What is anti-screening?

I'm going to try to answer this, but I may be just missing something. If I am, I hope someone can please correct me.

I think anti-screening is referring to QCD vs QED properties. In QED, the level of attraction (electromagnetic) gets stronger the closer the particles are together. The same is true with the repelling force of electromagnatism; where that the repulsion is stronger the closer the particles are together. The energy is damping off with distance.

In QCD, the strong attractive force gets weaker the closer the particles get. The energy is damping off with proximity. So if two bound quarks get far enough apart, the strong force binding them (the gluon particles) gain enough energy to either become quark and anti-quark pairs, or become additional gluons.

So the strong force, gluons can form other gluons, where the electromagnetic force, photons, can not generate other photons, or even interact with other photons. Photons are limited in either being absorbed by electrons, reflected or possibly becoming an electron-positron pair. This is an asymmetry between QCD and QED, where photons ignore other photons, but gluons can interact with and even create/absorb other gluons.

An important conclusion of the process of renormalization is that certain "constants" of Nature really are functions of energy. Screening and anti-screening are words used to describe different ways the coupling can depend on energy:

• a theory exhibits "screening" if its coupling constant increases with energy, and
• a theory exhibits "anti-screening" if its coupling constant decreases with energy.

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In quantum electrodynamics, the relevant constant is called the "fine-structure constant." At low energies (meaning, in processes we observe in a lab), the fine-structure constant takes a value begin{equation} alpha_{rm EM}(E=0) = frac{1}{4pi epsilon_0}frac{e^2}{hbar c} approx frac{1}{137} end{equation} where $hbar$ is the reduced Planck constant, $c$ is the speed of light, $epsilon_0$ is the polarizability of the vacuum, and $e$ is the charge of the electron. As the energy grows, the fine-structure constant increases. For example, at about 90 GeV, one measures that $alpha_{rm EM}(90 {rm GeV})approxfrac{1}{127}$ (see Ref [1]). This effect is what Wilczek refers to as screening. Because of the uncertainty principle, processes at higher energies probe shorter distances. Because of the running with energy of $alpha_{rm EM}$, the effective electromagnetic attraction between two charged particles $alpha_{rm EM}$ is weaker at large distances (low energies) than it is at short distances (high energies) -- this is called "screening."

A physical picture often used to describe this effect is that a charged particle "polarizes the vacuum", and is "dressed" by a cloud of virtual photons and other charged particles. An electron will attract virtual positively charged particles out of the vacuum that effective screen the electric charge seen by an observer far away from the electron, reducing the size of the coupling. By bringing two charged particles to shorter distances (so they interact at a higher energy), the effective coupling between them is stronger because each charge penetrates the other's cloud, and so the virtual particles swarming in the quantum vacuum are less able to screen the bare charge of each charged particle. The reason for the name "screening" is that (in this picture) the quantum vacuum is screening the bare charge by surrounding it with virtual particles of the opposite charge. I should emphasize that this is a nice physical picture, but ultimately is just a set of words draped around a rigorous calculation of the running of the electromagnetic coupling with energy.

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In quantum chromodynamics, the strong-force coupling constant is called $alpha_s$. The key property of QCD is that $alpha_s$ decreases with energy. This behavior is called asymptotic freedom, since at high energies the coupling constant vanishes and particles no longer interact via the strong force (so they are "free particles"). This behavior is exactly the opposite of electrodynamics. To recap: at large distances (low energies), the strong force coupling constant $alpha_s$ is stronger than it is at small distances (high energies) -- this is the opposite behavior of electrodynamics, so we refer to it as "anti-screening."

At low energies (meaning, below about a few hundred MeV, which is still a very large energy in human terms), the coupling constant becomes very large so we can't use perturbation theory to figure out what is going on. A combination of experimental measurements and computer simulations on a lattice tell us that in this regime, QCD enters a regime known as "confinement," where the quarks and gluons form tightly bound states, which appear to us as particles such as protons, neutrons, and pions.

As I said above, the dependence of $alpha_s$ on energy is the opposite of $alpha_{rm EM}$, instead of saying that QCD exhibits "screening", we say that it has "anti-screening." It is more difficult to come up with a pretty picture that describes this situation. One picture that is given is that two quarks interact as if they were connected via a rubber band (or "flux tube"). If you imagine a rubber band connecting the two quarks, then as you separate the two quarks, then the energy in the band increases and so the attraction between the quarks increases. Even though it is less intuitive (at least to me), the conclusion that QCD has anti-screening is based on a very similar calculation to the one that proves QED has screening, it is just that the answer has the opposite sign in QCD.

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In general, the running of the coupling constant $alpha$ with energy is determined by the beta function, where begin{equation} beta(g)=frac{partial g}{partial log mu} end{equation} This equation describes the running of the coupling $g$ with energy scale $mu$. Note that $g$ is related to $alpha$ by $alpha=g^2/4pi$. The sign of the beta function -- which tells us whether the theory exhibits screening or anti-screening -- is determined by the gauge group and matter content. More precisely, in a Yang-Mills theory, the beta function is given (to 1-loop order) by [2] begin{equation} beta(g)=-left(frac{11}{3} C_2(G) - frac{1}{3} n_s T(R_s) - frac{4}{3}n_f T(R_f)right) frac{g^3}{16pi^2} end{equation} where $C_2(G)$ is a constant characterizing the gauge group, $n_s$ is the number of complex scalar particles and $n_f$ is the number of fermions, and $T(R_s)$ and $T(R_f)$ are constants describing the group representation of the scalars and fermions, respectively. Screening occurs if this quantity is positive, and anti-screening if it is negative. This is the most precise answer, but not very intuitive. I personally find it difficult to understand how the pretty pictures of screening and anti-screening generate this formula -- in other words, I would not be able to tell you based on intuition and words alone, without a calculation of the beta function, whether a given theory screens or anti-screens.

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References

[1] https://en.wikipedia.org/wiki/Fine-structure_constant#Variation_with_energy_scale

[2] https://en.wikipedia.org/wiki/Beta_function_(physics)#SU(N)_Non-Abelian_gauge_theory