Measurements of differential two-particle number and transverse momentum correlation functions in pp collisions at $\sqrt{\textit{s}}$ = 13 TeV

TL;DR

This work measures differential two-particle number and transverse-momentum correlations, $R_2$ and $P_2$, in minimum-bias pp collisions at $\sqrt{s}=13$ TeV to probe soft particle production and possible collectivity in the smallest QCD systems. By reporting charged-particle correlations for like-sign and unlike-sign pairs and forming charge-independent and charge-dependent combinations, the study reveals near-side peaks and distinct width patterns that evolve with multiplicity. Comparisons to PYTHIA8 show qualitative agreement but reveal important omissions (notably Bose–Einstein correlations) and magnitude differences, highlighting the need for refined modeling of soft processes. The analysis also extracts a balance function and its integral, finding results consistent with Pb--Pb measurements, suggesting that charge conservation dynamics with limited acceptance persist across system sizes. Overall, the results constrain the soft dynamics in pp and inform model development for small-system correlations.

Abstract

Differential two-particle normalized cumulants ($R_2$) and transverse momentum correlations ($P_2$) are measured as a function of the relative pseudorapidity and azimuthal angle difference $( Δη, Δ\varphi )$ of charged particle pairs in minimum bias pp collisions at $\sqrt{\textit{s}}$ = 13 TeV. The measurements use charged hadrons in the pseudorapidity region of $|η| < 0.8$ and the transverse momentum range \mbox{0.2 $< \textit{p}_{\mathrm T} < $ 2.0 $\mathrm{GeV}/\textit{c}$} in order to focus on soft multiparticle interactions and to complement prior measurements of these correlation functions in p-Pb and Pb-Pb collisions. The correlation functions are reported for both unlike-sign and like-sign pairs and their charge-independent and charge-dependent combinations. Both the $R_2$ and $P_2$ measured in pp collisions exhibit features qualitatively similar to those observed in p--Pb and Pb--Pb collisions. The $Δη$ and $Δ\varphi$ root mean square widths of the near-side peak of the correlation functions are evaluated and compared with those observed in p-Pb and Pb-Pb collisions and show smooth evolution with the multiplicity of charged particles produced in the collision. The comparison of the measured correlation functions with predictions from PYTHIA8 shows that this model qualitatively captures their basic structure and characteristics but feature important differences. In addition, the $R_2^{\rm CD}$ is used to determine the charge balance function of hadrons produced within the detector acceptance of the measurements. The integral of the balance function is found to be compatible with those reported by a previous measurement in Pb--Pb collisions.

Figures (8)

• Figure 1: Correlation functions (a) $R_2^{\mathrm{US}}$, (b) $R_2^{\mathrm{LS}}$, (c) $P_2^{\mathrm{US}}$, (d) $P_2^{\mathrm{LS}}$ of charged hadrons measured in minimum bias pp collisions at $\sqrt{\textit{s}}$ = 13 TeV. Charged hadrons are selected in the range $0.2 < \textit{p}_{\rm T} < 2.0$ GeV/$c$ and with pseudorapidity $|\eta| < 0.8$.
• Figure 2: Correlation functions $R_2^{\mathrm{CI}}$ (left) and $P_2^{\mathrm{CI}}$ (right) of charged hadrons measured in minimum bias pp collisions at $\sqrt{\textit{s}}$ = 13 TeV. Charged hadrons are selected in the range $0.2 < \textit{p}_{\rm T} < 2.0$ GeV/$c$ and with pseudorapidity $|\eta| < 0.8$.
• Figure 3: Projections onto $\Delta \eta$ (left column) and $\Delta \varphi$ (right column) of $R_2^{\mathrm{CI}}$ (top row) and $P_2^{\mathrm{CI}}$ (bottom row) correlation functions of charged hadrons calculated in the selected $\textit{p}_{\rm T}$ range in pp collisions at $\sqrt{\textit{s}}$ = 13 TeV. The $\Delta \eta$ and $\Delta \varphi$ projections are calculated as averages of the two-dimensional correlations in the range $|\Delta \varphi| \leq \pi$ and $|\Delta \eta| \leq 1.6$, respectively. Vertical bars and boxes represent statistical and systematic uncertainties, respectively. Simulations using PYTHIA8 with the Monash 2013 tune and color reconnection (CR) enabled, as described in the text, are shown as green dashed lines.
• Figure 4: Correlation functions $R_2^{\mathrm{CD}}$ (left ) and $P_2^{\mathrm{CD}}$ (right) of charged hadrons in minimum bias pp collisions at $\sqrt{\textit{s}}$ = 13 TeV. Charged hadrons are selected in the range $0.2 < \textit{p}_{\rm T} < 2.0$ GeV/$c$ and with pseudorapidity $|\eta| < 0.8$.
• Figure 5: Projections onto the $\Delta \eta$ (left) and $\Delta \varphi$ (right) axes of the $R_2^{\mathrm{CD}}$ (top) and $P_2^{\mathrm{CD}}$ (bottom) correlation functions shown in Fig. \ref{['fig:r2p2CdSys']}. The $\Delta \eta$ and $\Delta \varphi$ projections are calculated as averages of the two-dimensional correlations in the range $|\Delta \varphi| \leq \pi$ and $|\Delta \eta| \leq 1.6$, respectively. Vertical bars and boxes represent statistical and systematic uncertainties, respectively. Simulations using PYTHIA8 with the Monash 2013 tune and color reconnection (CR) enabled, as described in the text, are shown as green dashed lines.