Die Monte-Carlo-Simulation für die Teilchenphysik

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In this episode:
the Monte Carlo simulation for particle physics.
A day with Monte Carlo begins in the kitchenette.
But instead of the Côte d’Azur, we are at the Karlsruhe Institute of Technology.
A physics procedure
on which Doctor Stefan Gieseke is working
is named after the famous district in Monaco.
The theoretical particle physicist has been researching the Monte Carlo Simulation
for over ten years.
With a warm drink in hand, he explains to us
what the Monte Carlo Simulation means and why particle physics needs it.
I’ll begin with the question of what the Monte Carlo Simulation actually is.
In it, things are simulated with random numbers through a computer.
Why random numbers? When we investigate something at the Large Hadron Collider,
we are investigating the characteristics of the smallest particles.
Protons are collided together with tremendous amounts of energy,
more energy
than a proton collision has ever had available to it before:
seven tera electron volts.
This energy is released in one extremely short moment,
thereby producing many new particles.
We would like to simulate this process.
Let’s imagine that we have a proton-proton collision at the LHC.
The protons collide in the detector.
We take a look at what happens,
and we do this before anything measurable actually appears in the detector.
This means the detector is quite a ways off,
and we are still in the incredibly small, microscopic realm.
The whole thing is about as big as a proton.
We have the protons here:
they come at each other either from the side or frontally,
and a parton—which is a quark or a gluon—
is extracted from the protons,
which then collide here in the middle and produce new particles.
We have a proton here and a proton there,
and seven tera-electron volts of centre-of-mass energy,
and they now produce, let’s say in a very small spatial area,
supersymmetric particles.
A few quarks would come out of this, for example,
and perhaps some neutralinos, which are not directly detectable.
If we take a single quark here,
then it will first emit further gluons or other quarks;
that is to say, a bundle of quarks and gluons come into existence here
in a so-called parton shower.
This means that some ten or fifteen particles emerge
out of a single quark.
These whole partons finally become hadrons
in a hadronization model.
This emission
is the first of our simulation.
In the parton shower, new partons come into existence
—a parton is simply the aggregate of quarks and gluons—
which are here beamed in a shower,
in a cascade.
What happens next? These quarks and gluons,
which are coloured and do not naturally occur as isolated particles,
now become so-called hadrons.
Highly excited hadrons... B mesons, D mesons, Kaon, etc.
They are all potential hadrons.
We usually have the Particle Data Book at hand.
That’s this book here. All the characteristics
of all particles are listed in it.
Some 500 or so different kinds of particles exist.
Individual hadrons, on the other hand,
are so unstable that they disintegrate into many new particles.
What’s left over at the end, after all of them have disintegrated,
are certain numbers of only seven different kinds of particles,
which we can measure directly in the detector.
We know protons and neutrons from school, the building blocks of atomic nuclei.
We also know electrons from our school days.
Muons are similar to electrons, only much much heavier
—they appear in cosmic radiation.
There are neutrinos too, but these cannot be detected, so we won’t count them here.
But we also have hadrons, and so-called pions and kaons,
all of which can be directly measured.
And of course photons, which we all know from light—these are very hard particles.
These are the seven particles
that a detector at the LHC can directly measure.
The thirty individual hadrons become many more here,
so that in the end we have perhaps fifty, seventy, or a hundred hadrons.
This keeps going until only those particles that are stable enough
to survive the run through the detector remain.
We make this step from the middle to here on the outside
in our Monte Carlo Simulation.
Since we can only make assertions concerning probabilities,
we do not say, “Aha, we’ve got a Higgs here now...,
and in the end we’ll have such and such a result.”
Rather, we always simulate only one specific story
through probabilities.
We say, therefore: With each disintegration,
we take a random number and decide, on the basis of that number
and the calculated probability,
how frequently something appears.
And then we simulate that exact disintegration with the above frequency,
and then the next disintegration, and so on and so forth.
Now you can see
that there are many decisions on the path that leads from the Higgs boson
to something else
that we want to measure.
These decisions are carried out randomly.
If we take a look at what we have actually measured at the end,
and if we do this enough times—i.e. if we carry out a large number of measurements—
we obtain probability distributions,
which we can measure again,
and which we can then in turn compare with simulated probability distributions.
Thus, with the Monte Carlo method
—with the help of random numbers, that is—we try to make predictions
about things that we can actually measure in the end.
On the one hand, we have the results
or calculations from the theoretical side.
These are compared to the measurements
obtained in experiments.
Yet we can’t actually do this,
because in our theoretical work we postulate particles
that cannot be directly measured in praxis.
However, there are seven particles that we can
directly measure in the detector.
We therefore need simulations,
and this is exactly what we do
with the Monte Carlo Programme.
This simulation allows us to compare apples with apples.