A generalized statistical model for fits to parton distributions

• DOI: 10.48550/arxiv.2406.01664
• Publication Date: 2024-06-03
• Authors: Mengshi Yan; Tie-Jiun Hou; Zhao Li; Kirtimaan A. Mohan; C. -P. Yuan
• Keywords: High Energy Physics - Theory; High Energy Physics - Phenomenology; High Energy Physics - Experiment (hep-ex); High Energy Physics - Phenomenology (hep-ph); High Energy Physics - Theory (hep-th); FOS: Physical sciences; High Energy Physics - Experiment

Parton distribution functions (PDFs) form an essential part of particle physics calculations. Currently, the most precise predictions for these non-perturbative are generated through fits to global data. A problem that several PDF fitting groups encounter is presence tension in data sets appear pull different directions. In other words, best fit depends on choice set. Several methods capture uncertainty PDFs seemingly inconsistent have been proposed and currently use. These important ensure not underestimated. Here we propose a novel method estimating by introducing generalized statistical model inspired unsupervised machine learning techniques, namely Gaussian Mixture Model (GMM). Using toy PDFs, demonstrate how GMM can be used faithfully reconstruct likelihood associated with fits, which turn accurately determine especially fitted sets. We further show this reduces usual chi-squared function consistent set provide measures optimize number Gaussians GMM.