Production of pions, kaons and protons in pp collisions at $\sqrt{s}=900$ GeV with ALICE at the LHC

The production of $\pi^+$, $\pi^-$, $K^+$, $K^-$, p, and pbar at mid-rapidity has been measured in proton-proton collisions at $\sqrt{s} = 900$ GeV with the ALICE detector. Particle identification is performed using the specific energy loss in the inner tracking silicon detector and the time projection chamber. In addition, time-of-flight information is used to identify hadrons at higher momenta. Finally, the distinctive kink topology of the weak decay of charged kaons is used for an alternative measurement of the kaon transverse momentum ($p_{\rm T}$) spectra. Since these various particle identification tools give the best separation capabilities over different momentum ranges, the results are combined to extract spectra from $p_{\rm T}$ = 100 MeV/$c$ to 2.5 GeV/$c$. The measured spectra are further compared with QCD-inspired models which yield a poor description. The total yields and the mean $p_{\rm T}$ are compared with previous measurements, and the trends as a function of collision energy are discussed.

Abstract. The production of π + , π − , K + , K − , p, and p at mid-rapidity has been measured in proton-proton collisions at √ s = 900 GeV with the ALICE detector. Particle identification is performed using the specific energy loss in the inner tracking silicon detector and the time projection chamber. In addition, time-of-flight information is used to identify hadrons at higher momenta. Finally, the distinctive kink topology of the weak decay of charged kaons is used for an alternative measurement of the kaon transverse momentum (pt) spectra. Since these various particle identification tools give the best separation capabilities over different momentum ranges, the results are combined to extract spectra from pt = 100 MeV/c to 2.5 GeV/c. The measured spectra are further compared with QCD-inspired models which yield a poor description. The total yields and the mean pt are compared with previous measurements, and the trends as a function of collision energy are discussed.

1
In pp collisions at ultra-relativistic energies the bulk of the 2 particles produced at mid-rapidity have transverse mo-3 menta, p t , below 1 GeV/c. Their production is not calcu-4 lable from first principles via perturbative Quantum Chro- 5 modynamics, and is not well modelled at lower collision 6 energies. This low p t particle production, and species com-7 position, must therefore be measured, providing crucial 8 input for the modelling of hadronic interactions and the 9 hadronization process. It is important to study the bulk 10 production of particles as a function of both p t and parti- 11 cle species. With the advent of pp collisions at the Large 12 Hadron Collider (LHC) at CERN a new energy regime is 13 being explored, where particle production from hard in-14 teractions which are predominantly gluonic in nature, is 15 expected to play an increasing role. Such data will pro- 16 vide extra constraints on the modelling of fragmentation 17 functions. The data will also serve as a reference for the 18 heavy-ion measurements. 19 The ALICE detector [1,2] is designed to perform mea- 20 surements in the high-multiplicity environment expected 21 in central lead-lead collisions at √ s NN = 5.5 TeV at the 22 LHC and to identify particles over a wide range of mo-23 menta. As such, it is ideally suited to perform these mea-24 surements also in pp collisions. 25 This paper presents the transverse momentum spectra 26 and yields of identified particles at mid-rapidity from the 27 first pp collisions collected in the autumn of 2009, during 28 the commissioning of the LHC, at √ s = 900 GeV. The 29 evolution of particle production in pp collisions with colli-30 sion energy is studied by comparing to data from previous 31 experiments. 32 We report π + , π − , K + , K − , p, and p distributions, 33 identified via several independent techniques utilizing spe-34 cific energy loss, dE/dx, information from the Inner Track- 35 ing System (ITS) and the Time Projection Chamber (TPC), 36 and velocity measurements in the Time-Of-Flight array 37 (TOF). The combination of these methods provides par-38 ticle identification over the transverse momentum range 39 0.1 GeV/c < p t < 2.5 GeV/c. Charged kaons, identified via 40 kink topology of their weak decays in the TPC, provide a 41 complementary measurement over a similar p t range. All 42 reported particle yields are for primary particles, namely 43 those directly produced in the collision including the prod-44 ucts of strong and electromagnetic decays but excluding 45 weak decays of strange particles. 46 The paper is organized as follows: In Section 2, the AL-47 ICE detectors relevant for these studies, the experimental 48 conditions, and the corresponding analysis techniques are 49 described. Details of the event and particle selection are 50 presented. In Section 3, the π + , π − , K + , K − , p, and p in-51 clusive spectra and yields, obtained by combining the var-52 ious techniques described in Section 2, are presented. The 53 results are compared with calculations from QCD-inspired 54 models and the p t -dependence of ratios of particle yields, 55 e.g. K/π and p/π, are discussed. Comparisons   approaches unity for events with more than two tracks.

