Measurements of \(\pi ^\pm \), K\(^\pm \), p and \({\bar{\text {p}}}\) spectra in protonproton interactions at 20, 31, 40, 80 and 158 \(\text{ GeV }/c\) with the NA61/SHINE spectrometer at the CERN SPS
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Abstract
Measurements of inclusive spectra and mean multiplicities of \(\pi ^\pm \), K\(^\pm \), p and \({\bar{\text {p}}}\) produced in inelastic p + p interactions at incident projectile momenta of 20, 31, 40, 80 and 158 \(\text{ GeV }/c\) (\(\sqrt{s} = \) 6.3, 7.7, 8.8, 12.3 and 17.3 \(\text{ GeV }\), respectively) were performed at the CERN Super Proton Synchrotron using the large acceptance NA61/SHINE hadron spectrometer. Spectra are presented as function of rapidity and transverse momentum and are compared to predictions of current models. The measurements serve as the baseline in the NA61/SHINE study of the properties of the onset of deconfinement and search for the critical point of strongly interacting matter.
1 Introduction
This paper presents experimental results on inclusive spectra and mean multiplicities of \(\pi ^\pm \), K\(^\pm \), p and \({\bar{\text {p}}}\) produced in inelastic p + p interactions at 20, 31, 40, 80 and 158 \(\text{ GeV }/c\). The measurements were performed by the multipurpose NA61/SHINE experiment [1, 2] at the CERN Super Proton Synchrotron (SPS). The new measurements complement previously published results from the same datasets on \(\pi ^\) production [3] obtained without particle identification as well as on fluctuations of charged particles [4]. These studies form part of the NA61/SHINE strong interaction programme investigating the properties of the onset of deconfinement and searching for the critical point of strongly interacting matter. The programme is mainly motivated by the observation of rapid changes of hadron production properties in central Pb + Pb collisions at about 30\(A\,\text{ GeV }/c\) by the NA49 experiment [5, 6] which were interpreted as the onset of deconfinement. These findings were recently confirmed by the RHIC beam energy programme [7] and the interpretation is supported by the LHC results (see Ref. [8] and references therein). Clearly, a two dimensional scan in collision energy and size of colliding nuclei is required to explore systematically the phase diagram of strongly interacting matter [9].
Pursuing this programme NA61/SHINE already recorded data on p + p, Be + Be, Ar + Sc and p + pb collisions and data taking on Xe + La collisions is scheduled for 2017. Moreover, measurements of Pb + Pb interactions are planned for the coming years [10].
An interpretation of the rich experimental results on nucleus–nucleus collisions relies to a large extent on a comparison to the corresponding data on p + p and p + A interactions. However, the published measurements mainly refer to basic features of unidentified charged hadron production and are sparse. Results on identified hadron spectra, fluctuations and correlations are mostly missing. Detailed measurements of hadron spectra in a large acceptance in the beam momentum range covered by the data in this paper exist only from the NA49 experiment for inelastic p + p interactions at 158 \(\text{ GeV }/c\) [11, 12, 13]. Thus new high precision measurements of hadron production properties in p + p and p + A interactions are essential. They are performed by NA61/SHINE in parallel with the corresponding measurements on nucleus–nucleus collisions using the same detector and thus covering the same acceptance. Precise data on pion, kaon and proton production properties are crucial for constraining basic properties of models of strong interactions.
This publication presents twodimensional spectra of positively and negatively charged pions, kaons, protons and antiprotons produced in p + p interactions in the SPS momentum range (20, 31, 40, 80, 158 \(\text{ GeV }/c\)). The paper is organized as follows: after this introduction the experiment is briefly described in Sect. 2. The analysis procedure is discussed in Sect. 3. Section 4 presents the results of the analysis. In Sect. 5 model calculations are compared to the new measurements. A summary in Sect. 6 closes the paper.
