1 Introduction

The measurement of charged particle production in proton–proton collisions at high energy gives insight into the dynamics of soft and hard interactions. Hard parton–parton scattering processes with large momentum transfer are quantitatively described by perturbative Quantum Chromodynamics (pQCD). Measurements at high transverse momenta (p T) at LHC-energies can help to constrain parton distribution and fragmentation functions in current next-to-Leading-Order (NLO) pQCD calculations [1] of charged particle production. As data at various \(\sqrt{s}\) become available at the LHC, a systematic comparison with current NLO-pQCD calculations over a large span of \(\sqrt{s}\) is now possible. However, most particles are produced at low momentum, where particle production is dominated by soft interactions and only phenomenological approaches can be applied (e.g. PYTHIA [24], PHOJET [5]) to describe the data. A systematic comparison to data at different values of \(\sqrt{s}\) is an essential ingredient to tune these Monte Carlo event generators.

Furthermore, the measurement of charged particle transverse momentum spectra in pp collisions serves as a crucial reference for particle spectra in Pb–Pb collisions. To quantify final state effects due to the creation of a hot and dense deconfined matter, commonly referred to as the Quark–Gluon Plasma (QGP), p T spectra in the two collision systems are compared. The observed suppression [6] in central Pb–Pb collisions at LHC-energies at high p T relative to an independent superposition of pp collisions is generally attributed to energy loss of the partons as they propagate through the hot and dense QCD medium. To enable this comparison a pp reference p T spectrum at the same \(\sqrt{s}\) with the same p T coverage has to be provided. Similarly, a pp reference spectrum is also needed for p–Pb collisions to investigate possible initial-state effects in the collision.

In this paper we present a measurement of primary charged particle transverse momentum spectra in pp collisions at \(\sqrt{s} = 0.9,\ 2.76 \ \mbox{and}\ 7\ \text{TeV}\). Primary charged particles are considered here as all charged particles produced in the collision and their decay products, except for particles from weak decays of strange hadrons. The measurement is performed in the pseudorapidity range |η|<0.8 for particles with p T>0.15 GeV/c. Reference spectra for comparison with Pb–Pb spectra at \(\sqrt {s_{\mathrm{NN}}} = 2.76\ \mbox{TeV}\) and p–Pb spectra at \(\sqrt{s_{\mathrm {NN}}} = 5.02\ \mbox{TeV}\) in the corresponding p T range up to p T=50 GeV/c are constructed.

2 Experiment and data analysis

The data were collected by the ALICE apparatus [7] at the CERN-LHC in 2009–2011. The analysis is based on tracking information from the Inner Tracking System (ITS) and the Time Projection Chamber (TPC), both located in the central barrel of the experiment. The minimum-bias interaction trigger was derived using signals from the forward scintillators (VZERO), and the two innermost layers of the ITS, the Silicon Pixel Detector (SPD). Details of the experimental setup used in this analysis are discussed in [8].

The events are selected based on the minimum-bias trigger MBOR requiring at least one hit in the SPD or VZERO detectors, which are required to be in coincidence with two beam bunches crossing in the ALICE interaction region. In addition, an offline event selection is applied to reject beam induced (beam-gas, beam-halo) background. The VZERO counters are used to remove these beam-gas or beam-halo events by requiring their timing signals to be in coincidence with particles produced in the collision. The background events are also removed by exploiting the correlation between the number of the SPD hits and the number of the SPD tracklets (short track segments reconstructed in the SPD and pointing to the interaction vertex). The beam-gas or beam-halo events typically have a large number of hits in the SPD compared to the number of reconstructed tracklets; this is used to reject background events. In total 6.8 M, 65 M and 150 M pp events at \(\sqrt{s}=0.9,\ 2.76\ \mbox{and}\ 7\ \text{TeV}\) fulfill the \(\rm {MB_{{OR}}}\) trigger and offline selection criteria. The typical luminosity for these data taking was about 1029 s−1 cm−2. The average number of interactions per bunch crossing varied from 0.05 to 0.1.

In this analysis the focus is on inelastic (INEL) pp events originating from single-diffractive, double-diffractive and non-diffractive processes. The INEL events are selected with an efficiency \(\varepsilon _{\mathrm{MB}_{\mathrm{OR}}}\) of \(91^{+3.2}_{-1.0}~\%\), \(88.1^{+5.9}_{-3.5}~\%\) and \(85.2^{+6.2}_{-3.0}~\%\) for the three energies. The trigger efficiencies are determined [9] based on detector simulations with PYTHIA6 [24] and PHOJET [5] event generators.

The primary event vertex is determined based on ITS and TPC information. If no vertex is found using tracks in the ITS and the TPC, it is reconstructed from tracklets in the SPD only. Tracks or tracklets are extrapolated to the experimental collision region utilizing the averaged measured beam intersection profile in the xy plane perpendicular to the beam axis.

