Letting the Machines Search for New Physics

Article: “Anomaly Detection for Resonant New Physics with Machine Learning”

Authors: Jack H. Collins, Kiel Howe, Benjamin Nachman

Reference : https://arxiv.org/abs/1805.02664

One of the main goals of LHC experiments is to look for signals of physics beyond the Standard Model; new particles that may explain some of the mysteries the Standard Model doesn’t answer. The typical way this works is that theorists come up with a new particle that would solve some mystery and they spell out how it interacts with the particles we already know about. Then experimentalists design a strategy of how to search for evidence of that particle in the mountains of data that the LHC produces. So far none of the searches performed in this way have seen any definitive evidence of new particles, leading experimentalists to rule out a lot of the parameter space of theorists favorite models.

A summary of searches the ATLAS collaboration has performed. The left columns show model being searched for, what experimental signature was looked at and how much data has been analyzed so far. The color bars show the regions that have been ruled out based on the null result of the search. As you can see, we have already covered a lot of territory.

Despite this extensive program of searches, one might wonder if we are still missing something. What if there was a new particle in the data, waiting to be discovered, but theorists haven’t thought of it yet so it hasn’t been looked for? This gives experimentalists a very interesting challenge, how do you look for something new, when you don’t know what you are looking for? One approach, which Particle Bites has talked about before, is to look at as many final states as possible and compare what you see in data to simulation and look for any large deviations. This is a good approach, but may be limited in its sensitivity to small signals. When a normal search for a specific model is performed one usually makes a series of selection requirements on the data, that are chosen to remove background events and keep signal events. Nowadays, these selection requirements are getting more complex, often using neural networks, a common type of machine learning model, trained to discriminate signal versus background. Without some sort of selection like this you may miss a smaller signal within the large amount of background events.

This new approach lets the neural network itself decide what signal to  look for. It uses part of the data itself to train a neural network to find a signal, and then uses the rest of the data to actually look for that signal. This lets you search for many different kinds of models at the same time!

If that sounds like magic, lets try to break it down. You have to assume something about the new particle you are looking for, and the technique here assumes it forms a resonant peak. This is a common assumption of searches. If a new particle were being produced in LHC collisions and then decaying, then you would get an excess of events where the invariant mass of its decay products have a particular value. So if you plotted the number of events in bins of invariant mass you would expect a new particle to show up as a nice peak on top of a relatively smooth background distribution. This is a very common search strategy, and often colloquially referred to as a ‘bump hunt’. This strategy was how the Higgs boson was discovered in 2012.

A histogram showing the invariant mass of photon pairs. The Higgs boson shows up as a bump at 125 GeV. Plot from here

The other secret ingredient we need is the idea of Classification Without Labels (abbreviated CWoLa, pronounced like koala). The way neural networks are usually trained in high energy physics is using fully labeled simulated examples. The network is shown a set of examples and then guesses which are signal and which are background. Using the true label of the event, the network is told which of the examples it got wrong, its parameters are updated accordingly, and it slowly improves. The crucial challenge when trying to train using real data is that we don’t know the true label of any of data, so its hard to tell the network how to improve. Rather than trying to use the true labels of any of the events, the CWoLA technique uses mixtures of events. Lets say you have 2 mixed samples of events, sample A and sample B, but you know that sample A has more signal events in it than sample B. Then, instead of trying to classify signal versus background directly, you can train a classifier to distinguish between events from sample A and events from sample B and what that network will learn to do is distinguish between signal and background. You can actually show that the optimal classifier for distinguishing the two mixed samples is the same as the optimal classifier of signal versus background. Even more amazing, this technique actually works quite well in practice, achieving good results even when there is only a few percent of signal in one of the samples.

An illustration of the CWoLa method. A classifier trained to distinguish between two mixed samples of signal and background events learns can learn to classify signal versus background. Taken from here

The technique described in the paper combines these two ideas in a clever way. Because we expect the new particle to show up in a narrow region of invariant mass, you can use some of your data to train a classifier to distinguish between events in a given slice of invariant mass from other events. If there is no signal with a mass in that region then the classifier should essentially learn nothing, but if there was a signal in that region that the classifier should learn to separate signal and background. Then one can apply that classifier to select events in the rest of your data (which hasn’t been used in the training) and look for a peak that would indicate a new particle. Because you don’t know ahead of time what mass any new particle should have, you scan over the whole range you have sufficient data for, looking for a new particle in each slice.

The specific case that they use to demonstrate the power of this technique is for new particles decaying to pairs of jets. On the surface, jets, the large sprays of particles produced when quark or gluon is made in a LHC collision, all look the same. But actually the insides of jets, their sub-structure, can contain very useful information about what kind of particle produced it. If a new particle that is produced decays into other particles, like top quarks, W bosons or some a new BSM particle, before decaying into quarks then there will be a lot of interesting sub-structure to the resulting jet, which can be used to distinguish it from regular jets. In this paper the neural network uses information about the sub-structure for both of the jets in event to determine if the event is signal-like or background-like.

The authors test out their new technique on a simulated dataset, containing some events where a new particle is produced and a large number of QCD background events. They train a neural network to distinguish events in a window of invariant mass of the jet pair from other events. With no selection applied there is no visible bump in the dijet invariant mass spectrum. With their technique they are able to train a classifier that can reject enough background such that a clear mass peak of the new particle shows up. This shows that you can find a new particle without relying on searching for a particular model, allowing you to be sensitive to particles overlooked by existing searches.

