Re: Mass increasing with temperature in QCD?

Adam,

In your question, you say "the mass increases with temperature of a
plasma".  I'm not sure which mass you mean, the mass of the plasma as
a whole or the mass of the 

virtual particles that are exchanged between the real particles
making up the plasma.  I shall do my best to address both
possibilities.

First, we need a definition of a plasma.  A plasma is a gas of free
charged particles that would be bound together if the temperature were
colder.  For example, at temperatures common for the Earth's surface,
electrons and protons are bound together in hydrogen atoms.  However,
in the Sun the electrons and protons have enough thermal energy to
break their bonds and roam freely; they form a plasma.  Plasma is often
called the fourth state of matter, along with solid, liquid, and gas.

The plasma in your question is most likely the quark-gluon plasma.
Under conditions favorable to humans, the quarks and gluons are bound
tightly together into the protons and neutrons found in every atomic
nucleus.  If two nuclei are smashed together with enough force, the
theory of Quantum Chromodynamics (QCD, or the theory of the strong
nuclear force) predicts that the quarks and gluons should roam freely
(this is the asymptotic freedom that you mentioned) for a very brief
instant before binding together again.

At higher temperatures, the particles that make up the plasma are moving
with greater speeds.  There is a special relativistic effect of the
particle's speed on the particle's mass -- the mass increases according
to the formula

                  m_o
       m(v) = ----------------
                           1/2
              (1 - v^2/c^2)

where m_o is the "rest mass" of the particle.  Therefore if all the
particles are moving more quickly, then they will all have greater
masses and consequently the mass of the whole plasma will increase.

Another way to see this is to note that the kinetic energy of the plasma
is related to its absolute temperature through the equation K.E.=3kT/2,
where k is Boltzmann's constant, 1.3807 x 10^(-23) joules/kelvin.  The
plasma has a mass M related to its total energy E through E=Mc^2.  These
two equations give a temperature-dependent mass

      M(T) = (plasma rest mass) + 3kT/(2c^2)

Clearly, M(T) increases as T increases.

By the way, this effect is not limited to QCD, or even to a plasma.
Given two objects identical in all respects except temperature,
the warmer object is more massive than the cooler object.  A hot
brick weighs more than a cold brick.
_______________________________________________________________________

Alternatively, the virtual particles that are exchanged between the
real particles in the plasma can be more massive if the energy of the
plasma is higher.  

At cooler temperatures, the energy of the plasma is low and quantum
fluctuations in the energy are small.  Fluctuations in the energy large
enough to create virtual particle-antiparticle pairs are relatively
rare.  Only the lightest virtual particles such as photons, electrons,
and positrons, occur with appreciable frequency.

At higher temperatures, the energy of the plasma is high and so is the
uncertainty in the energy.  Large fluctuations in the energy occur
more often, giving rise to particle-antiparticle pairs with larger
masses.  Virtual pions and antipions, with masses 270 times that of
electrons and positrons, are exchanged in large numbers.  At still
higher energies, virtual particles even more massive than pions are
exchanged.

A great website to learn about the quark-gluon plasma in QCD is 
the
Relativistic Heavy Ion Collider (or RHIC) at Brookhaven National
Laboratory on Long Island.  This experiment attempts to create the
quark-gluon plasma and study its properties.

--Randall J. Scalise    http://www.phys.psu.edu/~scalise/