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Re: the energy



David,
Aren't you missing the point that overall energy-momentum
conservation applies to every collision, be it quantum or classical?
Regards,
Jack

On Tue, 26 Oct 2004, David Bowman wrote:

Regarding the comments of John & Jack:

JD>>David Bowman wrote:

I believe you left out the effects of a very important
fact here. Protons are *not* elementary particles.

When a proton interacts deeply with another proton asymptotic
freedom becomes relevant. In the collision what may appear to us
to be a proton interacting with another proton is in fact a single
quark from one proton interacting with a single quark of the other
proton. The remaining 4 quarks are oblivious bystanders to what
is going on with the 2 colliding/interacting quarks. This means
that all the KE in these by-standing quarks is essentially
*unavailable* for creating particle-antiparticle pairs.

OK, I'll bite. Why then does the proton-smacking-proton
calculation give the empirically-correct answer?!

Clearly, I did not know that the [CM proton]-smacking-[CM proton]
calculation *did* give the correct answer. Apparently I was
mistaken. I stand corrected. Mea culpa. It seems that the
proton/anti-proton pair creation process at threshold is not a very
asymptotic process and at the energy level of the threshold the
strong interaction is still, well, quite strong even though the
interacting quarks get significantly closer to each other than their
Compton wavelength. I had thought that at such energy/distances the
QCD string tension had essentially gone slack and the relevant quarks
were well within the boundaries of their QCD "bags". It seems that
at the energy level of the p|p-bar pair creation threshold the
inter-quark strings are still stiff enough for a quark triplet proton
to act as a single structureless object.

I'm told this calculation was used in the early 1950s as the
basis for the design of the Bevatron ... which worked!
http://livefromcern.web.cern.ch/livefromcern/antimatter/history/
AM-history01-b.html

Obviously I didn't know the history of this process and made an
ignorant guess about the energy level when asymptotic freedom became
relevant, and I guessed wrong.


This was a decade or more before quarks were conceived of.

In any event, the problem has a high cuteness coefficient anyway.

Oh yeah.

The problem is quite nice, and your solution is about as elegant as
can be.

JU> We didn't, in our wildest imaginations, dream that the proton had
structure in those days. (I arrived at Berkeley in the fall of
'56).

I knew you were older than I was, but I didn't think you were *that*
old. I suspect that you may have some stories to trade with Leigh?

The kinematics of the Bevatron had nothing to do with quarks,
gluons or QCD. The kinematics is identical to that for car-car
collision where one of the cars was parked before the collision. A
lot of the energy in the final state just comes from center-of-mass
motion.

So you, John & CERN say. That's plenty good enough for me. But I
then wonder at what energy range *do* the quarks of a proton begin
behave independently and interact with those of another colliding
hadron on essentially a 1-to-1 rather than a composite basis? If
it is not at a few GeV then is it at a few 10s of GeV? Certainly,
by 100 GeV (above the rest energies of the weak vector bosons)
this independent quark regime must be dominant.?

To see this (this is where John's gamma's can be helpful),
first do the calculation for a collider, where the net spatial
momentum is zero before and after the collision. The final energy
(3 protons and a p-bar, all at rest in the center of momentum
system) must equal the the original energy. The square of the
total energy in the center-of-momentum system is an invariant,
S=(E^{2}-p^{{2})=16, since p=0. Now calculate the same quantity in
the lab system where one of the two initial protons is at rest, to
get the canonical result.

Which is pretty much equivalent to John's calculation.

David Bowman



--
"Trust me. I have a lot of experience at this."
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just before leading them into the Little Big Horn Valley