170
The results presented in this paper are normalized to 171 inelastic pp collisions, employing the strategy described in 172 [12,13]. In order to reduce the extrapolation and thus the  In order to compare to previous experimental results, 193 which are only published for the non-single-diffractive 194 (NSD) class, in Section 3, we scale our spectra for the mea-195 sured ratio dN ch /dη| N SD / dN ch /dη| IN EL ≃ 1.185 [12]. To ensure high 213 tracking efficiency and dE/dx-resolution, while keeping 214 the contamination from secondaries and fakes low, tracks 215 are required to have at least 80 clusters, and a χ 2 of the 216 momentum fit that is smaller than 4 per cluster. Since each 217 cluster in the TPC provides two degrees of freedom and 218 the number of parameters of the track fit is much smaller 219 than the number of clusters, the χ 2 cut is approximately 220 2 per degree of freedom. In addition, at least two clusters 221 in the ITS must be associated to the track, out of which 222 at least one is from the SPD. Tracks are further rejected 223 based on their distance-of-closest approach (DCA) to the 224 reconstructed event vertex. The cut is implemented as a 225 function of p t to correspond to about seven (five) stan-226 dard deviations in the transverse (longitudinal) coordi-227 nate, taking into account the p t -dependence of the impact 228 parameter resolution. These selection criteria are tuned to 229 select primary charged particles with high efficiency while 230 minimizing the contributions from weak decays, conver-231 sions and secondary hadronic interactions in the detector 232 material. The DCA resolution in the data is found to be 233 in good agreement with the Monte-Carlo simulations that 234 are used for efficiency corrections (see next Section).

235
Tracks reconstructed in the TPC are extrapolated to 236 the sensitive layer of the TOF and a corresponding signal 237 is searched for. The channel with the center closest to the 238 track extrapolation point is selected if the distance is less 239 than 10 cm. This rather weak criterion results in a high 240 matching efficiency while keeping the fraction of wrongly 241 associated tracks below 1% in the low-density environment 242 presented by pp collisions.

243
The dE/dx measurements in the ITS are used to iden-244 tify hadrons in two independent analyses, based on dif-245 ferent tracking algorithms. One analysis uses the ITS-246 TPC combined tracking, while the other is based on ITS 247 stand-alone tracks. The combined ITS-TPC tracking re-248 sult serves as a cross-check of both the ITS stand-alone 249 and the TPC results in the overlap region. The ITS stand-250 alone analysis extends the acceptance to lower p t than the 251 TPC or ITS-TPC analyses.

252
The combined ITS-TPC analysis uses the same track 253 selection criteria as the TPC only analysis, with the ad-254 ditional requirement of at least four clusters in the ITS, 255 out of which at least one must be in the SPD and at least 256 three in SSD+SDD. This further reduces the contamina-257 tion of secondaries and provides high resolution on track 258 impact parameter and optimal resolution on the dE/dx. 259 The ITS stand-alone tracking uses a similar selection, with 260 a different χ 2 selection and a different DCA selection. In 261 the current tracking algorithm, ITS clusters are assigned 262 a larger position error to account for residual misalign-263 ment of the detector. As a result, the χ 2 values are not 264 properly normalized, but the selection was adjusted to be 265 equivalent to the TPC χ 2 selection by inspecting the dis-266 tributions. The DCA cut in the ITS analysis uses the same 267 p t -dependent parametrization as for TPC tracks, but with 268 different parameters to account for the different resolution. 269

