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MARKUS KLUTE: Welcome
back to 8.701.

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So in this lecture, you want
to look at hadron colliders

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very briefly as an introductory
lecture to this topic,

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but also as the conclusion of
the discussion we had in QCD.

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So historically speaking,
hadron colliders

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might have been
the tool in order

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to probe the energy frontier.

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So, and that has to do with
accelerator technology,

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the fact that heavy particles
emit less synchrotron radiation

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allows them in
circular colliders

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to be collided at
higher energies.

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This plot here shows
as a function of year

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the energy of the constituents.

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So these are the
elementary particles

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used in the interaction, or the
energy of the quarks and gluons

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being part of the interaction.

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And you see that
typically we find

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that hadron colliders,
here in red,

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have an edge over lepton
colliders in terms

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of the maximum collision energy.

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So the energy
frontier usually is

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given by the hadron
collider as compared

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to the lepton colliders.

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The protocol is a
Livingston plot,

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and it's a little bit old.

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We are now here in 2020.

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We haven't built
this machine yet.

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We might build a lepton collider
at 250 GB in 10 years from now

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or 15 years from now.

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And also, the LHC is very
stable at this energy here.

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But the point of
this lecture is more

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to discuss how we can make
a cross-section calculation

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of important photon collisions.

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So we have already
seen how we can

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make this cross-section
calculation where we have,

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let's say, an initial quark
and an anti-quark colliding

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with exchange of a photon.

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We haven't seen how we can
do this with a Z boson.

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But we'll see that next week.

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This process is called
Drell-Yan production.

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And we're looking at the decay
either of the photon--virtual,

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so virtual photon, or the Z
boson and a pair of leptons,

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electrons, and muons at highest.

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So we can calculate this.

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And we call this cross-section
the hard scattering

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cross-section--
the cross-section

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of this hard scattering process.

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But we need to, in
order to calculate this,

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know the momentum
distribution and the abundance

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of the initial quarks
and anti-quarks.

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And so we do this
using the structure

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from the parton
distribution functions,

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as we discussed them before.

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We have to integrate.

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And those are labeled
here with those q's.

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We have to integrate them
over all possible momentum.

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And we have to
sum over the quark

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species inside the proton.

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For this process, we don't
have to consider the gluon.

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Because of leading order, we
cannot produce a lepton pair

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with gluons.

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Higher orders, we also have
to consider gluon densities

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in this discussion.

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And then the momentum
of the parton collision

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has to be equal
to the momentum--

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the center of mass
energy considered

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in the parton cross-section.

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This process, this technique,
here is called factorization.

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So we factorize the
hard shattering process

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from the structure
of the proton in

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the cross-section calculation.