Charged particle multiplicities in pp interactions at sqrt(s) = 0.9, 2.36, and 7 TeV

TL;DR

The study provides a comprehensive measurement of primary charged-hadron multiplicity distributions in non-single-diffractive pp collisions at sqrt(s) = 0.9, 2.36, and 7 TeV across multiple pseudorapidity intervals using CMS minimum-bias data. It employs Bayesian unfolding to correct for detector effects and SD subtraction, enabling precise P_n, its moments, and the mean p_T(n) to be extracted. The results show that high-multiplicity tails grow with energy and that KNO scaling is strongly violated at 7 TeV, challenging existing MC models, particularly for low-p_T particle production; PYTHIA8 provides the best overall description among tested generators but still falls short in some regimes. These findings highlight the increasing role of multiple parton interactions and semi-hard processes at higher energies and provide critical input for tuning event generators and refining theoretical descriptions of hadron production. Overall, the work establishes stringent benchmarks for minimum-bias event modeling in the LHC era and informs both phenomenology and detector-level analyses of soft QCD dynamics.

Abstract

Measurements of primary charged hadron multiplicity distributions are presented for non-single-diffractive events in proton-proton collisions at centre-of-mass energies of sqrt(s) = 0.9, 2.36, and 7 TeV, in five pseudorapidity ranges from |eta|<0.5 to |eta|<2.4. The data were collected with the minimum-bias trigger of the CMS experiment during the LHC commissioning runs in 2009 and the 7 TeV run in 2010. The multiplicity distribution at sqrt(s) = 0.9 TeV is in agreement with previous measurements. At higher energies the increase of the mean multiplicity with sqrt(s) is underestimated by most event generators. The average transverse momentum as a function of the multiplicity is also presented. The measurement of higher-order moments of the multiplicity distribution confirms the violation of Koba-Nielsen-Olesen scaling that has been observed at lower energies.

Figures (7)

• Figure 1: A comparison of the uncorrected and fully corrected multiplicity distribution at $\sqrt{s} = 7\,\text{Te\spaceV}\xspace$ for $|\eta|<2.4$ . The uncertainties before corrections are statistical only, while after corrections the statistical and systematic uncertainties are added in quadrature.
• Figure 2: The fully corrected charged hadron multiplicity spectrum for $|\eta|<0.5$, 1.0, 1.5, 2.0, and 2.4, (a) at $\sqrt{s} = 0.9\,\text{Te\spaceV}\xspace$, (b) 2.36$\,\text{Te\spaceV}$, and (c) 7$\,\text{Te\spaceV}$, compared with other measurements in the same $\eta$ interval and at the same centre-of-mass energy Alner:1984isAlner:1985wjAamodt:2010ftAamodt:2010pp. For clarity, results in different pseudorapidity intervals are scaled by powers of 10 as given in the plots. The error bars are the statistical and systematic uncertainties added in quadrature.
• Figure 3: The charged hadron multiplicity distributions with $|\eta|<2.4$ for (a) $p_{\mathrm{T}}\xspace > 0$ and (b) $p_{\mathrm{T}}\xspace > 500{\,\text{Me\spaceV\space/\space}c}\xspace$ at $\sqrt{s} = 0.9$, 2.36, and 7$\,\text{Te\spaceV}$, compared to two different pythia models and the phojet model. For clarity, results for different centre-of-mass energies are scaled by powers of 10 as given in the plots.
• Figure 4: (a) A comparison of $\langle p_{\mathrm{T}}\xspace \rangle$ versus $n$ for $|\eta|<2.4$ with two different pythia models and the phojet model at $\sqrt{s} = 0.9$, 2.36, and 7$\,\text{Te\spaceV}$. For clarity, results for different energies are shifted by the values of $a$ shown in the plots. Fits to the high-multiplicity part ($n>15$) with a linear form in $\sqrt{n}$ are superimposed. (b) The ratios of the higher-energy data to the fit at 0.9 TeV indicate the approximate energy independence of $\langle p_{\mathrm{T}}\xspace \rangle$ at fixed $n$.
• Figure 5: The charged hadron multiplicity distributions in KNO form at $\sqrt{s} = 0.9$ and 7$\,\text{Te\spaceV}$ in two pseudorapidity intervals, (a) $|\eta|<2.4$ and (b) $|\eta|<0.5$.