322
In both the ITS stand-alone and in the ITS-TPC analy-323 ses, the dE/dx measurement from the SDD and the SSD 324 is used to identify particles. The stand-alone tracking re-325 sult extends the momentum range to lower p t than can be 326 measured in the TPC, while the combined tracking pro-327 vides a better momentum resolution.

328
The energy loss measurement in each layer of the ITS 329 is corrected for the track length in the sensitive volume 330 using tracking information. In the case of SDD clusters, a 331 linear correction for the dependence of the reconstructed 332 raw charge as a function of drift time due to the com-333 bined effect of charge diffusion and zero suppression is 334 also applied [5]. For each track, dE/dx is calculated using 335 a truncated mean: the average of the lowest two points 336 in case four points are measured, or a weighted sum of 337 the lowest (weight 1) and the second lowest point (weight 338 1/2), in case only three points are measured.   For the ITS stand-alone track sample, the histograms 343 are fitted with three Gaussians and the integral of the 344 Gaussian centered at zero is used as the raw yield of the 345 corresponding hadron species. In a first step, the peak 346 widths σ of the peaks are extracted as a function of p t 347 for pions and protons in the region where their dE/dx 348 distributions do not overlap with the kaon (and electron) 349 distribution. For kaons, the same procedure is used at low 350 p t , where they are well separated. The p t -dependence of 351 the peak width is then extrapolated to higher p t with the 352 same functional form used to describe the pions and pro-353 tons. The resulting parametrizations of the p t dependence 354 of σ are used to constrain the fits of the ln[dE/dx] distri-355 butions to extract the raw yields.  nents, prompt particles, secondaries from strange particle 387 decays and secondaries produced in the detector material 388 for each hadron species. Alternatively, the contamination 389 from secondaries have been determined using Monte-Carlo 390 samples, after rescaling the Λ yield to the measured val-391 ues [24]. The difference between these two procedures is 392 about 3% for protons and is negligible for other particles. 393 Figure 3 shows the total reconstruction efficiency for 394 primary tracks in the ITS stand-alone, including the ef-395 fects of detector and tracking efficiency, the track selection 396 cuts and residual contamination in the fitting procedure, 397 as determined from the Monte-Carlo simulation. This ef-398 ficiency is used to correct the measured raw yields after 399 subtraction of the contributions from secondary hadrons. 400 The measured spectra are corrected for the efficiency of 401 the primary vertex reconstruction with the SPD using 402 the ratio between generated primary spectra in simulated 403 events with a reconstructed vertex and events passing the 404 trigger conditions. 405 Systematic errors are summarized in Table 1. The sys-406 tematic uncertainty from secondary contamination has been 407 estimated by repeating the full analysis chain with differ-408 ent cuts on the track impact parameter and by comparing 409 the two alternative estimates outlined above.    In the lowest p t -bins, a larger systematic error has been 426 assigned to account for the steep slope of the tracking effi-427 ciency as a function of the particle transverse momentum 428 (see Fig. 3). As in the case of the ITS, a truncated-mean procedure 443 is used to determine dE/dx (60% of the points are kept). 444 This reduces the Landau tail of the dE/dx distribution to 445 the extent that it is very close to a Gaussian distribution. 446 Examples of the dE/dx distribution in some p t bins 447 are shown in Fig. 5. The peak centered at zero is from 448 kaons and the other peaks are from other particle species. 449 As the background in all momentum bins is negligible, the 450 integrals of the Gaussian give the raw yields.  weak decays amounts to up to 14% and the correction for 478 secondaries from material up to 4% for protons with 400 479 MeV/c < p t < 600 MeV/c. For other particle species and 480 other transverse momenta the contamination is negligible. 481 The systematic errors in the track reconstruction and 482 in the removal of secondary particles have been estimated 483 by varying the number of standard deviations in the dis-484 tance-to-vertex cut, using a fixed cut of 3 cm instead of 485 the variable one, and varying the SPD-TPC matching cut. 486 Their impact on the corrected spectra is less than 5%. The 487 influence of the uncertainty in the material budget has 488 been examined by varying it by 7%. This resulted in the 489 systematic errors given in Table 2. The uncertainty due 490 to a possible deviation from a Gaussian shape has been 491 established by comparing the multi-Gauss fit with a 3-σ 492 band in well separated regions. The precision of the kink 493 rejection is estimated to be within 3%.

