From: mcirvin@husc8.harvard.edu (Mcirvin)
Newsgroups: sci.physics
Subject: Technicolor, etc. (was Re: Detecting crackpots - for laymen?)
Date: 22 Nov 92 19:52:13 GMT
Article-I.D.: husc8.mcirvin.722461933

antennae@gn.apc.org writes:

>Dear Scott, please don't say things like "technipions".  English *is*
>something I know about (I have made my living from writing ever since
>leaving Cambridge in the mid seventies).  If you really want to reach
>laymen, it might be a good idea to translate as much physics as you
>can into simple lay language.  

I'm afraid that was a physicist-to-physicist comment, maximized for
brevity rather than accessibility.  Translating technipions into lay
language would take several paragraphs, and the intended audience
would hit 'n.'  Nevertheless, I find the whole subject sufficiently
fascinating that I'm willing to make the explanatory remarks:

When you concoct a theory in particle physics, what that generally
means is that you postulate a number of fields, whose quanta are
going to be the particles of the theory; then you write down a
function called a Lagrangian.  This is a sum of various products and
products of derivatives of the fields, and it determines what the
particles can do.  If you multiply some fields together in one of
the terms, you make an interaction between the corresponding particles;
some derivative terms grant the particles the ability to carry kinetic
energy, and if there's a term in which a field is (roughly) squared,
that term gives the particle mass.  You can tell a lot about a theory
just by looking at the terms in the Lagrangian.  How the properties of
the particles emerge from the Lagrangian is a long story which isn't
necessary here.

Now, these Lagrangians can possess *symmetries.*  This means that you
can do something to the fields-- multiply them by a number, rotate them
in some abstract vector space, or some such thing-- and the Lagrangian
won't change, since it's constructed so that all the changes cancel each
other out.  There are global symmetries, where you have to perform the
same operation on the fields everywhere in spacetime, and there are local
or "gauge" symmetries, where you can do something independent at every
different point (perhaps subject to some smoothness requirements).  It
turns out that to put gauge symmetries into the Lagrangian you have to
introduce extra fields-- and, marvelously, the fields responsible for
the basic forces of nature seem to be just of this variety.  The strong,
weak, and electromagnetic interactions all follow from gauge symmetries, and
in a looser sense gravity seems to as well.

But there's a complication.  The gauge fields that you get from this
process are massless; the quanta have no rest mass.  And for a theory
of weak interactions to work, the quanta have to be rather massive--
eighty or ninety times as massive as a proton.  Also, the usual variety
of mass term for matter particles, like quarks and electrons, seems to
break the gauge symmetry, so you can't have that sort of mass term in
such a theory (I'm sweeping details under the rug; suffice it to say that
the symmetry needs to be absolutely obeyed in the Lagrangian for certain
kinds of mathematical consistency to be maintained).

So the gauge theory for the weak-interaction part of the theory seems
doomed by this requirement of establishing mass terms for both the
gauge particles and the matter particles.

The disease is not so fata, however:  there is a way of having your
cake and eating it too, which is called spontaneous symmetry breaking.
In spontaneous symmetry breaking, the world we see at low energies doesn't
obey the symmetry, but the Lagrangian still does.  So physics could behave
effectively as if there were these mass terms, without actually requiring
any mass terms in the Lagrangian.

Imagine (to use a favorite metaphor of people describing SSB) a Mexican
sombrero.  The hat is symmetric about its central axis; rotate it and it
looks the same.  Now put a marble on the hat and let it roll around freely.
In the marble's lowest-energy state, it's rolling in the trough formed by
the hat's brim.  The marble's state is *not* rotationally symmetric; it's
at some specific angle measured from the center.  Though the dynamics of
the system, as determined by the surface of the hat, is rotationally 
symmetric, the marble's "ground state" is not.  On the other hand, the
marble can roll around in the brim without gaining potential energy; there's
a direction of motion that involves no climb up a hill in potential energy.

