Production of pions, kaons and protons in pp collisions
at = 900 GeV
with ALICE at the LHC
The production of , , K, K, p, and at mid-rapidity has been measured in proton-proton collisions at = 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 () spectra. Since these various particle identification tools give the best separation capabilities over different momentum ranges, the results are combined to extract spectra from MeV/ to 2.5 GeV/. The measured spectra are further compared with QCD-inspired models which yield a poor description. The total yields and the mean are compared with previous measurements, and the trends as a function of collision energy are discussed.
pacs:25.75.DwParticle and resonance production and 13.85.NiInclusive production with identified hadrons
In pp collisions at ultra-relativistic energies the bulk of the particles produced at mid-rapidity have transverse momenta, , below 1 GeV/. Their production is not calculable from first principles via perturbative Quantum Chromodynamics, and is not well modelled at lower collision energies. This low particle production, and species composition, must therefore be measured, providing crucial input for the modelling of hadronic interactions and the hadronization process. It is important to study the bulk production of particles as a function of both and particle species. With the advent of pp collisions at the Large Hadron Collider (LHC) at CERN a new energy regime is being explored, where particle production from hard interactions which are predominantly gluonic in nature, is expected to play an increasing role. Such data will provide extra constraints on the modelling of fragmentation functions. The data will also serve as a reference for the heavy-ion measurements.
The ALICE detector Alessandro:2006yt (); Carminati:2004fp () is designed to perform measurements in the high-multiplicity environment expected in central lead-lead collisions at = 5.5 TeV at the LHC and to identify particles over a wide range of momenta. As such, it is ideally suited to perform these measurements also in pp collisions.
This paper presents the transverse momentum spectra and yields of identified particles at mid-rapidity from the first pp collisions collected in the autumn of 2009, during the commissioning of the LHC, at = 900 GeV. The evolution of particle production in pp collisions with collision energy is studied by comparing to data from previous experiments.
We report , , K, K, p, and distributions, identified via several independent techniques utilizing specific energy loss, d/d, information from the Inner Tracking System (ITS) and the Time Projection Chamber (TPC), and velocity measurements in the Time-Of-Flight array (TOF). The combination of these methods provides particle identification over the transverse momentum range . Charged kaons, identified via kink topology of their weak decays in the TPC, provide a complementary measurement over a similar range. All reported particle yields are for primary particles, namely those directly produced in the collision including the products of strong and electromagnetic decays but excluding weak decays of strange particles.
The paper is organized as follows: In Section 2, the ALICE detectors relevant for these studies, the experimental conditions, and the corresponding analysis techniques are described. Details of the event and particle selection are presented. In Section 3, the , , K, K, p, and inclusive spectra and yields, obtained by combining the various techniques described in Section 2, are presented. The results are compared with calculations from QCD-inspired models and the -dependence of ratios of particle yields, e.g. K/ and p/, are discussed. Comparisons with data from other experiments at different are made and the evolution of the ratio of strange to non-strange hadrons with collision energy is discussed. Finally, in Section 4 the results are summarized.
2 Experimental setup and data analysis
2.1 The ALICE detector
The ALICE detector and its expected performance are described in detail in Alessandro:2006yt (); Carminati:2004fp (); ALICE-JINST (). For the analyses described in this paper the following detectors are used: the ITS, the TPC and the TOF detector. These detectors are positioned in a solenoidal magnetic field of = 0.5 T and have a common pseudo-rapidity coverage of . Two forward scintillator hodoscopes (VZERO) are used for triggering purposes. They are placed on either side of the interaction region, covering regions and .
2.1.1 The Inner Tracking System
The ITS is the closest of the central barrel detectors to the beam axis. It is composed of six cylindrical layers of silicon detectors. The two innermost layers are equipped with pixel detectors (SPD), followed by two layers of drift detectors (SDD) and two layers of double-sided silicon strip detectors (SSD). The innermost layer is at 3.9 cm from the beam axis, while the outer layer is at 43.0 cm.
