The change of α s is the opposite to that of α em, and is much faster. In fact the color charge in QCD is anti-screened (for the commonly assumed number of colors and flavors).
(Note, that there is a different numerical factor in this relation for the two singlet configurations: octet–antioctet-gg pair, and triplet–antitriples configuration- q q ¯ pair however, this does not change the qualitative conclusion of our discussion.) This is a consequence of the different structure of charges in QCD compared to QED. The square of color charge q 2 = g 2 s = 4π α s at shorter distances decreases, i.e., α s → 0, which is known as asymptotic freedom. In QCD we get a qualitatively different behavior. In “Proceedings of 1999 European School of High Energy,” p. Qualitative dependence of the energy of a charge singlet pair, popped up from the vacuum, on the distance between the charges, in the case of QED (a) and in the case of QCD (b). The QED vacuum is filled with virtual charge pairs.įIGURE 2. The pair will then annihilate within the time scale 1/ E pair, which is again given by the uncertainty relation. As a consequence, when e + e − pairs pop up from a vacuum, they will be unstable because their energy is always positive (see Fig. (1) varies very little, between 0.987 and 0.993, when changing the pair separation between the Planck scale and infinity. So, in QED the numerical factor 1 − q 2/(4π) = 1 − α em in Eq. For example, at the electroweak scale, i.e., at 100 GeV or r ≃ 2 ♱0 −3 fm, the electromagnetic running constant rises to α em = 1/128, but even at the Planck scale, i.e., at 10 19 GeV or r∼10 −20 fm, its value will still be small, only about α em = 1/76. When going to shorter distances, the electromagnetic constant is therefore increasing, due to less efficient screening by vacuum polarization. The vacuum near the electron is polarized, which effectively lowers the observed charge of the electron.
These pairs tend to be in the configuration where the opposite charge of the pair is closer to the observed electron and the like-sign charge is further from it. From a large distance we, however, do not see the “true” electric charge of an electron because there are many other e + e − pairs in the vacuum around. The square of the electric charge q 2 = e 2 = 4 π α em is at large distances determined by the well-known electromagnetic fine-structure constant α em ≃ 1/137. Let us first look at what is happening in QED.
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