494
The correction for the event selection bias has been 495 tested with two event generators, PYTHIA [15,16] and 496 PHOJET [18] and the corresponding uncertainty is less 497 than 1%.   528 Finally, tracks whose particle identity as determined 529 from the TOF information is not compatible with the one 530 inferred from the dE/dx signal in the TPC within five σ 531 have been removed. This TOF-TPC compatibility crite-532 rion rejects about 0.6% of the tracks and further reduces 533 the small contamination coming from tracks incorrectly 534 associated with a TOF signal.
The symmetric treatment of kaons and pions in the defi-

587
The TOF matching efficiency has been tested with 588 data, using dE/dx in the TPC to identify the particles.

589
Good agreement between the efficiencies obtained from  systematic errors π ± K ± p and p TOF < 3% < 6% < 4% matching (pt> 1 GeV/c) efficiency < 7.5% (pt= 0.7 GeV/c) PID procedure < 2% < 7% < 3% the data and from Monte-Carlo simulations is observed in 591 case of pions and kaons, with deviations at the level of, 592 at most, 3% and 6% respectively, over the full transverse-593 momentum range. The observed differences are assigned 594 as systematic errors, see Table 3. In the case of protons 595 and antiprotons, larger differences are observed at p t be-596 low 0.7 GeV/c, where the efficiency varies very rapidly 597 with momentum. This region is therefore not considered 598 in the final results (see Table 3).

599
Other sources of systematic errors related to the TOF 600 PID procedure have been estimated from Monte-Carlo 601 simulations and cross-checked with data. They include the 602 effect of the residual contribution from tracks wrongly as-603 sociated with TOF signals, and the quality and stability 604 of the fit procedure used for extracting the yields. Table 3 605 summarizes the maximal value of the systematic errors ob-606 served over the full transverse momentum range relevant 607 in the analysis, for each of the sources mentioned above. (2) K ± → π ± + π 0 , (B.R. 20.66%). for the two-body decay (2) K → π + π 0 is 205 MeV/c.

649
All three limits can be seen as peaks in Fig. 10 (a), which 650 shows the q t distribution of all measured kinks inside the 651 selected volume and rapidity range |y| < 0.7. Selecting 652 kinks with q t > 40 MeV/c removes the majority of π-653 decays as shown by the dashed (before) and solid (after) 654 histograms.

655
The invariant mass for the decay into µ ± + ν µ is cal-656 culated from the measured difference between the mother 657 and daughter momentum, their decay angle, assuming zero 658 mass for the neutrino. Figure 10 Fig. 10. (Color online) (a) qt distribution of the daughter tracks with respect to mother momentum for all reconstructed kinks inside the analyzed sample. The dashed(solid) histograms show the distribution before (after) applying the qt > 40 MeV/c cut. (b) Invariant mass of the two-body decays K ± /π ± → µ ± + νµ for candidate kaon kinks. Solid curve: after applying qt >40 MeV/c; dashed curve: without this selection (hence also showing the pion decays). (c) dE/dx of kinks as a function of the mother momentum, after applying the full list of selection criteria for their identification. of kaons. The few tracks outside these limits are at mo-672 menta below 600 MeV/c (less than 5%) and they have 673 been removed in the last analysis step.