The ITS provides high-resolution space points that allow the extension of tracks reconstructed in the TPC towards the interaction vertex, thus improving momentum and angular resolution. The four layers equipped with SDD and SSD also provide a measurement of the specific energy loss d/d. The SPD yields an on-line measure of the multiplicity by counting the number of chips that have one or more hits (fast-OR), which is included in the minimum-bias trigger logic ALICE-JINST (); AglieriRinella:2007hm (). The ITS is also used as a stand-alone tracker to reconstruct charged particles with momenta below 200 MeV/ that are deflected or decay before reaching the TPC, and to recover tracks crossing dead regions of the TPC. A detailed description of the three sub-systems can be found in ALICE-JINST (). The d/d measurement in the SDD and SSD has been calibrated using cosmic ray data and pp events Alessandro:2010rq (). The 2198 ITS modules have been aligned using survey information, cosmic-ray tracks and pp data with the methods described in :2010ys (). The fraction of active modules per layer in the present setup is around 80% in the SPD and 90% - 95% both in SDD and SSD.
2.1.2 The Time Projection Chamber
The TPC is the main tracking device. It is a large volume, high granularity, cylindrical detector with an outer radius of 2.78 m and a length of 5.1 m. The active volume extends from 0.85 m to 2.47 m in radius. It covers 2 in azimuth and in polar angle for the full radial track length. Accepting one third of the full radial track length extends the range to 1.5. The 90 m drift volume is filled with a Ne (85.7%), CO (9.5%), and N (4.8%) gas mixture. A high voltage central membrane splits the drift region in two halves, resulting in a maximal drift time of 94 s. Each of the two read-out planes is composed of 18 inner and 18 outer chambers with a total of 159 pad rows, resulting in a total of 557 568 pads which are read out separately. The position resolution in direction varies from 1100 m to 800 m when going from the inner to the outer radius. Along the beam axis (, also the drift direction) the resolution ranges between 1250 m and 1100 m. A maximum of 159 clusters can be measured along a track in the TPC. For a detailed description see Alme:2010ke ().
2.1.3 The Time-Of-Flight Detector
The TOF detector consists of 18 azimuthal sectors, each containing 91 Multi-gap Resistive Plate Chambers (MRPCs) distributed in five gas-tight modules. It is positioned at 370-399 cm from the beam axis. The region at is not covered in order to minimize the material in front of the Photon Spectrometer, which is not used in this analysis. The MRPC detectors are installed with a projective geometry along the beam direction, minimizing the variation of the flight path of particles across the sensitive area of the detector. Each MRPC is segmented into 96 read-out pads (2.5 3.5 size), resulting in a total of 152928 channels. Test beam results demonstrated that the intrinsic time resolution of the detector is better than 50 , dominated by electronic effects and the time resolution of the time-to-digital converters Akindinov:2009zz (). Results from the TOF commissioning with cosmic rays are described in references Akindinov:2006hs (); Akindinov:2010zza (); Akindinov:2010zz (). In the present setup, 9.6% of the readout channels were inactive due to failures in the high- or low-voltage systems or in the readout electronics. The fraction of noisy channels, identified during data taking by online monitoring and excluded from the subsequent reconstruction, was below 0.1%.
2.2 Event selection and normalization
The data presented in this paper were collected during the commissioning of the LHC at CERN in the autumn of 2009, with pp collisions at GeV. The collider was run with four bunches per beam, resulting in two bunch crossings per beam circulation period (89 s) at the ALICE interaction point. The remaining two bunches per beam were not collided at ALICE, and served to estimate the contribution of beam-gas interactions. The average event rate was a few Hz, so the fraction of pile-up events was negligible.
The analysis is based on a sample of k inelastic pp collisions. The online trigger selection requires a signal in either of the VZERO counters or at least one hit in either of the SPD layers. The selection was improved offline with recomputed trigger input quantities using the time average over all VZERO hits and a suppression of noisy channels. The contamination from beam-induced background is rejected offline using the timing information of the VZERO and by cutting on the correlation between the number of clusters and track segments (tracklets) in the SPD detector Aamodt:2010ft (); Aamodt:2010my (). Selected events are further required to contain a reconstructed primary vertex. The vertex reconstruction efficiency calculated via Monte-Carlo simulations is 96.5% for events with one reconstructed track and approaches unity for events with more than two tracks.
The results presented in this paper are normalized to inelastic pp collisions, employing the strategy described in Aamodt:2010ft (); Aamodt:2010my (). In order to reduce the extrapolation and thus the systematic uncertainty on the normalization, the sample of selected events used for normalization includes triggered events without reconstructed tracks or vertices. Those events still contain a small contamination from very low multiplicity beam-induced background or accidentals from the trigger, which are not rejected by the selections described above. This contamination is of the order of 4% and is subtracted using the control triggers. From the analysis of empty bunch events the random contribution from cosmic rays is found to be negligible. The number of selected events is then converted to the number of inelastic collisions after correcting for the trigger efficiency, which is determined from the Monte-Carlo simulation, scaling the cross section for diffractive processes to the measurements of UA5 Ansorge:1986xq (). The subtraction of beam-gas events and the efficiency correction partially compensate each other: the overall correction factor is about 5% with a systematic uncertainty of about 2%, coming mainly from the uncertainties in the modelling of diffraction in the event generators.