The following variables and definitions are used in this paper. The particle rapidity is calculated in the collision center of mass system (cms), \(y = a\tanh (\beta _\mathrm {L})\), where \(\beta _\mathrm {L} = cp_\mathrm {L}/E\) is the longitudinal component of the velocity and \(p_\mathrm {L}\) and E are the longitudinal momentum and energy given in the cms. The transverse component of the momentum is denoted as \(p_{{\mathrm {T}}} \) and the transverse mass \(m_{{\mathrm {T}}} \) is defined as \(m_{{\mathrm {T}}} = \sqrt{m^2 + (cp_{{\mathrm {T}}})^2}\), where m is the particle mass in GeV. The momentum in the laboratory frame is denoted \(p_{{\mathrm {lab}}}\) and electric charge in units of the electron charge as q. The collision energy per nucleon pair in the center of mass system is denoted as \(\sqrt{s_\mathrm {NN}}\).
2 NA61/SHINE experiment
NA61/SHINE is a fixed target experiment employing a large acceptance hadron spectrometer situated in the North Area H2 beamline of the CERN SPS [1]. A schematic layout is shown in Fig. 1. The main components of the detection system used in the analysis are four large volume time projection chambers (TPC). Two of them, called vertex TPCs (VTPC), are located downstream of the target inside superconducting magnets with maximum combined bending power of 9 Tm. The TPCs are filled with Ar:CO\(_{2}\) gas mixtures in proportions 90:10 for the VTPCs and 95:5 for the Main TPCs. The MTPCs and two walls of pixel timeofflight (ToFL/R) detectors are placed symmetrically to the beamline downstream of the magnets. A GAPTPC (GTPC) between VTPC1 and VTPC2 improves the acceptance for highmomentum forwardgoing tracks.
Basic beam properties and number of events recorded for p + p interactions at incident proton momentum of 20, 31, 40, 80 and 158 \(\text{ GeV }/c\)
\(p_{beam}\; (\text{ GeV }/c)\)  \(\sqrt{s}\;(\text{ GeV })\)  Particles per spill \(\times 10^3\)  Proton fraction (%)  Number of recorded events 

20  6.2  1000  12  \(1.3\times 10^{6}\) 
31  7.7  1000  14  \(3.1\times 10^{6}\) 
40  8.8  1200  14  \(5.2\times 10^{6}\) 
80  12.3  460  28  \(4.3\times 10^{6}\) 
158  17.3  250  58  \(3.5\times 10^{6}\) 
A liquid hydrogen target (LHT) of 20.29 \(\text{ cm }\) length (2.8% interaction length) and 3 \(\text{ cm }\) diameter was placed 88.4 \(\text{ cm }\) upstream of VTPC1. Data were taken with full (denoted as target inserted, I) and empty (denoted as target removed, R) LHT. The event statistics collected in the two configurations are summarised in Table 2.
Interactions in the target are selected with the trigger system by requiring an incoming beam proton and no signal from S4, a small 2 \(\text{ cm }\) diameter scintillation counter placed on the beam trajectory between the two vertex magnets. This minimum bias trigger is based on the disappearance of the beam proton downstream of the target.
3 Analysis procedure
This section starts with a brief overview of the data analysis procedure and the applied corrections. It also defines to which class of particles the final results correspond. A description of the calibration and the track and vertex reconstruction procedure can be found in Ref. [3].
 (i)
application of event and track selection criteria,
 (ii)
determination of spectra of identified hadrons using the selected events and tracks,
 (iii)
evaluation of corrections to the spectra based on experimental data and simulations,
 (iv)
calculation of the corrected spectra and mean multiplicities,
 (v)
calculation of statistical and systematic uncertainties.
 (i)
geometrical acceptance,
 (ii)
contribution from offtarget interactions,
 (iii)
contribution of particles other than primary (see below) hadrons produced in inelastic p + p interactions,
 (iv)
losses of inelastic p + p interactions due to the trigger and the event and track selection criteria employed in the analysis as well as losses of produced hadrons in accepted interactions due to their decays and secondary interactions.
The analysis was performed independently in (y, \(p_{{\mathrm {T}}}\)) bins. The bin sizes were selected taking into account the statistical uncertainties and the resolution of the momentum reconstruction [3]. Corrections as well as statistical and systematic uncertainties were calculated for each bin.