674
Efficiency and acceptance The total correction factor in-675 cludes both the acceptance of kinks and their efficiency 676 (reconstruction and identification). The study has been 677 performed for the rapidity interval |y| < 0.7, larger than 678 the corresponding rapidity interval for the other studies 679 in order to reduce the statistical errors.

680
The acceptance is defined as the ratio of weak decays 681 (two-and three-body decays) whose daughters are inside 682 the fiducial volume of the TPC to all kaons inside the same 683 rapidity window (Fig. 11, upper part). It essentially re-684 flects the decay probability. However, the acceptance is not  The efficiency is the ratio of reconstructed and identi-

699
The contamination due to random associations of pri-700 mary and secondary charged tracks has been established 701 using Monte-Carlo simulations and it is systematically 702 smaller than 5% in the studied p t -range as also shown 703 in Fig. 11. Hadronic interactions are the main source of 704 these fake kinks (65%).

705
The systematic error due to the uncertainty in the ma-706 terial budget is about 1% as for the TPC analysis. The 707 quality cuts remove about 8% of all real kaon kinks, which 708 leads to a systematic error of less than 1%. The main un-709 certainty originates from the efficiency of the kink finding 710 algorithm which has an uncertainty of 5%. 711 3 Results Figure 12 shows a comparison between the results from the 713 different analyses. The spectra are normalized to inelastic 714 collisions, as explained in Sec. 2.2. The kaon spectra ob-715 tained with various techniques, including K 0 s spectra [24], 716 are compared in Fig. 13. The very good agreement demon-717 strates that all the relevant efficiencies are well reproduced 718 by the detector simulation.

719
The spectra from ITS stand-alone, TPC and TOF are 720 combined in order to cover the full momentum range. The 721 analyses from the different detectors use a slightly differ-722 ent sample of tracks and have largely independent sys-723 tematics (mainly coming from the PID method and the 724 contamination from secondaries). The spectra have been 725 averaged, using the systematic errors as weights. From this 726 weighted average, the combined, p t -dependent, systematic 727 error is derived. The combined spectra have an additional 728 overall normalization error, coming primarily from the un-729 certainty on the material budget (3%, Sec. 2.5) and from 730 the normalization procedure (2%, Sec. 2.2).

731
The combined spectra shown in Fig. 14 are fitted with 732 the Lévy (or Tsallis) function (see e.g. [26,27] (2) with the fit parameters C, n and the yield dN/dy. This 734 function gives a good description of the spectra and has 735 been used to extract the total yields and the p t , summa-736 rized in Table 4. The χ 2 /degree-of-freedom is calculated 737 using the total error. Due to residual correlations in the 738 point-by-point systematic error, the values are less than 1. 739 Also listed are the lowest measured p t -bin and the fraction 740 of the yield contained in the extrapolation of the spectra to 741 zero momentum. The extrapolation to infinite momentum 742 gives a negligible contribution. The systematic errors take 743 into account the contributions from the individual detec-744 tors, propagated to the combined spectra, the overall nor-745 malization error and the uncertainty in the extrapolation. 746 The latter is evaluated using different fit functions (mod-747 ified Hagedorn [28] and the UA1 parametrization [29]) or 748 using a Monte-Carlo generator, matched to the data for 749  p t < 1 GeV/c (PYTHIA [15], with tunes D6T [16], CSC 750 and Perugia0 [30], or PHOJET [18]). While none of these  The ratios of π + /π − and K + /K − as a function of p t are 756 close to unity within the errors, allowing the combination 757 of both spectra in the Lévy fits. The p/p ratio as a function 758 of p t has been studied with high precision in our previous 759 publication [22]. It is p t -independent with a mean value of 0.957±0.006(stat)±0.014(syst). Also here we used the sum 761 of both charges. Table 5 summarizes the fit parameters 762 along with the yields and mean p t . The errors have been 763 determined as for the individual fits.