In order to compare to previous experimental results, which are only published for the non-single-diffractive (NSD) class, in Section 3, we scale our spectra for the measured ratio Aamodt:2010ft (). PYTHIA and PHOJET simulations indicate that the -dependence of the ratio of spectra for NSD and inelastic collisions is less than 5% in the reported range. Particle ratios are found to be insensitive to the conversion from inelastic to non-single-diffractive events.
2.3 Track selection
The identified particle spectra were measured independently with the ITS, TPC and TOF, and combined in the final stage of the analysis. The rapidity range was used for all analyses except for the kink analysis ().
For the TPC and TOF analyses, tracks reconstructed in the TPC are used. The TPC has full acceptance for tracks with . However, shorter tracks at higher can still be used for physics analysis, in particular protons with a transverse momentum of = 400 MeV/ and which correspond to . To ensure high tracking efficiency and d/d-resolution, while keeping the contamination from secondaries and fakes low, tracks are required to have at least 80 clusters, and a of the momentum fit that is smaller than 4 per cluster. Since each cluster in the TPC provides two degrees of freedom and the number of parameters of the track fit is much smaller than the number of clusters, the cut is approximately 2 per degree of freedom. In addition, at least two clusters in the ITS must be associated to the track, out of which at least one is from the SPD. Tracks are further rejected based on their distance-of-closest approach (DCA) to the reconstructed event vertex. The cut is implemented as a function of to correspond to about seven (five) standard deviations in the transverse (longitudinal) coordinate, taking into account the -dependence of the impact parameter resolution. These selection criteria are tuned to select primary charged particles with high efficiency while minimizing the contributions from weak decays, conversions and secondary hadronic interactions in the detector material. The DCA resolution in the data is found to be in good agreement with the Monte-Carlo simulations that are used for efficiency corrections (see next Section).
Tracks reconstructed in the TPC are extrapolated to the sensitive layer of the TOF and a corresponding signal is searched for. The channel with the center closest to the track extrapolation point is selected if the distance is less than 10 cm. This rather weak criterion results in a high matching efficiency while keeping the fraction of wrongly associated tracks below 1% in the low-density environment presented by pp collisions.
The d/d measurements in the ITS are used to identify hadrons in two independent analyses, based on different tracking algorithms. One analysis uses the ITS-TPC combined tracking, while the other is based on ITS stand-alone tracks. The combined ITS-TPC tracking result serves as a cross-check of both the ITS stand-alone and the TPC results in the overlap region. The ITS stand-alone analysis extends the acceptance to lower than the TPC or ITS-TPC analyses.
The combined ITS-TPC analysis uses the same track selection criteria as the TPC only analysis, with the additional requirement of at least four clusters in the ITS, out of which at least one must be in the SPD and at least three in SSD+SDD. This further reduces the contamination of secondaries and provides high resolution on track impact parameter and optimal resolution on the d/d. The ITS stand-alone tracking uses a similar selection, with a different selection and a different DCA selection. In the current tracking algorithm, ITS clusters are assigned a larger position error to account for residual misalignment of the detector. As a result, the values are not properly normalized, but the selection was adjusted to be equivalent to the TPC selection by inspecting the distributions. The DCA cut in the ITS analysis uses the same -dependent parametrization as for TPC tracks, but with different parameters to account for the different resolution.
2.4 Monte-Carlo Calculations
The efficiency and other correction factors including acceptance (jointly called efficiency in the following discussion) used in this paper are calculated from a Monte-Carlo simulation, based on over two million events produced with the PYTHIA 6.4 event generator Sjostrand:2006za () (tune D6T D6T ()), propagated through the detector with the GEANT3 :1994zzo () transport code. Dead and noisy channels as well as beam position and spread have been taken into account. A simulation based on the PHOJET event generator Engel:1995sb () is also used as a cross check.