3.1 Event and track selection
3.1.1 Event selection
 (i)
no offtime beam particle detected within a time window of \(\pm 2~\upmu \hbox {s}\) around the trigger particle,
 (ii)
beam particle trajectory measured in at least three planes out of four of BPD1 and BPD2 and in both planes of BPD3,
 (iii)
at least one track reconstructed in the TPCs and fitted to the interaction vertex,
 (iv)
z position of the interaction vertex (fitted using the beam trajectory and TPC tracks) not farther away than 20 \(\text{ cm }\) from the center of the LHT,
 (v)
events with a single, positively charged track with absolute momentum close to the beam momentum (see [3]) are removed in order to eliminate elastic scattering reactions.
3.1.2 Track selection
 (i)
track momentum fit at the interaction vertex should have converged,
 (ii)
fitted x component of particle rigidity \(\left( p_{lab,x}/q\right) \) is positive. This selection minimizes the angle between the track trajectory and the TPC pad direction for the chosen magnetic field direction, reducing uncertainties of the reconstructed cluster position, energy deposition and track parameters,
 (iii)
total number of reconstructed points on the track should be greater than 30,
 (iv)
sum of the number of reconstructed points in VTPC1 and VTPC2 should be greater than 15 or the number of reconstructed points in the GAPTPC should be greater than 4,
 (v)
the distance between the track extrapolated to the interaction plane and the interaction point (impact parameter) should be smaller than 4 \(\text{ cm }\) in the horizontal (bending) plane and 2 \(\text{ cm }\) in the vertical (drift) plane,
 (vi)
the total number of reconstructed \({\mathrm {d}} E/{\mathrm {d}} x\) points on the track should be greater than 30,
 (vii)in case of tof\({\mathrm {d}} E/{\mathrm {d}} x\) identification, three additional selection criteria were used:
 (i)
the hit in the ToF pixel should be matched only with one TPC track,
 (ii)
proper measurement of the hit in charge to digital converter (QDC) and time to digital converter (TDC)
 (iii)
the last point of the track should be in the last 2 padrows of the MTPC to ensure good matching with the ToF hit.
 (i)
Statistics of events and tracks used in \({\mathrm {d}} E/{\mathrm {d}} x\) and tof\({\mathrm {d}} E/{\mathrm {d}} x\) identification methods for target inserted and removed configurations. Events with removed target were used to evaluate corrections for offtarget interactions
Momentum \((\text{ GeV }/c)\)  Number of events  Number of tracks (\({\mathrm {d}} E/{\mathrm {d}} x\) method)  Number of tracks (tof\({\mathrm {d}} E/{\mathrm {d}} x\) method) 

Target inserted  
20  234,758  244,813  17,023 
31  832,608  859,573  44,228 
40  1,604,483  1,625,595  199,775 
80  1,591,076  1,592,538  214,316 
158  1,625,578  4,464,269  158,520 
Target removed  
20  3184  2175  402 
31  12,618  10,080  691 
40  42,115  39,893  4745 
80  51,588  38,132  8003 
158  26,837  41,234  3373 
3.2 Identification techniques
3.2.1 Identification based on energy loss measurement (\({\mathrm {d}} E/{\mathrm {d}} x\))
The contributions of e\(^{+}\), e\(^{}\), \(\pi ^{+}\), \(\pi ^{}\), K\(^{+}\), K\(^{}\), p and \({\bar{\text {p}}}\) are obtained by fitting the \({\mathrm {d}} E/{\mathrm {d}} x\) distributions separately for positively and negatively charged particles in bins of \(p_{{\mathrm {lab}}}\) and \(p_{{\mathrm {T}}} \) with a sum of four functions [16, 17] each corresponding to the expected \({\mathrm {d}} E/{\mathrm {d}} x\) distribution for a given particle type.
In order to ensure similar particle multiplicities in each bin, 20 logarithmic bins are chosen in \(p_{{\mathrm {lab}}}\) in the range 1–100 \(\text{ GeV }/c\) to cover the full detector acceptance. Furthermore the data are binned in 20 equal \(p_{{\mathrm {T}}} \) intervals in the range 0–2 \(\text{ GeV }/c\).