764
Our values on yield and p t given in Table 4 and 5 765 agree well with the results from pp collisions at the same 766 √ s [31]. Figure 15 compares the p t with measurements 767 in pp collisions at √ s = 200 GeV [32,33] and in pp re-768 actions at √ s = 900 GeV [31]. The mean p t rises very 769 little with increasing √ s despite the fact that the spectral 770 shape clearly shows an increasing contribution from hard 771 processes. It was already observed at RHIC that the in-772 crease in mean p t at √ s= 200 GeV compared to studies at 773 √ s= 25 GeV is small. The values obtained in pp collisions 774 are lower than those for central Au+Au reactions at √ s= 775 200 GeV [32].

776
The spectra presented in this paper are normalized 777 to inelastic events. In a similar study by the STAR Col-778 laboration the yields have been normalized to NSD colli-779 sions [32]. In order to compare these two results, the yields 780 in Table 4 have been scaled to NSD events, multiplying by 781 1.185 (see Section 2.2). The yields of pions increase from 782 √ s= 200 GeV to 900 GeV by 23%, while K + rises by 45% 783 and K − by 48%. 784 Figure 16 shows the K/π ratio as a function of √ s both 785 in pp (full symbols, [32,34,35]) and in pp (open symbols, 786 [36-38]) collisions. For most energies, (K + +K − )/(π + +π − ) 787 is plotted, but for some cases only neutral mesons were 788 measured and K 0 /π 0 is used instead. The p t -integrated 789 (K + +K − )/(π + +π − ) ratio shows a slight increase from 790 √ s= 200 GeV (K/π = 0.103 ± 0.008) to √ s= 900 GeV 791 (K/π=0.123 ± 0.004 ± 0.010) [32], yet consistent within 792 the error bars. The results at 7 TeV will show whether 793 Table 4. Integrated yield dN /dy (|y| < 0.5) with statistical and systematic errors, and pt , as obtained from the fit with the Lévy function together with the lowest pt experimentally accessible, the fraction of extrapolated yield and the χ 2 /ndf of the fit (see text). The systematic error of dN /dy and of the pt includes the contributions from the systematic errors of the individual detectors, from the choice of the functional form for extrapolation and from the absolute normalization.  the K/π ratio keeps rising slowly as a function of √ s or 794 saturates.

795
Protons and antiprotons in Table 4 have been cor-

815
The upper panel of Figure 18 shows the p t -dependence 816 of the K/π and also the measurements by the E735 [36] 817 and STAR Collaborations [32]. It can be seen that the 818 observed increase of K/π with p t does not depend strongly 819 on collision energy.

820
A comparison with event generators shows that at p t > 821 1.2 GeV/c, the measured K/π ratio is larger than any of

833
In the bottom panel of Figure 18, the measured p/π 834 ratio is compared to results at √ s= 200 GeV from the 835 PHENIX Collaboration [41]. Both measurements are feed-836 down corrected. At low p t , there is no energy-dependence 837 of the p/π ratio visible, while at higher p t > 1 GeV/c, the 838 p/π ratio is larger at √ s= 900 GeV than at √ s= 200 GeV 839 energy.

840
Event generators seem to separate into two groups, 841 one with high p/π ratio (PYTHIA CSC and D6T), which 842 agree better with the data and one group with a lower 843 p/π ratio (PHOJET and PYTHIA Perugia0), which are 844 clearly below the measured values. These comparisons can 845 be used for future tunes of baryon production in the event 846 generators. 847

848
We present the first analysis of transverse momentum spec-849 tra of identified hadrons, π + , π − , K + , K − , p, and p in pp 850 collisions at √ s = 900 GeV with the ALICE detector. The 851 identification has been performed using the dE/dx of the 852 inner silicon tracker, the dE/dx in the gas of the TPC, 853 the kink topology of the decaying kaons inside the TPC 854 and the time-of-flight information from TOF. The combi-855 nation of these techniques allows us to cover a broad range 856 of momentum.