Measurements of particle production in proton-nucleus collisions at high energies enable the study of fundamental properties of Quantum Chromodynamics (QCD) over a broad range of parton fractional momentum \(x\) and parton densities (see [1] for a review). They also provide reference measurements for the studies of deconfined matter created in nucleus–nucleus collisions [2].

The first measurements of charged-particle production in minimum-bias p–Pb collisions at the LHC at a centre-of-mass energy per nucleon-nucleon pair of \(\sqrt{s_\mathrm {NN}}\)  = 5.02 \(\mathrm {TeV}\) [3, 4] showed that: (i) the charged particle multiplicity density at midrapidity scales approximately with the number of participating nucleons (\(\langle N_{\mathrm {part}}\rangle =7.9\pm 0.6\) for minimum-bias collisions) calculated in a Glauber model [5] and (ii) the transverse momentum (\(p_\mathrm {T}\)) spectrum, measured in the range 0.5–20 \(\mathrm {GeV}\!/c\) [4], exhibits binary collision scaling above a few  \(\mathrm {GeV}\!/c\), as expected in the absence of any significant nuclear modification effect. The latter is quantified by the nuclear modification factor, \(R_{\mathrm {pPb}}\), the ratio of the \(p_\mathrm {T}\) spectrum in p–Pb collisions and a reference obtained by scaling the measurement in pp collisions with the number of binary nucleon-nucleon collisions in p–Pb. The preliminary result by the CMS collaboration [6] hints at an enhancement of particle production in p–Pb collisions above binary collision scaling, leading to \(R_{\mathrm {pPb}}>1\), for \(p_\mathrm {T}\) exceeding about 30 \(\mathrm {GeV}\!/c\). The preliminary result by the ATLAS collaboration [7] exhibits also, for collisions corresponding to 0–90 % centrality, \(R_{\mathrm {pPb}}\) values above unity for \(p_\mathrm {T}\) in the range 20–100 \(\mathrm {GeV}\!/c\).

In this letter we present an update of our previously published \(p_\mathrm {T}\) spectra of primary charged particles [4] based on the 60 times larger sample size collected with the ALICE detector [8] in 2013 in minimum-bias collisions. These data allow a significant extension of the transverse momentum range. The present analysis is essentially identical to the previous and therefore we update only the information related to the enlarged data set; the reader is referred to the earlier publications [4, 911] for a more detailed and complete description.

The ALICE minimum-bias trigger is defined by a coincidence of signals in detectors covering in pseudorapidityFootnote 1 \(2.8<\eta <5.1\) (VZERO-A) and \(-3.7<\eta <-1.7\) (VZERO-C). In the 2013 data sample, 106 million events (corresponding to an integrated luminosity of \(50.7\pm 1.6\) \(\upmu \)b\(^{-1}\)) satisfy the trigger and offline event-selection criteria, which select essentially non-single-diffractive (NSD) minimum-bias collisions. The centre-of-mass pseudorapidity is defined as \(\eta _{\mathrm {cms}} = -\eta - |y_{\mathrm {NN}}|\), with the proton beam at positive rapidity; \(|y_{\mathrm {NN}}|=0.465\) is the rapidity of the centre-of-mass for nucleon-nucleon collisions. This equation is exact only for massless or very high \(p_\mathrm {T}\) particles. The spectra are corrected on a statistical basis using the measurements by ALICE in p–Pb collisions of the \(\eta \) distribution of inclusive charged particle production [3] and of the pion, kaon, and proton yields [12]; this correction depends on the \(\eta _\mathrm {cms}\) range and on \(p_\mathrm {T}\), reaching about 20 % for the lowest \(p_\mathrm {T}\) bin. The systematic uncertainty of the particle composition [12] leads to a systematic uncertainty in our spectra of up to 0.4 %.

The systematic uncertainties on the spectra are evaluated as in previous analyses of pp [10], Pb–Pb [9], and p–Pb [4] data. The uncertainty due to the \(p_\mathrm {T}\) scale is negligible below 20 \(\mathrm {GeV}\!/c\) and reaches 1.5 % at 50 \(\mathrm {GeV}\!/c\). The main contributions and the total uncertainties are listed in Table 1.

Table 1 Systematic uncertainties on the \(p_{\mathrm T}\)-differential yields in p–Pb and pp collisions. The quoted ranges span the \(p_{\mathrm T}\) dependence of the uncertainties in the measured range, 0.15–50 \(\mathrm {GeV}\!/c\). Normalization uncertainties are also quoted
Fig. 1
figure 1

Transverse momentum distributions of charged particles in minimum-bias (NSD) p–Pb collisions for different pseudorapidity ranges (upper panel). The spectra are scaled by the factors indicated. The histogram represents the reference spectrum (cross section scaled by the nuclear overlap function, \(T_{\mathrm {pPb}}\)) in inelastic pp collisions, determined in \(|\eta |<0.8\). The lower panel shows the ratio of spectra in p–Pb at backward pseudorapidities to that at \(|\eta _{\mathrm {cms}}|<0.3\). The vertical bars (boxes) represent the statistical (systematic) uncertainties