 (i)
relative positions of electrons, kaons and protons to pions were assumed to be \(p_{{\mathrm {T}}} \)independent,
 (ii)
in the analysed data, the asymmetry parameter \(\delta \) is smaller than 0.001 and thus was fixed to zero,
 (iii)
the fitted amplitudes were required to be greater than or equal to 0,
 (iv)
the electron amplitude was set to zero for total momentum \(p_{{\mathrm {lab}}}>\)23.4 \(\text{ GeV }/c\) (i.e. starting from the 13th bin), as the electron contribution vanishes at high \(p_{{\mathrm {lab}}}\),
 (v)
if possible, the relative position of the positive kaon peak was taken to be the same as that of negative kaons determined from the negatively charged particles in the bin of the same \(p_{{\mathrm {lab}}}\) and \(p_{{\mathrm {T}}} \). This procedure helps to overcome the problem of the large overlap between K\(^+\) and protons in the \({\mathrm {d}} E/{\mathrm {d}} x\) distributions.
Examples of fits are shown in Fig. 5 and the values of the fitted peak positions \(x_i\) are plotted in Fig. 6 versus momentum for different particle types i in p + p interactions at 158 \(\text{ GeV }/c\). As expected, the values of \(x_i\) increase with \(p_{{\mathrm {lab}}}\) but do not depend on \(p_{{\mathrm {T}}} \).
In order to ensure good fit quality, only bins with number of tracks grater than 300 are used for further analysis. The Bethe–Bloch curves for different particle types cross each other at low values of the total momentum. Thus, the proposed technique is not sufficient for particle identification at low \(p_{{\mathrm {lab}}}\) and bins with \(p_{{\mathrm {lab}}}<\) 3.98 \(\text{ GeV }/c\) (bins 1–5) are excluded from the analysis based solely on \({\mathrm {d}} E/{\mathrm {d}} x\).
3.2.2 Identification based on time of flight and energy loss measurements (tof\({\mathrm {d}} E/{\mathrm {d}} x\))
 (i)
\(y_i = m_i^2\), where \(m_i\) is a particle mass [19],
 (ii)
relative \({\mathrm {d}} E/{\mathrm {d}} x\) positions of electrons, kaons and protons to pions were assumed to be \(p_{{\mathrm {T}}} \)independent,
 (iii)
the fitted amplitudes were required to be greater than or equal to 0,
 (iv)
if possible, the relative \({\mathrm {d}} E/{\mathrm {d}} x\) position of the positive kaon peak was taken to be the same as that of negative kaons determined from the negatively charged particles in the bin of the same \(p_{{\mathrm {lab}}}\) and \(p_{{\mathrm {T}}} \). This procedure helps to overcome the problem of the large overlap between K\(^+\) and protons in the \({\mathrm {d}} E/{\mathrm {d}} x\) distributions,
 (v)
\(\sigma _{y1} < \sigma _{y2} \) and \(f > 0.7 \), the ”core” distribution dominates the \(m^2\) fit.
The tof\({\mathrm {d}} E/{\mathrm {d}} x\) method allows to fit the kaon yield close to midrapidity. This is not possible using the \({\mathrm {d}} E/{\mathrm {d}} x\) method. Moreover, the kinematic domain in which pion and proton yields can be fitted is enlarged. The results from both methods partly overlap at the highest beam momenta. In these regions the results from the \({\mathrm {d}} E/{\mathrm {d}} x\) method were selected since they have smaller uncertainties.
3.2.3 Probability method
3.3 Corrections
In order to determine the true number of each type of identified particle produced in inelastic p + p interactions a set of corrections was applied to the extracted raw results. The main effects for which corrections were introduced are the following: contribution of interactions outside the liquid hydrogen of the target (offtarget events), detector effects (acceptance, efficiency) and particles from weak decays (feeddown). Note that the manner of application and the number of used correction factors depend on the particle identification technique (i.e. \({\mathrm {d}} E/{\mathrm {d}} x\) or tof\({\mathrm {d}} E/{\mathrm {d}} x\))
3.3.1 Correction for offtarget interactions
To estimate the offtarget interactions about 10% of the data were collected without the liquid hydrogen in the target (socalled target removed data denoted as R). Before the identification procedure (see Sect. 3.2.1) a suitably normalized target removed yield was subtracted from target inserted data. This correction was applied for each bin of total momentum and transverse momentum.