GEANT3 is known to reproduce the absorption cross sections of hadrons incorrectly. The transport code FLUKA contains a more accurate description of these cross sections Bendiscioli:1994uv (); Zhang:1996ev (); Klempt:2002ap (), and a dedicated simulation is used to calculate a correction to the GEANT3 efficiency calculation Aamodt:2010dx (). This is relevant mainly for antiprotons at low , where the correction is on the order of 10%. For other particles and at higher , the difference between GEANT and FLUKA calculations is negligible.
2.5 Particle Identification
The d/d and TOF signals are used for particle identification as a function of the momentum , whereas the final spectra are given as a function of the transverse momentum .
In the case of the TPC and ITS analyses, particles were identified via the specific energy loss d/d. Unique identification on a track-by-track basis is possible in regions of momentum where the bands are clearly separated from each other. In overlapping areas, particle identification is still possible on a statistical basis using fits to the energy loss distribution in each -bin. The fits are performed on the distribution of the difference between the measured and the expected energy deposition for tracks within the selected rapidity range 0.5. This compensates for the very steep slope of the Bethe-Bloch in the region which would make the d/d-distribution in a simple or -slice non-Gaussian. The calculated expected energy loss depends on the measured track momentum and the assumed mass for the particle. The procedure is therefore repeated three times for the entire set of tracks, assuming the pion, kaon, and proton mass.
In the TPC analysis, the difference
[d/d][d/d is used. For the ITS the difference of the logarithm of the measured and calculated energy deposit d/dd/d(, is taken to suppress the non-gaussian tails originating from the smaller number of d/d measurements.
In the case of the TOF, the identification is based on the time-of-flight information. The procedure for the extraction of the raw yields differs slightly from the one used for TPC and ITS, and is described in Section 2.5.3.
2.5.1 Particle identification in the ITS
In both the ITS stand-alone and in the ITS-TPC analyses, the d/d measurement from the SDD and the SSD is used to identify particles. The stand-alone tracking result extends the momentum range to lower than can be measured in the TPC, while the combined tracking provides a better momentum resolution.
The energy loss measurement in each layer of the ITS is corrected for the track length in the sensitive volume using tracking information. In the case of SDD clusters, a linear correction for the dependence of the reconstructed raw charge as a function of drift time due to the combined effect of charge diffusion and zero suppression is also applied Alessandro:2010rq (). For each track, d/d is calculated using a truncated mean: the average of the lowest two points in case four points are measured, or a weighted sum of the lowest (weight 1) and the second lowest point (weight 1/2), in case only three points are measured.
For the ITS stand-alone track sample, the histograms are fitted with three Gaussians and the integral of the Gaussian centered at zero is used as the raw yield of the corresponding hadron species. In a first step, the peak widths of the peaks are extracted as a function of for pions and protons in the region where their d/d distributions do not overlap with the kaon (and electron) distribution. For kaons, the same procedure is used at low , where they are well separated. The -dependence of the peak width is then extrapolated to higher with the same functional form used to describe the pions and protons. The resulting parametrizations of the dependence of are used to constrain the fits of the ln[d/d] distributions to extract the raw yields.
For the ITS-TPC combined track sample, a non-Gau-ssian tail is visible. This tail is a remnant of the tail of the Landau distribution for energy loss. It was verified using simulations that the shape and size of the tail are compatible with the expectations for a truncated mean using two out of four samples. The tail is not as pronounced for the ITS stand-alone track sample, due to the limited momentum resolution. The distribution is fitted with a combination of a Gaussian and an exponential function for the main peak and another exponential function to describe the tail of a background peak. This functional form provides an accurate description of the peak shape in the detector simulation, as well as the measured shape.
Examples of d/d distributions are shown in Fig. 2 for negative tracks using the kaon mass hypothesis in two different intervals for both ITS stand-alone tracks (right panels) and ITS-TPC combined tracks (left panels).
The raw hadron yields extracted from the fits to the d/d distributions are corrected for the reconstruction efficiency determined from Monte-Carlo simulations, applying the same analysis criteria to the simulated events as to the data. Secondary particles from interactions in the detector material and strange particle decays have been subtracted from the yield of both simulated and real data. The fraction of secondaries after applying the track impact-parameter cut depends on the hadron species and amounts to 1-3% for pions and 5-10% for protons depending on . The secondary-to-primary ratio has been estimated by fitting the measured track impact-parameter distributions with three components, prompt particles, secondaries from strange particle decays and secondaries produced in the detector material for each hadron species. Alternatively, the contamination from secondaries have been determined using Monte-Carlo samples, after rescaling the yield to the measured values strange (). The difference between these two procedures is about 3% for protons and is negligible for other particles.
