Self Organizing Maps for the Extraction of Deep Inelastic Scattering Observables

Abstract

The most fundamental composite particles in nuclear physics are hadrons, which can be composed of two or three quarks. Hadrons which consist of three quarks are Baryons; two notable types of Baryons are protons and neutrons which are the fundamental particles that comprise atomic nuclei and therefore are the fundamental building blocks of matter. Hadrons which consist of two quarks are mesons; this type of hadron forms from interactions in matter occurring at very high energies. Currently, nuclear scattering experiments are used to probe the structure of hadrons. The experiments consist of beams of leptons fired at designated target hadrons; leptons are a type of spin $\frac{1}{2}$ particle that like quarks and gluons has an unknown substructure. The leptons used in the scattering experiments of interest for this analysis are electrons and muons. Deep inelastic scattering (DIS) collisions are a critical example of scattering experiments that use leptons fired at high enough energies at the target hadrons to enable the user to determine the structure of these hadrons; the goal of these computations is to create theoretical models based on DIS data. The DIS between leptons and target hadrons can be probed using Quantum Chromo Dynamics, or QCD. QCD is a field theory used to describe and analyze strong interactions which occur among partons within the hadron. QCD provides a framework for separating the cross section of DIS into components that can be computed by expansions of the strong couplings and components that can only be computed by experiment, or the ``soft'' parts. Artificial neural networks (ANNs) provide a novel method for modeling the ``soft'' parts of DIS that eliminate user bias in making these models fit the experimental data. ANNs are sets of data organized into nodes, referred to as neurons, that take input data models and use layers of neurons containing computational algorithms to transform them into final sets of data neurons. Previous attempts to use ANNs to model DIS data have used supervised networks, where the final data set was used as a guidance step each time the ANN algorithm is used; this has led to success in eliminating bias in theoretical models but has not made it possible to visualize and classify these models. A new type of neural network, capable of dimensional reduction of data, without the supervising process of the previous networks is needed to effectively model functions describing nuclear scattering for a range of kinematics and to enable us to analyze the models formed during the ANN algorithm based on their behaviors and quality of fit to experimental data sets. The Self Organizing Map (SOM) is an ANN, using unsupervised learning, that was successfully used to create such desired, unbiased theoretical models of the Parton Distribution Functions, or PDFs. In addition, the SOM successfully showed the relationship between how well the generated models fit data sets and the models' behavior by making it possible to observe how the PDFs cluster on two dimensional maps. The SOM was…