Measured fraction of outoftarget events in recorded p + p interactions at SPS energies
Beam momentum (GeV/c)  Fraction of target removed events (%) 

20  20.22 
31  26.17 
40  15.84 
80  12.53 
158  9.62 
3.3.2 Corrections for detector effects and particles from weak decays (feeddown)
A simulation of the NA61/SHINE detector is used to correct the data for reconstruction efficiency and acceptance. Only inelastic p + p interactions on the hydrogen in the target cell were simulated and reconstructed. The EPOS model [21] was selected to generate the primary interactions as it best describes the NA61/SHINE measurements. A Geant3 based program chain was used to track particles through the spectrometer, generate decays and secondary interactions and simulate the detector response (for more detail see Ref. [3]). The reconstructed tracks were matched to the simulated particles based on the cluster positions. The derived corrections can be applied only for inelastic events. The contribution of elastic events in the data was eliminated by the event and track selection cuts. Hadrons which were not produced in the primary interaction can amount to a significant fraction of the selected track sample. Thus a special effort was undertaken to evaluate and subtract this contribution (see above). As mentioned before correction factors depend on the particle identification technique and are described separately.
The \({\mathrm {d}} E/{\mathrm {d}} x\) method.

\(\left( n_{i}\right) \ ^{MC}_{gen}\): multiplicity of particle type i \(\left( i=\pi ^{+/},\ \text {K}^{+/},\ {\text {p}},\ {\bar{\text {p}}} \right) \) generated by the EPOS model,

\(\left( n_{i}\right) \ ^{MC}_{sel}\): multiplicity of particle type i \(\left( i=\pi ^{+/},\ \text {K}^{+/},\ {\text {p}},\ {\bar{\text {p}}} \right) \) after applying the selection criteria described in the previous section,
The tof\({\mathrm {d}} E/{\mathrm {d}} x\) method.
Due to the lack of a simulation of the ToF system the corrections for the tof\({\mathrm {d}} E/{\mathrm {d}} x\) identification procedure had to be done in a different way than for the \({\mathrm {d}} E/{\mathrm {d}} x\) method, namely they partially employed a data based approach. Each simulated and reconstructed track was extrapolated to the ToF walls and if it crossed one of the ToF pixels it was classified as having a ToF hit. This defined the geometrical acceptance. The efficiency of the ToF pixels was estimated from data.
 (i)
Correction for the detector efficiency and geometrical acceptance
Based on the event and detector simulation the combined geometrical and reconstruction efficiency \(C_i^{{\mathrm geo}}\) was calculated as:where \(\left( n_{i}\right) ^{MCrec}_{{\mathrm {geo}}}\) is the multiplicity of particle type \(i=\pi ^{},\ \pi ^{+}\), K\(^{}\), K\(^{+}\), p, \({\bar{\text {p}}}\) after the TPC selection criteria and track extrapolation to the ToF wall resulting in a ToF hit, and \(\left( n_{i}\right) ^{MCgen}\) is the multiplicity of particle type i generated by the EPOS model. In addition, the last point on the track was required to be located in the last two padrows of a MTPC. The resulting geometrical correction factors for p + p interactions at 158 \(\text{ GeV }/c\) are presented in Fig. 46. Differences between efficiencies for pions, kaons and protons are due to the different particle lifetimes.$$\begin{aligned} C_i^{{\mathrm {geo}}} = \frac{\left( n_{i}\right) ^{MCrec}_{{\mathrm {geo}}}}{\left( n_{i}\right) ^{MCgen}}, \end{aligned}$$(11)  (ii)
Correction for the pixel efficiency of ToFL and ToFR detectors
The pixel efficiency was calculated from data as the ratio between \(\left( n_{i}\right) ^{tof}_{{\mathrm {hit}}}\), the number of tracks with ToF hits in working pixels (pixel efficiency from data higher than 50%) with correct TDC and QDC measurements and \(\left( n_{i}\right) ^{tof}_{{\mathrm {geo}}}\), the number of all tracks which were extrapolated to the particular pixel.The pixel efficiency obtained for p + p interactions at 158 \(\text{ GeV }/c\) is shown in Fig. 47.$$\begin{aligned} C_i^{pixel} = \frac{\left( n_{i}\right) ^{tof}_{{\mathrm {hit}}}}{\left( n_{i}\right) ^{tof}_{{\mathrm {geo}}}}, \end{aligned}$$(12)  (iii)
Correction for decays and interactions between the last measured point in the MTPC and the ToF detectors