Demonstration of the bump hunt search. The shaded histogram is the amount of signal in the dataset. The different levels of blue points show the data remaining after applying tighter and tighter selection based on the neural network classifier score. The red line is the predicted amount of background events based on fitting the sideband regions. One can see that for the tightest selection (bottom set of points), the data forms a clear bump over the background estimate, indicating the presence of a new particle

This paper was one of the first to really demonstrate the power of machine-learning based searches. There is actually a competition being held to inspire researchers to try out other techniques on a mock dataset. So expect to see more new search strategies utilizing machine learning being released soon. Of course the real excitement will be when a search like this is applied to real data and we can see if machines can find new physics that us humans have overlooked!

Read More:

  1. Quanta Magazine Article “How Artificial Intelligence Can Supercharge the Search for New Particles”
  2. Blog Post on the CWoLa Method “Training Collider Classifiers on Real Data”
  3. Particle Bites Post “Going Rogue: The Search for Anything (and Everything) with ATLAS”
  4. Blog Post on applying ML to top quark decays “What does Bidirectional LSTM Neural Networks has to do with Top Quarks?”
  5. Extended Version of Original Paper “Extending the Bump Hunt with Machine Learning”

CMS catches the top quark running


CMS catches the top quark running

Article : “Running of the top quark mass from proton-proton collisions at √ s = 13 TeV“

Authors: The CMS Collaboration

Reference: https://arxiv.org/abs/1909.09193

When theorists were first developing quantum field theory in the 1940’s they quickly ran into a problem. Some of their calculations kept producing infinities which didn’t make physical sense. After scratching their heads for a while they eventually came up with a procedure known as renormalization to solve the problem.  Renormalization neatly hid away the infinities that were plaguing their calculations by absorbing them into the constants (like masses and couplings) in the theory, but it also produced some surprising predictions. Renormalization said that all these ‘constants’ weren’t actually constant at all! The value of these ‘constants’ depended on the energy scale at which you probed the theory.

One of the most famous realizations of this phenomena is the ‘running’ of the strong coupling constant. The value of a coupling encodes the strength of a force. The strong nuclear force, responsible for holding protons and neutrons together, is actually so strong at low energies our normal techniques for calculation don’t work. But in 1973, Gross, Wilczek and Politzer realized that in quantum chromodynamics (QCD), the quantum field theory describing the strong force, renormalization would make the strong coupling constant ‘run’ smaller at high energies. This meant at higher energies one could use normal perturbative techniques to do calculations. This behavior of the strong force is called ‘asymptotic freedom’ and earned them a Nobel prize. Thanks to asymptotic freedom, it is actually much easier for us to understand what QCD predicts for high energy LHC collisions than for the properties of bound states like the proton.  

Figure 1: The value of the strong coupling constant (α_s) is plotted as a function of the energy scale. Data from multiple experiments at different energies are compared to the prediction from QCD of how it should run.  From [5]
Now for the first time, CMS has measured the running of a new fundamental parameter, the mass of the top quark. More than just being a cool thing to see, measuring how the top quark mass runs tests our understanding of QCD and can also be sensitive to physics beyond the Standard Model. The top quark is the heaviest fundamental particle we know about, and many think that it has a key role to play in solving some puzzles of the Standard Model. In order to measure the top quark mass at different energies, CMS used the fact that the rate of producing a top quark-antiquark pair depends on the mass of the top quark. So by measuring this rate at different energies they can extract the top quark mass at different scales. 

Top quarks nearly always decay into W-bosons and b quarks. Like all quarks, the b quarks then create a large shower of particles before they reach the detector called a jet. The W-bosons can decay either into a lepton and a neutrino or two quarks. The CMS detector is very good at reconstructing leptons and jets, but neutrinos escape undetected. However one can infer the presence of neutrinos in an event because we know energy must be conserved in the collision, so if neutrinos are produced we will see ‘missing’ energy in the event. The CMS analyzers looked for top anti-top pairs where one W-boson decayed to an electron and a neutrino and the other decayed to a muon and a neutrino. By using information about the electron, muon, missing energy, and jets in an event, the kinematics of the top and anti-top pair can be reconstructed. 

The measured running of the top quark mass is shown in Figure 2. The data agree with the predicted running from QCD at the level of 1.1 sigma, and the no-running hypothesis is excluded at above 95% confidence level. Rather than being limited by the amount of data, the main uncertainties in this result come from the theoretical understanding of the top quark production and decay, which the analyzers need to model very precisely in order to extract the top quark mass. So CMS will need some help from theorists if they want to improve this result in the future. 

Figure 2: The ratio of the top quark mass compared to its mass at a reference scale (476 GeV) is plotted as a function of energy. The red line is the theoretical prediction of how the mass should run in QCD.

Read More:

  1. “The Strengths of Known Forces” https://profmattstrassler.com/articles-and-posts/particle-physics-basics/the-known-forces-of-nature/the-strength-of-the-known-forces/
  2. “Renormalization Made Easy” http://math.ucr.edu/home/baez/renormalization.html
  3. “Studying the Higgs via Top Quark Couplings” https://particlebites.com/?p=4718
  4. “The QCD Running Coupling” https://arxiv.org/abs/1604.08082
  5. CMS Measurement of QCD Running Coupling https://arxiv.org/abs/1609.05331