Author: Raktim Mukherjee, Department of Physics, St. Xavier's College (Autonomous), Kolkata
Introduction
People often talk about High Energy Physics, but what’s the threshold for high and low energies? It actually depends upon the particle we’re considering. If we accelerate a particle much above its rest mass energy, then it’s said to be High Energy. Let’s consider the energy of 500 MeV. Now if we accelerate a pion (150 MeV) and a proton (938 MeV) at this energy, we can say that the study involving the pion is at High Energy. In this article, the focus will be purely on High Energy Physics, and we’ll also discuss one of the very interesting upcoming experiments and how it’ll help us study the strong force. We’ll also demonstrate one of the ways in which Machine Learning can help us in this endeavor and how various models perform.
Studying the QCD Soup
Who doesn’t love a nice hot soup? We first need to boil the water of course. We can put it on the stove and start heating it or we can also increase the pressure at the same time and the water will gain more energy before it starts to boil (like in a pressure cooker). It’s the same for the Quantum Chromodynamics soup or QCD soup. By QCD soup, we mean Quark-Gluon Plasma (QGP). We’ll talk about the second process i.e., providing energy by compressing matter.
When we take two heavy ions like Pb or Au and collide them at high energy, the nucleons bump into each other and there are many such collisions taking place, somewhat like billiard balls. But unlike billiards, most of the collisions of nucleons are inelastic, i.e., they damage each other. Due to so many collisions, the collision fireball becomes quite hot, and the nucleons get broken down into their constituents - quarks and gluons. This soup remains hot for a very short time (lifetime of ~10 raised to the power of -23 seconds) after which it starts to clump - Hadronisation. Remember, the collision fireball is expanding, and the temperature is not very high either since it’s made from compression of matter. The clumping results in the formation of various kinds of particles, π, p, ρ, K, etc.. After some time, the clumping stops but the expansion continues - Chemical Freezeout. And then the medium gets so dilute that the expansion stops as well - Thermal Freezeout.
In case it’s not apparent already, we point out that such compression of matter is only possible when we’re colliding heavy nuclei together such that there are ample nucleons for not only primary but secondary, tertiary or more collisions. Such collisions create a very dense medium (3-4 times the normal nuclear matter density) in the fireball. This causes the nucleons to overlap, and the quarks and gluons become relatively free, resulting in QGP. Such experiments are called Relativistic Heavy Ion Collision experiments or RHIC experiments. There are a lot of such experiments going on across the world but let's discuss an upcoming experiment which will explore dense cold nuclear matter, the kind expected in the core of neutron stars.
The Compressed Baryonic Matter Experiment
The Compressed Baryonic Matter (CBM) experiment at the Facility for Antiproton and Ion Research (FAIR) is a remarkable endeavor, poised to study the behavior of strongly interacting matter under low temperatures and very high baryonic density conditions. The CBM experiment is expected to have an unprecedented interaction rate, up to 10 MHz. The QCD phase diagram as shown in figure 1 is yet to be fully verified experimentally and the CBM experiment will aid the research in the aforementioned extreme conditions.
Figure 1: The QCD phase diagram. [Source: https://www.researchgate.net/figure/A-possible-sketch-of-the-QCD-phase-diagram_fig3_269116454]
There are many ways to study the different stages of QGP. We can use vector mesons as probes which are created in the early stages of the collision fireball. One such probe is the ω meson (780 MeV). The ω meson has a very short lifetime and decays into e+e- or μ+μ-. The electrons are detected using the RICH (Ring-imaging Cherenkov) detector and the muons using the MUCH (Muon Chamber). Upon detection, we create an invariant mass spectrum to confirm the production of the ω meson and further study its behavior to gain insight on the physics of the fireball.
Demonstrating Machine Learning Techniques
For a long time, physicists have been using univariate cut analysis/graphical cuts for the separation of signal from background. Such analysis proves to be inefficient as the complexity of the data increases. Machine learning techniques help us in multivariate analysis by creating a complex decision boundary over the multivariate phase space. We’ll see how different ML techniques compare to traditional cut analysis. In a way, it can recognize the complex pattern of the data easily.
The data used is generated through Monte-Carlo simulations through the CBM geometry involving the Muon Chamber or MUCH. The MUCH is being designed and built at VECC (Variable Energy Cyclotron Centre), Kolkata. The signal data comprises muons produced from ω decay, and all muon-like tracks are background. The number of tracks is almost the same. The data is divided into a training and a testing set equally.
Figure 2: The input variables.
Upon training and testing, we can see from the ROC curve in figure 3 that almost all the multivariate analysis techniques except for Linear Discriminant perform better than traditional univariate cuts. We can see the same for Signal Efficiency in figure 6. BDTG is Boosted Decision Trees with Gradient Boosting whereas BDT has been implemented with AdaBoost. The other models tested are Multi-layer Perceptron, k-Nearest Neighbours, Friedman's Rule Fit method, Deep Neural Network and HMatrix.
Figure 3: ROC of all the MVA methods
Figure 4: Structure of the Multi-layered Perceptron
After training and testing, we obtain an output distribution on which a graphical cut is applied. This distribution shows the separability of the data by the model. We then measure the purity and efficiency of the cut used. Usually, the cut with the highest value of significance is used since at this value, efficiency = purity.
Figure 5: Output Distribution of the Models
Figure 6: The Classifier Cut Efficiency values for cut corresponding to the highest Significance
These models can also be trained and tested for other probes. People in the CBM community have been using ML for various tasks like the separation of protons and kaons as well as the reconstruction of hyperon. From the high values of efficiency and large AUC-ROC (purity), we can infer the crucial role of machine learning while handling complex data in High Energy Physics.
References
The CBM physics book: Compressed baryonic matter in laboratory experiments. Bengt Friman (Darmstadt, GSI)(ed.) et al. DOI: 10.1007/978-3-642-13293-3 Published in: Lect. Notes Phys. 814 (2011), pp.1-980
Chattopadhyay, S. Physics of strongly interacting matter at high net-baryon density. Eur. Phys. J. Spec. Top. 230, 689–696 (2021). https://doi.org/10.1140/epjs/s11734-021-00024-0.
P. P. Bhaduri, “The physics goals of the CBM experiment at FAIR,” PoS, vol. CPOD2021, p. 031, 2022.
S. Chattopadhyay, Y. Viyogi, P. Bhaduri, and A. Dubey, “Participation in the compressed baryonic matter experiment at FAIR,” 03 2011. [Online]. Available: https://www.currentscience.ac.in/Volumes/100/05/0682.pdf
A. Hoecker et al., “TMVA - Toolkit for Multivariate Data Analysis,” 3 2007.