The probability of decays and interactions between the last measured point in the MTPC and the ToF detectors was estimated by simulations. The survival probability is defined in the following way:where \(\left( n_{i}\right) ^{MCrec}_{{\mathrm {survive}}}\) is the number of particles which hit a working ToF pixel and which did not decay or interact between the last measured point in the MTPC and the ToF walls. The survival probability is lower than expected from decay only, due to interactions in the Forward Time of Flight detector. The survival probability \(C_i^{{\mathrm {survive}}}\) is presented in Fig. 48.$$\begin{aligned} C_i^{{\mathrm {survive}}}= \frac{\left( n_{i}\right) ^{MCrec}_{{\mathrm {survive}}}}{\left( n_{i}\right) ^{MCrec}_{{\mathrm {geo}}}}, \end{aligned}$$(13)
3.4 Corrected spectra and uncertainties
3.4.1 Corrected spectra

\(C_{i}\): correction factor defined in Eq. (10),

\(\sum \limits _{I} P_{i}(dE/dx)_{p_{{\mathrm {lab}}}, p_{{\mathrm {T}}}} \equiv \sum \limits _{I} P_{i}\): sum over probabilities \(P_{i}\) defined in Eq. (5) for all tracks for inserted target (abbreviated as “I”),

\(\sum \limits _{R} P_{i}(dE/dx)_{p_{{\mathrm {lab}}}, p_{{\mathrm {T}}}} \equiv \sum \limits _{R} P_{i}\): sum over probabilities \(P_{i}\) defined in Eq. (5) for all tracks for removed target (abbreviated as “R”),

B: the normalization factor applied to target removed events,

\(N_{I}\) and \(N_{R}\): the number of events of target inserted and removed, respectively.
3.4.2 Statistical uncertainties
3.4.3 Systematic uncertainties
 (i)
Methods of event selection.
The first uncertainty is related to the acceptance of events with additional tracks from offtime particles. This systematic uncertainty was estimated by changing the width of the time window in which no second beam particle is allowed by \(\pm ~1~\upmu s\) (variation by \(\pm \,50\)%) with respect to the nominal value of ±2\(~\upmu \)s. The maximal difference of the results was assigned as the systematic uncertainty of the selection.
The second source of possible systematic bias are losses of inelastic events due to the interaction trigger. The S4 detector veto mainly selects inelastic and removes elastic scattering events. However, it can also result in some losses of inelastic events. To estimate this effect, the analysis was done using correction factors calculated with and without applying the S4 trigger in the simulation. The difference between these two results was taken as a contribution to the systematic uncertainty.
The next source of systematic uncertainty related to the normalization came from the selection window for the zposition of the fitted vertex. To estimate the systematic uncertainty the selection criteria for the data and the EPOS model were varied in the range of ±10 \(\text{ cm }\) (50%) around the nominal value.
 (ii)
Methods of track selection.
To estimate systematic uncertainty related to the track selection the following variations were performed independently: number of requested points on a track in all TPCs was changed by ± 5 (33% of the standard selection), number of requested points on a track in the VTPCs was reduced and increased by 5 (18% of the criterion).
 (iii)
Identification techniques.
Moreover, uncertainties of the \({\mathrm {d}} E/{\mathrm {d}} x\) identification method were studied and estimated by a 10% variation of the parameter constraints for the function Eq. (1) used for particle identification. In case of tof\({\mathrm {d}} E/{\mathrm {d}} x\) identification uncertainties were estimated by changing the selection criteria related to this technique – the last point of the track should be in the last 2 ± 1 padrows of the MTPC, the QDC signal is or is not required.
 (iv)
Feeddown correction.
The determination of the feeddown correction is based on the EPOS model which describes well the available cross section data for strange particles (see e.g. for \(\Lambda \) at 158 \(\text{ GeV }/c\) Ref. [22] and at 40 \(\text{ GeV }/c\) Ref. [23] and Figs. 23 and 24 in this paper for K\(^{+}\) and K\(^{}\)). Systematic uncertainty comes from the lack of precise knowledge of the production cross section of K\(^{+}\), K\(^{}\), \(\Lambda \), \(\Sigma ^{+}\), \(\Sigma ^{}\), K\(^{0}_{s}\) and \(\bar{\Lambda }\) in case of pions, and in addition of \(\Sigma ^{+}\) in case of protons, and \(\bar{\Lambda }\) in case of antiprotons. Since the corrections are only at the level of a few percent in the phase space region of the measurements a small additional systematic error of 1% was assumed in case of pions and 2% for protons and antiprotons.