An event is accepted if the z-coordinate of the vertex is within ±10 cm of the center of the interaction region along the beam direction. This corresponds to about 1.6 standard deviations from the mean of the reconstructed event vertex distribution for all three energies. In this range, the vertex reconstruction efficiency is independent of z. The event vertex reconstruction is fully efficient for events with at least one track in the pseudorapidity range |η|<1.4 for all three energies.

Only tracks within a pseudorapidity range of |η|<0.8 and transverse momenta p T>0.15 GeV/c are selected. A set of standard cuts based on the number of space points and the quality of the track fit in ITS and TPC is applied to the reconstructed tracks [10].

Efficiency and purity of the primary charged particle selection are estimated using simulations with PYTHIA6 [24] and GEANT3 [11] for particle transport and detector response. The overall p T-dependent efficiency (tracking efficiency × acceptance) is 40–73 %, 36–68 % and 40–73 % at \(\sqrt{s}=0.9,\ 2.76\ \mbox{and}\ 7\ \text{TeV}\). At \(\sqrt{s}=2.76~\text{TeV}\) the overall efficiency is lower than at \(\sqrt {s}=0.9\ \text{and}\ 7\ \text{TeV}\) due to the smaller number of operational channels in the SPD. Contamination of secondary tracks which passed all selection criteria amounts to 7 % at p T=0.15 GeV/c and decreases to ∼0.6 % for p T>4 GeV/c. In addition, the contribution from secondary tracks originating from weak decays of strange hadrons was scaled up by a factor of 1–1.5 (p T-dependent) to match the contribution in data. The secondary tracks were subtracted bin-by-bin from the p T spectra.

The p T resolution is estimated from the space point residuals of the track fit. It is verified by the width of the invariant mass peaks of Λ, \(\overline{\varLambda}\) and \(\mathrm{K}^{0}_{\mathrm{{s}}}\), reconstructed from their decays into two charged particles. The relative p T resolution is 3.5 %, 5.5 % and 9 % at the highest p T of 20, 32 and 50 GeV/c at \(\sqrt{s}=0.9,\ 2.76\ \text{and}\ 7~\text{TeV}\), respectively. From invariant mass distributions M inv(p T) of Λ and \(\mathrm{K}^{0}_{\mathrm{{s}}}\), the relative uncertainty on the p T resolution is estimated to be ≈20 % for all three energies. To account for the finite p T resolution of tracks, correction factors to the spectrum for p T>10 GeV/c are derived using an unfolding procedure. The determination of the correction factors is based on measured tracks without involving simulation. The choice of the unfolding procedure is based on the observation that p T smearing has a small influence on the measured spectrum. As input to the procedure a power-law parametrization of the measured p T spectrum for p T>10 GeV/c is used. This parametrization is folded with the p T resolution obtained for a given p T from the measured track covariance matrix. The p T dependent correction factors are extracted from the ratio of the input to the folded parametrization and are applied (bin-by-bin) to the measured p T spectrum. It was checked that the derived correction factors are the same when replacing the measured with the corrected p T distribution in the unfolding procedure. The correction factors depend on \(\sqrt{s}\) due to the change of the spectral shape and reach 2 %, 4 % and 6.5 % at \(\sqrt{s}=0.9,~2.76~\text{and}~7~\text{TeV}\) for the highest p T. The systematic uncertainty of the momentum scale is |Δ(p T)/p T|<0.01 at p T=50 GeV/c, as determined from the mass difference between Λ and \(\overline{\varLambda}\) and the ratio of positively to negatively charged tracks, assuming charge symmetry at high p T.

A summary of the systematic uncertainties is given in Table 1. The systematic uncertainties on the event selection are determined by changing the lower and upper limits on the z-coordinate of the vertex. Track selection criteria [10] are varied to determine the corresponding systematic uncertainties resulting in a maximal contribution of 4.3–5.5 % for p T<0.6 GeV/c. The systematic uncertainties on the tracking efficiency are estimated from the difference between data and simulation in the TPC-ITS track matching efficiency. The systematic uncertainties related to the p T resolution correction are derived from the unfolding procedure including a relative uncertainty on the p T resolution, and reach maximum values at the highest p T covered. The systematic uncertainties on the material budget (∼11.5 % X 0 [12], where X 0 is the radiation length) are estimated by changing the material density (conservatively) by ±10 % in the simulation, contributing mostly at p T<0.2 GeV/c. To assess the systematic uncertainties on the tracking efficiency related to the primary particle composition the relative abundance of π, K, p was varied by 30 % in the simulation; they contribute mostly at p T<0.5 GeV/c. The Monte Carlo (MC) event generator dependence was studied using PHOJET as a comparison, with the largest contribution at p T<0.2 GeV/c. The yield of secondary particles from decays of strange hadrons has been varied by 30 % to determine the corresponding uncertainty of maximum 0.3 % at p T≈1 GeV/c. The total p T dependent systematic uncertainties for the three energies amount to 6.7–8.2 %, 6.4–8.0 % and 6.6–7.9 % and are shown in