Figure 3 shows the total reconstruction efficiency for primary tracks in the ITS stand-alone, including the effects of detector and tracking efficiency, the track selection cuts and residual contamination in the fitting procedure, as determined from the Monte-Carlo simulation. This efficiency is used to correct the measured raw yields after subtraction of the contributions from secondary hadrons. The measured spectra are corrected for the efficiency of the primary vertex reconstruction with the SPD using the ratio between generated primary spectra in simulated events with a reconstructed vertex and events passing the trigger conditions.
Systematic errors are summarized in Table 1. The systematic uncertainty from secondary contamination has been estimated by repeating the full analysis chain with different cuts on the track impact parameter and by comparing the two alternative estimates outlined above. The effect of the uncertainty in the material budget has been estimated by modifying the material budget in the Monte-Carlo simulations by %, which is the present uncertainty of the ITS material budget. The systematic contribution from the fitting procedure to the ln[d/d]ln[d/d(i)] distributions has been estimated by varying the fit condition and by comparing to an independent analysis using a track-by-track identification approach based on the distance between the measured and expected d/d values normalized to its resolution. The residual imperfections in the description of the ITS detector modules and dead areas in the simulation introduce another uncertainty in the ITS tracking efficiency. This is estimated by varying the cuts on the number of clusters and on the track both in data and in Monte-Carlo simulations.
In the lowest -bins, a larger systematic error has been assigned to account for the steep slope of the tracking efficiency as a function of the particle transverse momentum (see Fig. 3).
|systematic errors||K||p and|
|from weak decay|
2.5.2 Particle identification in the TPC
Particle identification is based on the specific energy deposit of each particle in the drift gas of the TPC, shown in Fig. 4 as a function of momentum separately for positive and negative charges. The solid curves show the calibration curves obtained by fitting the ALEPH parametrization of the Bethe-Bloch curve ALEPH () to the data points in regions of clear separation.
The calibration parameters have mostly been determined and tested via the analysis of cosmic rays. The pad-gain factors have been measured using the decay of radioactive Kr gas released into the TPC volume (for a detailed description see Alme:2010ke ()).
As in the case of the ITS, a truncated-mean procedure is used to determine d/d (60% of the points are kept). This reduces the Landau tail of the d/d distribution to the extent that it is very close to a Gaussian distribution.
Examples of the d/d distribution in some bins are shown in Fig. 5. The peak centered at zero is from kaons and the other peaks are from other particle species. As the background in all momentum bins is negligible, the integrals of the Gaussian give the raw yields.
The raw hadron spectra are corrected for the reconstruction efficiency, shown in Fig. 6, determined by doing the same analysis on Monte-Carlo events. The efficiency is calculated by comparing the number of reconstructed particles to the number of charged primary particles from PYTHIA in the chosen rapidity range. For transverse momenta above 800 MeV/ the efficiency saturates at roughly 80%. For kaons, the decay reduces the efficiency by about 30% at 250 MeV/ and 12% at 1.5 GeV/. The range with a reconstruction efficiency lower than 60% (for pions and protons) is omitted for the analysis corresponding to a low- cut-off of 200 MeV/ for pions, 250 MeV/ for kaons, and 400 MeV/ for protons.
Protons are corrected for the contamination of secondaries from material and of feed down from weak decays. The feed down was determined by two independent methods. Firstly, the contamination obtained from Monte-Carlo simulation was scaled such that it corresponds to the measured yield of s in the data strange (). Secondly, the shape of the impact parameter distribution was compared to the Monte-Carlo simulation. Weak decays produce a non-Gaussian tail in the distribution of primary particles whereas secondaries from material generate a flat background Aamodt:2010dx (). The remaining difference between the methods is included in the systematic error. The correction for weak decays amounts to up to 14% and the correction for secondaries from material up to 4% for protons with 400 MeV/ MeV/. For other particle species and other transverse momenta the contamination is negligible.