4 Results
4.1 Spectra
4.2 Mean multiplicities
Next, mean multiplicities produced in the forward region \(y > 0\) were calculated by integrating the rapidity distributions shown in Fig. 34. The distributions are seen to be nearly Gaussian at all energies except for protons. In order to obtain a good description of the data points, fits were performed with a sum of two identical Gaussian functions with mean position symmetrically displaced around midrapidity. The integrated result was taken as the sum of measured values plus a contribution from the unmeasured region obtained from the fit function. The statistical uncertainty is obtained as the square root of the sum of squares of statistical uncertainties of the measured data points and the square of the statistical error of the extrapolation. The systematic uncertainty was estimated by repeating the complete analysis procedure by varying the components described in Sect. 3.4.3. Doubling of the results gives the \(4\pi \) multiplicities which are listed in Table 4 for \(\pi ^+\), K\(^+\) and p and in Table 5 for \(\pi ^\), K\(^\) and \({\bar{\text {p}}}\).
Mean multiplicity of positively charged particles at SPS energies with statistical and systematic uncertainties
K\(^{+}\)  \(\pi ^{+}\)  p  

20 \(\text{ GeV }/c\)  \( 0.097\pm 0.014\pm 0.006\)  \( 1.884\pm 0.012\pm 0.20\)  \(1.069\pm 0.010\pm 0.13\) 
31 \(\text{ GeV }/c\)  \( 0.157\pm 0.010\pm 0.015\)  \(2.082\pm 0.021\pm 0.20\)  \(0.977\pm 0.003\pm 0.14\) 
40 \(\text{ GeV }/c\)  \( 0.170\pm 0.009\pm 0.023\)  \( 2.390\pm 0.022\pm 0.16\)  \(1.095\pm 0.003\pm 0.09\) 
80 \(\text{ GeV }/c\)  \( 0.201\pm 0.010\pm 0.010\)  \( 2.671\pm 0.022\pm 0.14\)  \(1.093\pm 0.004\pm 0.07\) 
158 \(\text{ GeV }/c\)  \( 0.234\pm 0.014\pm 0.017\)  \( 3.110\pm 0.030\pm 0.26\)  \(1.154\pm 0.010\pm 0.04\) 
Mean multiplicity of negatively charged particles at SPS energies with statistical and systematic uncertainties
K\(^{}\)  \(\pi ^{}\)  \({\bar{\text {p}}}\)  

20 \(\text{ GeV }/c\)  \( 0.024\pm 0.006\pm 0.002\)  \( 1.082\pm 0.021\pm 0.20\)  – 
31 \(\text{ GeV }/c\)  \( 0.045\pm 0.004\pm 0.003\)  \( 1.474\pm 0.031\pm 0.19\)  \( 0.0047\pm 0.0007\pm 0.0003\) 
40 \(\text{ GeV }/c\)  \( 0.084\pm 0.006\pm 0.003\)  \( 1.711\pm 0.028\pm 0.17\)  \( 0.0059\pm 0.0006\pm 0.0004\) 
80 \(\text{ GeV }/c\)  \( 0.095\pm 0.004\pm 0.005\)  \( 2.030\pm 0.031\pm 0.17\)  \( 0.0183\pm 0.0015\pm 0.0010\) 
158 \(\text{ GeV }/c\)  \( 0.132\pm 0.011\pm 0.009\)  \( 2.404\pm 0.034\pm 0.18\)  \( 0.0402\pm 0.0020\pm 0.0030\) 
4.2.1 Energy dependence of mean multiplicities
5 Comparison with hadron production models
This section compares the NA61/SHINE measurements with predictions from the publicly available codes of the microscopic models EPOS 1.99 [21] and UrQMD 3.4 [27, 28]. In EPOS the reaction proceeds via excitation of strings according to Gribov–Regge theory which subsequently fragment into hadrons. UrQMD generates a hadron cascade using elementary cross sections and supplements this process by string production and fragmentation at higher energies.