The \(p_{\mathrm T}\) spectra of charged particles measured in minimum-bias (NSD) p–Pb collisions at \(\sqrt{s_\mathrm{{NN}}} = 5.02\) TeV are shown in Fig. 1 for the ranges \(|\eta _{\mathrm {cms}}|<0.3\), \(-0.8<\eta _{\mathrm {cms}}<-0.3\), and \(-1.3<\eta _{\mathrm {cms}}<-0.8\). The pp reference spectrum, \({\langle T_{\mathrm {pPb}} \rangle (1/2\pi p_\mathrm {T}) {\mathrm d}^{2}\sigma ^{\mathrm {pp}}/{\mathrm d}\eta {\mathrm d}p_{\mathrm T} }\), is also included. \(\langle T_{\mathrm {pPb}}\rangle \) is the average nuclear overlap function, calculated using the Glauber model [13], which gives \(\langle T_{\mathrm {pPb}}\rangle =\langle N_{\mathrm {coll}}\rangle / \sigma _{\mathrm {NN}} =0.0983 \pm 0.0035\) mb\(^{-1}\), with \(\langle N_{\mathrm {coll}}\rangle =6.9\pm 0.6\) and \(\sigma _{\mathrm {NN}}=70\pm 5\) mb. Since the data in pp collisions [10] indicate only a very small \(\eta \) dependence of the \(p_\mathrm {T}\) spectrum in the range measured by ALICE (\(|\eta |<0.8\)), our current reference spectrum is, differently than in [4, 10], for \(|\eta |<0.8\). It was obtained by data interpolation at low \(p_\mathrm {T}\) and by scaling the measurement at \(\sqrt{s} = 7\) TeV with the ratio of spectra calculated with NLO pQCD at \(\sqrt{s} = 5.02\) and 7 TeV [10].

In the lower panel of Fig. 1 the ratios of the spectra for backward (\(-0.8<\eta _{\mathrm {cms}}<-0.3\) and \(-1.3<\eta _{\mathrm {cms}}<-0.8\)) pseudorapidity ranges to that at \(|\eta _{\mathrm {cms}}|<0.3\) are shown. The indication of a slight softening of the \(p_{\mathrm T}\) spectrum when going from central to backward (Pb-side) pseudorapidity, observed already in the pilot-run data of 2012 [4] (note opposite \(\eta _\mathrm {cms}\) sign convention in [4]) is confirmed with better significance and extended in \(p_{\mathrm T}\) down to 0.15 \(\mathrm {GeV}\!/c\).

A good description of our earlier measurement of spectra in p–Pb collisions [4] was achieved in the EPOS3 model [14] including a hydrodynamical description of the collision, while the PHSD model [15] significantly underestimated the spectra for \(p_\mathrm {T}\) values of several  \(\mathrm {GeV}\!/c\).

Fig. 2
figure 2

The nuclear modification factor of charged particles as a function of transverse momentum, measured in minimum-bias (NSD) p–Pb collisions at \(\sqrt{s_{\mathrm {NN}}} = 5.02\) TeV in two pseudorapidity ranges, \(|\eta _{\mathrm {cms}}|<0.3\) and \(-1.3<\eta _{\mathrm {cms}}<0.3\). The statistical errors are represented by vertical bars, the systematic errors by boxes around data points. The relative systematic uncertainties on the normalization are shown as boxes around unity near \(p_{\mathrm {T}}=0\)

In order to quantify nuclear effects in p–Pb collisions, the \(p_{\mathrm T}\)-differential yield relative to the pp reference, the nuclear modification factor, is calculated as:

$$\begin{aligned} R_{\mathrm {pPb}} (p_{\mathrm T} ) = \frac{{\mathrm d}^{2}N^{\mathrm {pPb}}/ {\mathrm d}\eta {\mathrm d}p_{\mathrm {T}} }{\langle T_{\mathrm {pPb}} \rangle {\mathrm d}^{2}\sigma ^{\mathrm {pp}}/{\mathrm d}\eta {\mathrm d}p_{\mathrm T} }, \end{aligned}$$
(1)

where \(N^{\mathrm {pPb}}\) is the charged particle yield in p–Pb collisions.

The measurement of the nuclear modification factor \(R_{\mathrm {pPb}}\) for charged particle production in \(|\eta _{\mathrm {cms}}|<0.3\) and \(-1.3<\eta _{\mathrm {cms}}<0.3\) is shown in Fig. 2. The uncertainties of the p–Pb and pp spectra are added in quadrature, separately for the statistical and systematic uncertainties. The systematic uncertainties are largely correlated between adjacent \(p_\mathrm {T}\) bins. The total systematic uncertainty on the normalization, the quadratic sum of the uncertainty on \(\langle T_{\mathrm {pPb}} \rangle \), the normalization of the pp reference spectrum and the normalization of the p–Pb data, amounts to 6.0 %. The \(R_{\mathrm {pPb}}\) factor is consistent with unity up to \(p_\mathrm {T}\)  \(=\) 50 \(\mathrm {GeV}\!/c\). The average values of \(R_{\mathrm {pPb}}\) in \(|\eta _{\mathrm {cms}}|<0.3\) are \(0.995\pm 0.007\) (stat.) \(\pm \)0.084 (syst.) for the \(p_\mathrm {T}\) range 10–20 \(\mathrm {GeV}\!/c\), \(0.990\pm 0.031\) (stat.)\(\pm \)0.090 (syst.) in the ra