...

5

Here is an experimentalist's answer. Color confinement is a theoretical concept arising from the plethora of experimental observations that are summed up theoretically in the Standard Model. We have no free quarks or gluons, we do have quark jets and gluon jets. So confinement as predicted by the SU(3)xSU(2)xU(1) SM is consistent with all the existing ...

5

In order to understand asymptotic freedom, you need to be aware of the concept of renormalization. Since you want a qualitative description, just think of renormalization a modification of the coupling strengths and masses of particles at high energies. This is roughly like pushing a ball through the water; the harder you push, the more the water sticks ...

4

I don't know that much about lattice QCD, but I do know a few things about string theory and the gauge/string duality approach to QCD. I'm pretty sure the answer to your question is that ideas in string theory have not been used to improve Monte-Carlo simulations of QCD. Unified versions of string theory can't since they involve physics much above the QCD ...

4

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 ...

4

Let me add one obvious thing: There is an exact equation for the strong force. It is what Gross, Politzer and Wilczek got the Nobel prize for. It is called quantum chromodynamics (QCD). Google it or look it up in Wikipedia, and you can see the Lagrangian for QCD, and compare it to the Lagrangian for electrodynamics. Of course, you could argue about the ...

4

Because of $u\leftrightarrow d$ isospin symmetry. For a more detailed explanation, see e.g. chapter 8 of 't Hooft's lecture notes. The pdf file is available here.

4

Recent developments on lattice computations in QCD have shown that the beta function for a pure Yang-Mills theory (let me emphasize that is not true for the full QCD) goes to zero lowering momenta and so, the theory seems to reach a trivial infrared fixed point (see here, fig. 5). The matter about low-energy behavior of a Yang-Mills theory seems rather well ...

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