Probing Soft Interactions in Collider Experiments: From the Standard Model to Beyond

In modern experimental particle physics with colliders, the most common particle collisions of interest are those containing hard interactions to probe physics at high energy scales, while the soft interactions are considered backgrounds. However, the soft interactions are related to many fundamental aspects of quantum field theory, which lead to rich experimental phenomena. Due to the non-perturbative nature of these interactions and difficulties in first-principle predictions, the theoretical description relies heavily on experimental inputs, which motivated the three analyses of experimental data in this thesis. Inelastic proton-proton (pp) collisions are predominantly governed by quantum chromodynamics (QCD) interactions with low energy transfer, referred to as soft QCD interactions. The event shapes of these collisions encode key interaction properties through the kinematics of outgoing particles. The first analysis in this dissertation measures event shapes at a center-of-mass energy of 13 TeV using the pp collision data taken by the CMS detector in 2018, demonstrating the need for further theoretical developments to improve event shape predictions. The second analysis examines the intrinsic kT models in event generators, alongside the initial-state radiation in parton showers, to describe transverse recoils in the hard scattering process. The tuning of intrinsic kT parameters to experimental data at center-of-mass energies from 38.8 GeV to 13 TeV taken by either fixed-target or collider experiments, along with their scaling behavior with regard to colliding energy and hard-scattering scales, provides insights into soft emissions not accounted for in parton showers. The third analysis searches for new physics within hidden valley models, which predict exotic soft particle emissions through QCD-like extensions of the Standard Model. Sphericity, an event shape observable, along with multiplicity, is used to distinguish these soft unclustered energy patterns from the QCD multijet background. By leveraging the scouting stream of CMS Run 2 data (2016-2018) at 13 TeV, this search achieves high sensitivity across a broad range of signal hypotheses, placing constraints on signal parameters and excluding the models that are incompatible with the data.