The systematic errors in the track reconstruction and in the removal of secondary particles have been estimated by varying the number of standard deviations in the distance-to-vertex cut, using a fixed cut of 3 cm instead of the variable one, and varying the SPD-TPC matching cut. Their impact on the corrected spectra is less than 5%. The influence of the uncertainty in the material budget has been examined by varying it by 7%. This resulted in the systematic errors given in Table 2. The uncertainty due to a possible deviation from a Gaussian shape has been established by comparing the multi-Gauss fit with a 3- band in well separated regions. The precision of the kink rejection is estimated to be within 3%.
|systematic errors||K||p and|
|from weak decay|
|energy loss and||1%||1%||2%|
|absorption in material|
|matching to ITS||3%|
2.5.3 Particle identification with the TOF
Particles reaching the TOF system are identified by measuring their momentum and velocity simultaneously.
The velocity is obtained from the measured time of flight and the reconstructed flight path along the track trajectory between the point of closest approach to the event vertex and the TOF sensitive surface. The measured velocities are shown as a function of the momentum at the vertex in Fig. 7. The bands corresponding to charged pions, kaons and protons are clearly visible. The width of the bands reflects the overall time-of-flight resolution of about 180 ps, which depends on the TOF timing signal resolution, the accuracy of the reconstructed flight path and the uncertainty of the event start time, . This last contribution is related to the uncertainty in establishing the absolute time of the collision. In the present sample this fluctuated with respect to the nominal time signal from the LHC with a of about 140 ps due to the finite size of the bunches.
To improve the overall time-of-flight resolution, the TOF information itself is used to determine in events having at least three tracks with an associated TOF signal. This is done with a combinatorial algorithm which compares the TOF times with the calculated times of the tracks for each event for different mass hypotheses. Using this procedure, the start-time has been improved for 44% of the tracks having an associated TOF signal and is rather independent on the momentum of the tracks. In this way the precision on the event start-time is about 85 ps on average.
Finally, tracks whose particle identity as determined from the TOF information is not compatible with the one inferred from the d/d signal in the TPC within five have been removed. This TOF-TPC compatibility criterion rejects about 0.6% of the tracks and further reduces the small contamination coming from tracks incorrectly associated with a TOF signal.
For each particle species , the expected time of flight is calculated by summing up the time-of-flight increments at each tracking step, with being the local value of the track momentum, the mass of the particle, and the track-length increment along its trajectory. The yields of , K and p are obtained from the simultaneous fit of the distribution of the time difference between measured and the average between the calculated time for pions and kaons
The symmetric treatment of kaons and pions in the definition of ensures that the kaon and pion peak are both Gaussian. Extracting the yield for different species in a simultaneous fit guarantees that the resulting number of pions, kaons and protons matches the total number of tracks in the given momentum bin.
The distribution of the variable is shown in Fig. 8 for three different transverse momentum bins for positive particles. The curves show the results of the three-Gaussian fit used to extract the raw yields. The integral of the fit result has been constrained to the number of entries in the distribution, and the means and the widths are allowed to vary within 5% and 10%, respectively, of their nominal values. The only free parameters in the fit are therefore the relative normalizations between the Gaussians.
The raw yields are extracted in different -bins using a rapidity selection , where is the rapidity calculated with the proton mass. For pions and kaons, this condition results in a larger -acceptance and in both cases, the fraction outside of has been subtracted in each -bin taking into account the -distribution of the yields within the pions and kaons peaks.
Since the track selection used in the TOF analysis is the same as the one described in the TPC analysis (subsection 2.5.2), the same tracking and feed-down corrections are applied. In the case of the TOF analysis, an additional correction is needed in order to take into account the fraction of the particles reconstructed by the TPC with an associated signal in TOF. This matching efficiency includes all sources of track losses in the propagation from the TPC to the TOF (geometry, decays and interactions with the material) and its matching with a TOF signal (the TOF intrinsic detector efficiency, the effect of dead channels and the efficiency of the track-TOF signal matching procedure). The TOF matching efficiency has been derived from Monte-Carlo events as the fraction of TPC reconstructed tracks having an associated TOF signal and is shown in Fig. 9 for each hadron species. The main factors limiting the TOF matching efficiency are the loss due to geometrical acceptance ( 15%), the number of dead or noisy channels ( 10%) and the absorption of particles in the material of the transition radiation detector ( 8%).
The TOF matching efficiency has been tested with data, using d/d in the TPC to identify the particles. Good agreement between the efficiencies obtained from the data and from Monte-Carlo simulations is observed in case of pions and kaons, with deviations at the level of, at most, 3% and 6% respectively, over the full transverse-momentum range. The observed differences are assigned as systematic errors, see Table 3. In the case of protons and antiprotons, larger differences are observed at below 0.7 GeV/, where the efficiency varies very rapidly with momentum. This region is therefore not considered in the final results (see Table 3).
