Novel approach to probe the underlying event activity through transverse spherocity and relative transverse multiplicity activity event classifier

This study presents a novel multidifferential approach to probe the underlying event (UE) activity in proton--proton collisions at $\sqrt{\mathbit{s}}=\mathbf{13}\text{ }\text{ }\mathrm{TeV}$ using a combination of transverse spherocity (${\mathbit{S}}_{\mathbf{0}}$) and relative transverse multiplicity activity (${\mathbit{R}}_{\mathbf{T}}$) event classifiers. These two observables are used in conjunction to disentangle soft and hard quantum chromodynamics (QCD) processes while minimizing autocorrelation effects typically arising in event selection based solely on multiplicity. Events are categori\ifmmode \bar{o}\else \={o}\fi{}zed into isotropic and jetlike topologies via ${\mathbit{S}}_{\mathbf{0}}$, and further stratified based on UE activity using ${\mathbit{R}}_{\mathbf{T}}$. The study reveals that isotropic events at low ${\mathbit{R}}_{\mathbf{T}}$ exhibit enhanced baryon-to-meson ratios, $\mathbit{p}/\mathbit{\ensuremath{\pi}}$, $\mathbf{\ensuremath{\Lambda}}/\mathbf{2}{\mathbit{K}}_{\mathbit{S}}^{\mathbf{0}}$, and ${\mathbf{\ensuremath{\Lambda}}}_{\mathbf{c}}^{+}/{\mathbit{D}}^{\mathbf{0}}$, with a distinct peak at intermediate ${p}_{\mathrm{T}}$, indicative of collectivelike effects. In contrast, jetlike events show flatter distributions. The analysis is performed using pythia8.309 with Monash, rope hadronization, and QCD based new color reconnection (newCR) tunes. The rope model increases both strangeness and light baryon yields through amplified string tension, while the QCD based newCR model significantly enhances baryon production including charm baryons via the formation of junctions. Notably, ${\mathbf{\ensuremath{\Lambda}}}_{\mathbf{c}}^{+}/{\mathbit{D}}^{\mathbf{0}}$ shows strong sensitivity to newCR and rope models, highlighting the role of junction dynamics in charm hadronization. Our results show that collectivelike signatures in small systems can arise from initial- and intermediate-state QCD effects such as multiparton interactions and color reconnection without requiring final-state medium formation. This new event classification framework provides a powerful tool to probe nonperturbative QCD dynamics and improve hadronization models for current and future LHC data.