It turns out that something similar can be established in a quantum field
theory:  a "sombrero-hat" potential at every point in spacetime, produced
by a couple of terms in the Lagrangian.  The "hat" is in an abstract vector
space of fields.  The middle of the hat corresponds to no field at all;
but the lowest-energy state, what we call the vacuum, is like the marble in
the hat's brim, with a field pervading space that has a specific "angle" in
this abstract space.  The symmetry is spontaneously broken.  The degree
of freedom corresponding to radial motion on the sombrero corresponds to
a massive particle, and the "flat" direction along the brim corresponds to
a massless particle called a Goldstone boson.

Now, something interesting happens when the symmetry that is spontaneously
broken corresponds to part of a gauge symmetry.  There's no Goldstone boson
any more-- instead, you can see by rearranging the formula that the gauge
boson becomes massive, just like we wanted!  By putting in other couplings
to the field that does the symmetry breaking, you can make the matter
particles massive as well.

This is the purpose of the Higgs particle in the standard model; it
lives in a sombrero-like potential (roughly), and it conveys mass to the
W and Z particles and to the quarks and the electron, muon and tauon
via interactions.  

But the only reason the Higgs particle is put into the theory the way it
is is that it's the simplest way to get the right results.  It's somewhat
inelegant:  it's different from all the other particles in the theory,
a spinless particle instead of the spin-1/2 particles that make up matter
and the gauge bosons, which have spin 1.  Also, it's possible to argue that 
the theory is "unnatural":  very fine tuning of coupling constants is
necessary to get it to work out.

Also, the Higgs has never been detected (definitely), so it's reasonable
to look at different possiblities in case experiment turns up something
more complicated.

It appears that spontaneous symmetry breaking can happen without the need
to put in an extra fundamental particle in a sombrero potential.  Though
the calculations are hard or impossible to do at the present time, it is
strongly believed that something similar is happening in the theory of
strong interactions, QCD.  Interactions between quarks and gluons (the
gauge particles associated with the strong nuclear force) somehow produce
spontaneous breaking of an approximate global symmetry of the Lagrangian.
The idea is that the Goldstone bosons correspond to particles well-known
to nuclear and particle physicists:  pions, kaons, and the eta meson.
These are all particles that consist of a quark and an antiquark bound
together.  If the global symmetry were exact, the Goldstone bosons would
be massless.  But the symmetry is actually only approximate; the sombrero
is tilted, so to speak.  So the Goldstone bosons get small masses, and
relations between the masses can be estimated from the theory.  This
seems to agree passably with experiment; the pion, kaon and eta masses
more or less follow the rules.

Now, if you've followed me this far, let me summarize:  Gauge theories
provide an elegant description of strong, weak, and electromagnetic
interactions, except that by themselves they seem to imply that some
particles will be massless that are in fact massive.  Spontaneous symmetry
breaking provides a means of overcoming this difficulty.  In the standard
model this is done with a Higgs particle, but there are some problems with
this, at least from some points of view.  But it can also be done in a
certain kind of theory with strong interactions, if these particle masses
are doing what we think they are.

The idea behind technicolor is to propose a second bunch of quark-like
particles with their own strong interactions.  (The strong interaction
between quarks is often called the color force, so "technicolor" is a 
cute play on that.)  The difference is that the symmetry that is
an approximate global symmetry of the color force is an exact symmetry
here, and at least part of it is in the gauge symmetry of the other
interactions.  So the particle that gets "eaten" to produce mass isn't
a Higgs Goldstone boson, it's the technicolor equivalent of a pion--
it's a "chiral Goldstone boson," or a technipion!

Now, if I understand Scott correctly, you can arrange things so that
some of these "technipions" survive, and they might be detected
experimentally.  That's what he was talking about.

There are all kinds of problems.  It's easy to get this spontaneous
symmetry breaking to endow the weak gauge particles with mass; it's
harder to give masses to the quarks and electrons and such.  The
theory gets rather complicated quickly.  But this is the basic idea.

You can see now why Scott didn't express his statement in lay language--
he'd have to write all this out!

-- 
Matt McIrvin
Newsgroups: sci.physics