Relative transverse activity as an event classifier to investigate collectivity-like phenomena in proton$-$proton collisions at the LHC energies

Abstract

Two-particle number ($R_{2}$) and transverse-momentum ($P_{2}$) correlation functions are studied in proton$-$proton collisions at $\sqrt{s}=13$ TeV simulated with PYTHIA 8, in the low-transverse-momentum region where soft QCD processes dominate the particle production. Events are classified using the relative transverse activity observable $R_{\mathrm{T}}$, which provides a differential characterization of predominantly soft underlying-event (UE) activity. A finite long-range near-side component emerges in the charge-independent correlator $R_{2}^{\mathrm{CI}}$ for UE-dominated events ($2.5 < R_{\mathrm{T}} \leq 5.0$), whereas no corresponding long-range structure is observed in the charge-dependent correlators. This behavior suggests that the ridge-like feature is primarily driven by charge-independent QCD dynamics rather than short-range charge-balancing effects. In contrast, the transverse-momentum correlator $P_{2}^{\mathrm{CI}}$ remains dominated by localized, jet-like structures across all $R_{\mathrm{T}}$ intervals. The near-side correlation peak exhibits a systematic narrowing in $Δ\varphi$ for the charge-independent case with increasing $R_{\mathrm{T}}$, while the charge-dependent correlators remain localized in both $Δη$ and $Δ\varphi$ and show only mild broadening. These results indicate that enhanced UE activity can give rise to collectivity-like long-range correlation structures within a non-hydrodynamic framework and provide a PYTHIA baseline for interpreting small-system measurements at the LHC.

Figures (12)

• Figure 1: Schematic illustration of the Toward, Transverse, and Away regions in the azimuthal ($XY$) plane, defined relative to the azimuthal direction of the leading charged particle alice2019underlying.
• Figure 2: Probability distribution of $R_{\rm T}$ for pp collisions at $\sqrt{s}=13$ TeV generated with PYTHIA 8, evaluated for events containing a leading charged particle with $5 \leq p_{\rm T}^{\rm lead} \leq 40$ GeV/$c$.
• Figure 3: Charged-particle multiplicity ($N_{\rm ch}$) distributions for particles within $|\eta| < 0.8$ and $0.2 < p_{\rm T} < 2$ GeV/$c$ in pp collisions at $\sqrt{s}=13$ TeV, shown for different $R_{\rm T}$ intervals.
• Figure 4: Charge-independent two-particle number correlation functions ($R_{2}^{\rm CI}$) in pp collisions at $\sqrt{s}=13$ TeV, obtained with PYTHIA 8, shown for different $R_{\rm T}$ event classes. Charged particles are selected within $|\eta| < 0.8$ and $0.2 < p_{\rm T} < 2$ GeV/$c$.
• Figure 5: Charge-independent two-particle transverse-momentum correlation functions ($P_{2}^{\rm CI}$) in pp collisions at $\sqrt{s}=13$ TeV, obtained with PYTHIA 8, shown for different $R_{\rm T}$ event classes.