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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?!
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
This was a decade or more before quarks were conceived of.
In any event, the problem has a high cuteness coefficient anyway.
Oh yeah.