Two dimensional distributions \(d^{2}n/(dp_{T}dy)\) of \(\pi ^{}\), \(\pi ^{+}\), K\(^{}\), K\(^{+}\), p and \({\bar{\text {p}}}\) produced in inelastic p + p interactions divided by the EPOS model prediction are presented in Fig. 39 at 20 \(\text{ GeV }/c\) and in Fig. 40 at 158 \(\text{ GeV }/c\) and divided by the UrQMD model calculations in Fig. 41 at 20 \(\text{ GeV }/c\) and in Fig. 42 at 158 \(\text{ GeV }/c\).
As demonstrated by Figs. 39 and 40 the EPOS model provides a good description of the measurements in most regions of phase space. Only at larger transverse momenta, where particle yields are low, some underprediction occurs. This conclusion is supported by Figs. 23 and 24 which show projected \(p_{T}\) distributions in selected rapidity intervals.
6 Summary and outlook
Spectra and multiplicities of \(\pi ^{+}\), \(\pi ^{}\), K\(^{+}\), K\(^{}\), p and \({\bar{\text {p}}}\) produced in inelastic p + p interactions were measured with the NA61/SHINE spectrometer at beam momenta of 20, 31, 40, 80, 158 \(\text{ GeV }/c\) at the CERN SPS. New probabilistic analysis techniques based on the energy loss \({\mathrm {d}} E/{\mathrm {d}} x\) in the TPCs and the combination of the measurement of time of flight and energy loss tof\({\mathrm {d}} E/{\mathrm {d}} x\) were employed. Statistical and systematic uncertainties were carefully evaluated. The NA61/SHINE results significantly improve the world data both in precision and momentum coverage. The EPOS 1.99 model [21] provides a good description of the measurements in the SPS energy range, while predictions of the UrQMD 3.4 model [27, 28] significantly differ from the data.
The new NA61/SHINE measurements of particle production in inelastic p + p collisions provide the baseline for the systematic study of the system size dependence of the onset of deconfinement observed by the NA49 experiment in central Pb + Pb collisions in the SPS energy range. In the nearest future the NA61/SHINE collaboration will extend the p + p energy scan by results from p + p interactions at 400 \(\text{ GeV }/c\) beam momentum.
Notes
Acknowledgements
We would like to thank the CERN EP, BE and EN Departments for the strong support of NA61/SHINE. This work was supported by the Hungarian Scientific Research Fund (Grants OTKA 68506 and 71989), the János Bolyai Research Scholarship of the Hungarian Academy of Sciences, the Polish Ministry of Science and Higher Education (Grants 667/NCERN/2010/0, NN 202 48 4339 and NN 202 23 1837), the Polish National Center for Science (Grants 2011/03/N/ST2/03691, 2013/11/N/ST2/03879, 2014/13/N/ST2/02565, 2014/14/E/ST2/00018, 2014/12/T/ST2/00692, 2015/18/M/ST2/00125, 2015/19/N/ST2 /01689 and 2014/15/B/ST2/02537) , the Foundation for Polish Science — MPD program, cofinanced by the European Union within the European Regional Development Fund, the Federal Agency of Education of the Ministry of Education and Science of the Russian Federation (SPbSU research Grant 11.38.242.2015), the Russian Academy of Science and the Russian Foundation for Basic Research (Grants 080200018, 090200664 and 120291503CERN), the Ministry of Education, Culture, Sports, Science and Technology, Japan, GrantinAid for Scientific Research (Grants 18071005, 19034011, 19740162, 20740160 and 20039012), the German Research Foundation (Grant GA 1480/22), the EUfunded Marie Curie Outgoing Fellowship, Grant PIOFGA2013624803, the Bulgarian Nuclear Regulatory Agency and the Joint Institute for Nuclear Research, Dubna (bilateral contract No. 4418115/17), Bulgarian National Science Fund (Grant DN08/11), Ministry of Education and Science of the Republic of Serbia (Grant OI171002), Swiss Nationalfonds Foundation (Grant 200020117913/1), ETH Research Grant TH01 073 and the US Department of Energy, the National Research Nuclear University MEPhI in the framework of the Russian Academic Excellence Project (contract No. 02.a03.21.0005, 27.08.2013).
Supplementary material
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