Emergence of Long-Range Angular Correlations in Low-Multiplicity Proton-Proton Collisions

This Letter presents the measurement of near-side associated per-trigger yields, denoted ridge yields, from the analysis of angular correlations of charged hadrons in proton-proton collisions at $\sqrt{s}=13\mathrm{TeV}$. Long-range ridge yields are extracted for pairs of charged particles with a pseudorapidity difference of $1.4<|\mathrm{\Delta }\eta |<1.8$ and a transverse momentum of $1<p_{\mathrm{T}}<2\mathrm{GeV}/c$, as a function of the charged-particle multiplicity measured at midrapidity. This Letter extends the measurements of the ridge yield to the low multiplicity region, where in hadronic collisions it is typically conjectured that a strongly interacting medium is unlikely to be formed. The precision of the new low multiplicity results allows for the first direct quantitative comparison with the results obtained in ${\mathrm{e}}^{+}{\mathrm{e}}^{-}$ collisions at $\sqrt{s}=91\mathrm{GeV}$ and $\sqrt{s}=183–209\mathrm{GeV}$, where initial-state effects such as preequilibrium dynamics and collision geometry are not expected to play a role. In the multiplicity range $8\lesssim ⟨N_{\mathrm{ch}}⟩\lesssim 24$ where the ${\mathrm{e}}^{+}{\mathrm{e}}^{-}$ results have good precision, the measured ridge yields in $pp$ collisions are substantially larger than the limits set in ${\mathrm{e}}^{+}{\mathrm{e}}^{-}$ annihilations. Consequently, the findings presented in this Letter suggest that the processes involved in ${\mathrm{e}}^{+}{\mathrm{e}}^{-}$ annihilations do not contribute significantly to the emergence of long-range correlations in $pp$ collisions.

Figure 1

Two-particle per-trigger yield measured for charged track pairs with $1<p_{\mathrm{T},\mathrm{trig}}<2\mathrm{GeV}/c$ and $1<p_{\mathrm{T},\mathrm{assoc}}<2\mathrm{GeV}/c$ within the multiplicity range $32<N_{\mathrm{ch}}\le 37$. The jet fragmentation peak has been truncated to ensure a better visibility of the long-range structure. The right panel shows the zero-suppressed projection to $\mathrm{\Delta }\phi$ overlaid with $F(\mathrm{\Delta }\phi )$ (red line) and the area in which the ridge yield is extracted (shaded area). The blue and purple lines represent the second and third harmonic terms of $F(\mathrm{\Delta }\phi )$.

Figure 2

Ridge yield as a function of multiplicity. The black points correspond to the measurement presented in this Letter, while data from CMS [8, 38] are drawn as green and blue markers. Vertical bars denote statistical uncertainties while systematic uncertainty is shown as a shaded area. For both results, at low multiplicity where the lower uncertainty reaches zero, an upper limit is reported, which is drawn as a bar and down arrow. Such points are given at 95% CL for the results from this Letter and at 67% for the results from CMS. The “MB” arrow at $⟨N_{\mathrm{ch}}⟩=11.3$ indicates the multiplicity averaged over the entire studied multiplicity range.

Figure 3

Ridge yield as a function of multiplicity, compared to the upper limits on the ridge yield in ${\mathrm{e}}^{+}{\mathrm{e}}^{-}$ collisions. Vertical bars denote statistical uncertainties while systematic uncertainty is shown as the shaded areas. The orange limits represent the measurement in the thrust-axis reference frame with ALEPH [34]. The horizontal bars in the ALEPH points represent the uncertainty related to the multiplicity conversion from the ALEPH to the ALICE acceptance (see text). All limits are given at 95% CL.

Figure 4

Ridge yield as a function of multiplicity compared to the predictions of pythia8.3 [40] with Monash tune [46] (green) and string shoving [50] (orange) as well as EPOS LHC simulations [42] (blue). Because of a larger jet fragmentation peak width in the simulations than in data, the yield is extracted within $2<|\mathrm{\Delta }\eta |<4$ for the model calculations. A 95% CL is indicated for model calculations when the lower limit of statistical uncertainty is below zero. Some points are slightly displaced along the $x$ axis for better visualization. The band indicates the statistical uncertainty from the event generation and the extraction procedure.