Other sources of systematic errors related to the TOF PID procedure have been estimated from Monte-Carlo simulations and cross-checked with data. They include the effect of the residual contribution from tracks wrongly associated with TOF signals, and the quality and stability of the fit procedure used for extracting the yields. Table 3 summarizes the maximal value of the systematic errors observed over the full transverse momentum range relevant in the analysis, for each of the sources mentioned above.
|systematic errors||K||p and|
2.6 Kaon Identification using their decay within the TPC
In this section, the determination of the yields of charged kaons identified by their weak decay (kink topology) inside the TPC detector is described. These tracks are rejected in the previously described TPC analysis. This procedure allows an extension of the study of kaons to intermediate momenta, on a track-by-track level, although in this analysis the reach is limited by statistics.
The kinematics of the kink topology, measured as a secondary vertex with one mother and one daughter track of the same charge, allows the separation of kaon decays from the main source of background kinks coming from charged pion decays. The decay channels with the highest branching ratio (B.R.) for kaons are the two-body decays
, (B.R. 63.55%)
, (B.R. 20.66%).
Three-body decays with one charged daughter track (B.R. 9.87%) as well as three-body decays into three charged pions (B.R. 5.6%) are also detected.
The algorithm for reconstructing kinks as secondary vertices is applied inside a fiducial volume of the TPC with radius 120 cm 210 cm in order to have a minimum number of clusters for reconstructing both the mother and daughter tracks. Inside this volume a sufficient number of kinks can be found since the of kaon and pion decays are 3.7 m and 7.8 m, respectively. The mother track of the kink has been selected with similar criteria to those of the TPC tracks used for the d/d analysis, except that the minimum required number of clusters per track is 30, because the kink mother track does not traverse the entire TPC. The relation between the number of clusters per mother track and the radius of the kink is used as a quality check of the kink reconstruction procedure.
The identification of kaons from kink topology and its separation from pion decay is based on the decay kinematics. The transverse momentum of the daughter with respect to the mother’s direction, , has an upper limit of 236 MeV/ for kaons and 30 MeV/ for pions for the two-body decay to . The corresponding upper limit for the two-body decay (2) is 205 MeV/. All three limits can be seen as peaks in Fig. 10 (a), which shows the distribution of all measured kinks inside the selected volume and rapidity range 0.7. Selecting kinks with MeV/ removes the majority of -decays as shown by the dashed (before) and solid (after) histograms.
The invariant mass for the decay into is calculated from the measured difference between the mother and daughter momentum, their decay angle, assuming zero mass for the neutrino. Figure 10 (b) shows the invariant mass for the full sample of kinks (dashed line) and for the sample after applying the preceding cuts (full line). The masses of pions and kaons are reconstructed at their nominal values. The third peak at 0.43 GeV/ originates from the decay for which the invariant mass is calculated with wrong mass assumptions for the daughter tracks. The broad structure originates from three-body decays of kaons.
At this stage, we have a rather clean sample of kaons as demonstrated in Fig. 10 (c) showing the d/d vs. the mother momentum. Most of the tracks are within a band with respect to the corresponding Bethe-Bloch curve of kaons. The few tracks outside these limits are at momenta below 600 MeV/ (less than 5%) and they have been removed in the last analysis step.
Efficiency and acceptance
The total correction factor includes both the acceptance of kinks and their efficiency (reconstruction and identification). The study has been performed for the rapidity interval 0.7, larger than the corresponding rapidity interval for the other studies in order to reduce the statistical errors.
The acceptance is defined as the ratio of weak decays (two- and three-body decays) whose daughters are inside the fiducial volume of the TPC to all kaons inside the same rapidity window (Fig. 11, upper part). It essentially reflects the decay probability. However, the acceptance is not the same in the low-momentum region for both charges of kaons, since the interaction cross section of the negative kaons with the ITS material is higher than that of the positive kaons. As a result, the acceptance of positive kaons is larger at low momenta.
The efficiency is the ratio of reconstructed and identified kaons divided by the number of kaon decays within the acceptance as shown in Fig. 11 (lower part), as a function of the kaon . It reaches about 60% at 0.7 GeV/ and decreases gradually at higher transverse momenta, as the angle between mother and daughter tracks becomes smaller. The decay angle of kaon kinks allows their identification up to high momenta, e.g. at of 5 GeV/ the values are between and .
