Sunday, August 31, 2014

Frank Wilczek QED—electric charge QCD has three different kinds of charge

Frank Wilczek

The Origin

of Mass

QED—namely, electric charge—QCD has three different kinds of charge.

And instead of one photon that responds to electric charge, QCD has eight color

gluons that can either respond to different color charges or change one into another.

So there is quite a large varietyof sticks, and there are also many different kinds

of hubs that connect them. It seems like things could get terribly complicated and

messy. And so theywould, were it not for the overwhelming symmetryof the theory.

If you interchange red with blue everywhere, for example, you must still get the

same rules. The more complete symmetry allows you to mix the colors continuously,

forming blends, and the rules must come out the same for blends as for pure

colors. I won’t be able to do justice to the mathematics here, of course. But the final

result is noteworthy, and easy to convey: there is one and only one way to assign

rules to all the possible hubs so that the theory comes out fully symmetric. Intricate

it may be, but messy it is not!

With these understandings, QCD is faithfully encoded in squiggles like

Figure 1c, and the force between quarks emerges from squiggles like Figure 1d. We

have definite rules to predict how quarks and gluons behave and interact. The calculations

involved in describing specific processes, like the organization of quarks and

gluons into protons, can be very difficult to carry through, but there is no ambiguity

about the outcome. The theory is either right or wrong—there’s nowhere to hide.

This distinction explains whyon the one hand there are jets, and on the other

hand why the jets are not single particles. A QCD event begins as the materialization

of quark and antiquark, similar to how a QED event begins as the materialization

of lepton-antilepton. They usually give us two jets, aligned along the

original directions of the quark and antiquark, because only hard radiation can

change the overall flow of energy and momentum significantly,

and asymptotic freedom tells us hard radiation is rare.

When a hard radiation does occur, we have an extra jet! But

we don’t see the original quarks or antiquarks, individually,

because they are always accompanied by their soft radiation,

which is common.

The key, again, is asymptotic freedom. Previously, I discussed this phenomenon

in terms of hard and soft radiation. Hard radiation is rare, soft radiation is

common. There’s another wayof looking at it, mathematically equivalent, that is

useful here. From the classical equations of QCD, one would expect a force field

between quarks that falls off as the square of the distance, as in ordinary electromagnetism

(Coulomb’s law). Its enhanced coupling to soft radiation, however, means

that when quantum mechanics is taken into account a “bare” color charge, inserted

into empty space, will start to surround itself with a cloud of virtual color gluons.

These color gluons fields themselves carry color charge, so they are sources of additional

soft radiation. The result is a self-catalyzing enhancement that leads to runaway

growth. A small color charge, in isolation, builds up a

big color thundercloud.

All this structure costs energy, and theoretically the energy

for a quark in isolation is infinite. That’s whywe never see

individual quarks. Having only a finite amount of energy

to work with, Nature always finds a way to short-circuit

the ultimate thundercloud.

This competition can result in a number of compromise solutions, where

the quark and antiquark (or three quarks) are brought close together, but are not

perfectly coincident. Their distribution is described by quantum mechanical wave

functions. Many different stable wave-patterns are possible, and each corresponds

to a different kind of particle that you can observe. There are patterns for protons,

neutrons, and for each entry in the whole Greek and Latin smorgasbord. Each pattern

has some characteristic energy, because the color fields are not entirely cancelled

particles and because the wavicles are somewhat localized. And that, through

is the origin of mass.