Estimation of Impact Parameter and Transverse Spherocity in heavy-ion collisions at the LHC energies using Machine Learning

Recently, machine learning (ML) techniques have led to a range of numerous developments in the field of nuclear and high-energy physics. In heavy-ion collisions, the impact parameter of a collision is one of the crucial observables which has a significant impact on the final state particle production. However, calculation of such a quantity is nearly impossible in experiments as the length scale ranges in the level of a few fermi. In this work, we implement the ML-based regression technique via Boosted Decision Tree (BDT) to obtain a prediction of impact parameter in Pb-Pb collisions at $\sqrt{s_{\rm NN}}$ = 5.02 TeV using A Multi-Phase Transport (AMPT) model. In addition, we predict an event shape observable, transverse spherocity in Pb-Pb collisions at $\sqrt{s_{\rm NN}}$ = 2.76 and 5.02 TeV using AMPT and PYTHIA8 based on Angantyr model. After a successful implementation in small collision systems, the use of transverse spherocity in heavy-ion collisions has potential to reveal new results from heavy-ion collisions where the production of a QGP medium is already established. We predict the centrality dependent spherocity distributions from the training of minimum bias simulated data and it was found that the predictions from BDT based ML technique match with true simulated data. In the absence of experimental measurements, we propose to implement Machine learning based regression technique to obtain transverse spherocity from the known final state observables in heavy-ion collisions.