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[DIGITAL EFFECTS]

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PROFESSOR: Welcome
back to 8.701.

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So we'll start a
new chapter now,

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QCD or quantum chromodynamics.

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And then, this first
lecture of this chapter, we

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talk about the
production of hadrons.

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This is really meant as
an introductory lecture,

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but we will also
already see some very

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interesting and useful concepts.

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So we want to produce
quarks and anti-quark pairs,

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and we do this
electron-positron collisions.

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We have studied in detail this
first part of the diagram.

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Specifically, we
calculated a cross-section

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of muon and
anti-muon production,

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and we also have
seen more changes

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than we have same
kind of particle

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in the final state of the
electron-positron scattering

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to electron-positrons.

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So now, we've replaced
the muons with our quarks

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and anti-quark pairs.

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And the first step, we
want to remind ourselves

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of the available quarks
in this discussion.

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So we have the up quark, the
down quark, charm, strange,

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top, and bottom.

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You see that the
charges are given here,

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and the photon
couples to the charge.

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So the charge is not 1, but
it's either 2/3 or minus 1/3.

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Third

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We have also here
in the table mass

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is given for those particles.

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They range from a few MeV to
173 GeV for the top quark.

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The bottom quark is
about 5 GeV heavy.

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Remember, when we
discussed re-normalization,

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we discussed that those masses
are not fixed parameters,

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but in our perturbation
series, they

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run like the [INAUDIBLE] one.

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So that might cause some
difficulties later on.

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OK so now we want to
produce an up quark

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and an anti-up quark
in this collision.

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So what happens?

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So we now have
collisions, and then we

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produce those particles.

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So let's say an up quark,
and an anti-up here, and then

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your plus and minus collision.

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Those quarks only live
for a very short time,

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or travel a very short
distance in space--

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about 10 to the minus 15 meters.

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And then, they
start to pull in out

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of the vacuum gluons, and
quarks, and anti-quark pairs,

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and those then form into the
actual hadrons after some time.

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And those two pictures here
will look very much the same.

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The difference is
the way we treat

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the hadronization-- the actual
fact of forming hadrons.

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In this first picture,
we are thinking

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about clustering energy
particles together

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and that way form hadrons.

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In this picture here, we connect
them with so-called strings.

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And those are two different
ways to model and model

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the production of hadrons.

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Remember, when we look
at this process here,

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we are looking at
very low-energy kind

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of or lower-energy
kind of phenomena,

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and at lower energies,
the strength of the strong

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interaction, the
strength of QCD, is--

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the coupling is
on the order of 1.

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It can be larger than 1.

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So perturbation theory
is not possible.

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That's why we need
specific models.

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This is all I want
to say at this point.

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We'll come back to this
discussion later on.

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What I actually want to discuss
is what we can learn out

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of measuring cross-section
of hadron production--

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for example, by comparing
directly the cross-section

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of [INAUDIBLE] production
with a cross-section we just

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calculated for
muon/anti-muon production.

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And experimental
results are given here.

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So you see as a
function of energy,

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here from 1 GeV to 7 GeV
center of mass energy,

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and then the lower
plot just continuing

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from about 10 to 60 GeV.

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What you see here is that
there is a rich structure.

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So you see those
resonances here,

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and you also see that there
seem to be some sort of increase

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in the value of this ratio.

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So how can we now
understand this?

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At leading order, we
can just write this down

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we just calculate
its cross-section

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for electron-muon scattering,
or for electron-muon production.

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And we can write this
very same cross-section

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of the leading order for
quark-antiquark production.

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What we find as differences
is the coupling,

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the coupling itself.

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Here, we have to use
the charge of the quarks

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and not the charge
of the electron.

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So there is an additional
factor here, 1/3 or 2/3 squared.

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And then, there's the number
of possible quark pairs

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which are available,
and that depends

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on the number of colors.

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Remember, each quark appears
with three different colors,

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so we have to account
for this factor.

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All right, and then
we built the ratio.

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And the ratio, everything
just cancels out--

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great.

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So we have just a
number of colors

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times the sum of
the charges squared

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of the quarks available.

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What do I mean by "the
quarks available?"

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As we go from lower-energies
to higher energies in this plot

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here, the kinematic--

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the energy is sufficient
to produce particles

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based on the masses available.

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So we find that this
explains a step function.

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Let's look at a
specific example.

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So if you look at center
of mass energies, which

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are larger than 2 times the
mass of the bottom quark,

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and maybe lower than 2 times
the mass of the top quark,

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we are in this
specific regime here.

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Can you see, this
is almost flat,

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and the number we
get is almost 4, OK?

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What we get from this
leading order calculation

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is 3 times 4 over 9 for our
up quark, 1 over 9 for down,

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1 over 9 for strange, 4 over
9 for charm, and 1 over 9

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for our bottom quark, OK?

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So we built the sum here
for all quarks which

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are kinematically available, and
as an answer, we get 11 over 3.

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So this is in very
good agreement--

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a leading order,
very good agreement

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with the experimental results.

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11 over 3 is almost 4.

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Excellent, so this
is clear indication,

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experimental indication,
that this color factor here

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is a real thing.

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There seemed to be 3 up quarks,
3 down quarks, 3 charm quarks,

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and so on.

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And we also see that
this leading order effect

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here, the leading
order calculation,

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is already very precise.

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And the reason for this
is that this process here

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is a QED process.

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So the production
cross-section is QED process,

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as we just discussed.

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So now, why do I actually
have this as part

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of our QCD introduction?

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First, you learned about
the color factor here, OK?

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And second, there is,
indeed, corrections,

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and one of the
correction is the one

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where you actually produce a
real gluon in the final state.

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And those corrections
can be calculated.

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If you go to higher order,
you get a correction

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from this radiated gluon.

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You also get corrections
which looks like this--

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vertex corrections--
and you find

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that the correction here to
[? r ?] is about 1 plus alpha

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s at a specific scale over pi.

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Now, at a reasonable scale,
this is then about 0.1 the value

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of alpha s, and
pi is 3.14, and so

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you get about a few percent, 3%
correction to the r value rate.

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Why is it so important when
there's a small correction?

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It's a percent or few
percent level correction.

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What is really important
is that this process can

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be used in order to demonstrate
the existence of gluons,

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and so gluons have been
discovered this way.

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And the way this was done is
by producing the plus and minus

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collisions and detecting
three bunches of particles--

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too from the quarks,
and one from the gluons.

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And then, to identify
that this gluon on here

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is actually a gluon and
not some other particle,

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one can look at
angular distributions.

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One can identify that this is
a spin 1 particle, and so on.

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So there's a little
bit more work

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needed beyond just showing
that there's [INAUDIBLE],,

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but identifying this
kind of topology

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in the plus and minus conditions
led to the discovery of gluons

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in this kind of conditions.

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So that was my introduction.

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As a next step, I want to
add one more step of, now,

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how can we learn about
this kind of structures

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before we then dive
into Feinmann diagrams,

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or Feinmann calculations,
Feinmann rules for QCD.