# Tag Info

19

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 ...

19

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 ...

18

In QED there are 4 kinds of divergences: 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 renormalization) give sensible results. Landau pole. The coupling ...

13

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 ...

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 ...

9

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 ...

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

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

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

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

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 ...

8

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 ...

7

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 ...

7

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 ...

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

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 ...

6

No, quarks couldn't turn out to be non-existent anymore. The evidence that quarks exist involves more than just some playful games in which we add electric charges to construct hadrons. Quarks show up in many processes. Historically, the important experimental observation was that of the deep inelastic scattering. Much like Rutherford observed the nucleus ...

6

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 ...

6

The particles that communicate the Weak interaction, i.e W Bosons and Z bosons are massive. So unlike Electromagnetism which is communicated by massless particles(Photons), the weak interaction has a very short range. For Massive particles the Potential of interaction falls as $V(x) = -K \frac{1}{r} e^{-m r}$ The range of this force is approximately ...

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 ...

6

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 ...

6

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 ...

6

That really depends on what you call necessary. If you completely forget all about $SU(2)_L$ (say, in an alternate universe with no Weak Interactions). Then mass terms in the Lagrangian for quarks and leptons are not forbidden by any symmetry and you would not need the Higgs field to generate the mass of the quarks or of the electron. Now, in OUR ...

6

The Lagrangian has many parts that are each guessed at according to symmetry principles, requirements that the theory be well behaved, and reproduce experimental results. It's not something you can do from first principles, because the first principles aren't known. But the aforementioned process took about a 75 years and many Nobel prizes and PhDs were ...

5

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 ...

5

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 ...

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