Monte Carlo Generators in a Nutshell

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Both experimental and theoretical high energy physicists make use of monte carlo event generators to make predictions about new physics processes and to discover what certain backgrounds will look like. While I’m not going to describe monte carlo methods in experimental high energy physics (HEP) in too much detail, I want to quickly go over a few concepts that I think are especially important and interesting – basic things that I wish I had learned when I first started doing research.

Using a random-number generator to randomly sample some area of phase space, a monte carlo generator makes calculations at leading order or next to leading order (NLO) of the cross-sections (a cross-section is the probability that a specific event occurs) of particular physics processes (because you can’t simulate all possibilities at once) in some kinematic region. A lot happens in a collision, and a monte carlo (MC) event generator has to simulate all of the sub-processes that occur.

First, the MC generator calculates the hard process – the very first step when the protons collide – using parton distribution functions (also known as PDFs) and perturbation theory, which can tell us the probabilistic distributions of the particles going into the collision and the particles coming out of the collision. A program like the Les Houches Accord PDF Interface (LHAPDF) is used to calculate this step, though some generators can calculate the entire process from start to finish (that is, from hard process to stable final state particles).

What happens next is called parton showering. Protons are composed of quarks and gluons, which are called “partons” and each have a color charge. When you collide protons, you are colliding a bunch of colored partons, and thus have a lot of outgoing partons flying everwhere. Since all of these quarks and gluons have color charges,  these high-energy partons radiate gluons (a kind of “parton bremming”, if you will) until you are left with lower-energy partons, which then can hadronize. Detectors can’t see this part of the process, due to color confinement, but most MC generators, including PYTHIA, Sherpa, and Herwig++ are able to simulate all of this (that is, everything at the parton level).

As the gluons and quarks scatter, they hadronize, becoming color-neutral particles, which we can see in our detector – this is called hadronization, and the events that happen at this level are called the underlying events. After they hadronize, these heavy, unstable particles begin to decay into lighter, stable particles. Once a MC generator reaches this step, it has all of the information about the particles: the four-vectors of the particles and which particles (known as parent particles) have decayed to lighter particles (daughter or child particles).

At this point, you have your final state particles, and can run all the generator-level information through detector simulation software (like Geant4, Delphes, or PGS), that reconstructs what the particle interactions look like in an actual detector. Once you’ve done this, you can treat this simulated monte carlo sample like it is data, and analyze the events to better understand them.

Of course, MC isn’t perfect, and we often apply multiple corrections to our samples to make up for some shortcomings. There are quite a few, but there are two which I think are relatively simple to understand: (1) we have to re-weight our monte carlo to match our data; (2) sometimes, in order to account for higher-order corrections, you have to include what are called K-factors, which are usually calculated by looking at the differences between cross-sections at next-to-leading order and the cross sections at leading order. I’ll cover these in a bit more detail in a later post. That’s all for now!

(photo courtesy of Eram Rizvi)

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