The contamination due to random associations of primary and secondary charged tracks has been established using Monte-Carlo simulations and it is systematically smaller than 5% in the studied -range as also shown in Fig. 11. Hadronic interactions are the main source of these fake kinks (65%).
The systematic error due to the uncertainty in the material budget is about 1% as for the TPC analysis. The quality cuts remove about 8% of all real kaon kinks, which leads to a systematic error of less than 1%. The main uncertainty originates from the efficiency of the kink finding algorithm which has an uncertainty of 5%.
Figure 12 shows a comparison between the results from the different analyses. The spectra are normalized to inelastic collisions, as explained in Sec. 2.2. The kaon spectra obtained with various techniques, including K spectra strange (), are compared in Fig. 13. The very good agreement demonstrates that all the relevant efficiencies are well reproduced by the detector simulation.
The spectra from ITS stand-alone, TPC and TOF are combined in order to cover the full momentum range. The analyses from the different detectors use a slightly different sample of tracks and have largely independent systematics (mainly coming from the PID method and the contamination from secondaries). The spectra have been averaged, using the systematic errors as weights. From this weighted average, the combined, -dependent, systematic error is derived. The combined spectra have an additional overall normalization error, coming primarily from the uncertainty on the material budget (3%, Sec. 2.5) and from the normalization procedure (2%, Sec. 2.2).
with the fit parameters , and the yield . This function gives a good description of the spectra and has been used to extract the total yields and the , summarized in Table 4. The /degree-of-freedom is calculated using the total error. Due to residual correlations in the point-by-point systematic error, the values are less than 1. Also listed are the lowest measured -bin and the fraction of the yield contained in the extrapolation of the spectra to zero momentum. The extrapolation to infinite momentum gives a negligible contribution. The systematic errors take into account the contributions from the individual detectors, propagated to the combined spectra, the overall normalization error and the uncertainty in the extrapolation. The latter is evaluated using different fit functions (modified Hagedorn Hagedorn:1983wk () and the UA1 parametrization Albajar:1989an ()) or using a Monte-Carlo generator, matched to the data for (PYTHIA Sjostrand:2006za (), with tunes D6T D6T (), CSC and Perugia0 perugia (), or PHOJET Engel:1995sb ()). While none of these alternative extrapolations provides a description as good as the one from the Lévy fit, we estimate from this procedure an uncertainty of about 25% of the extrapolated part of the yield.
The ratios of /and K/K as a function of are close to unity within the errors, allowing the combination of both spectra in the Lévy fits. The /p ratio as a function of has been studied with high precision in our previous publication Aamodt:2010dx (). It is -independent with a mean value of . Also here we used the sum of both charges. Table LABEL:tab:levy_values summarizes the fit parameters along with the yields and mean . The errors have been determined as for the individual fits.
|K + K||8.46/24|
Our values on yield and given in Table 4 and LABEL:tab:levy_values agree well with the results from p collisions at the same Ansorge:1987cj (). Figure 15 compares the with measurements in pp collisions at = 200 GeV :2008ez (); Adare:2010fe () and in p reactions at = 900 GeV Ansorge:1987cj (). The mean rises very little with increasing despite the fact that the spectral shape clearly shows an increasing contribution from hard processes. It was already observed at RHIC that the increase in mean at = 200 GeV compared to studies at = 25 GeV is small. The values obtained in pp collisions are lower than those for central Au+Au reactions at = 200 GeV :2008ez ().
The spectra presented in this paper are normalized to inelastic events. In a similar study by the STAR Collaboration the yields have been normalized to NSD collisions :2008ez (). In order to compare these two results, the yields in Table 4 have been scaled to NSD events, multiplying by 1.185 (see Section 2.2). The yields of pions increase from = 200 GeV to 900 GeV by 23%, while K rises by 45% and K by 48%.
Figure 16 shows the K/ ratio as a function of both in pp (full symbols, :2008ez (); Alt:2005zq (); Anticic:2010yg ()) and in p (open symbols, Alexopoulos:1993wt (); Alner:1985ra (); Alexopoulos:1992ut ()) collisions. For most energies, (K+K)/(+) is plotted, but for some cases only neutral mesons were measured and K is used instead. The -integrated (K+K)/(+) ratio shows a slight increase from = 200 GeV (K/ = ) to = 900 GeV (K/=) :2008ez (), yet consistent within the error bars. The results at 7 TeV will show whether the K/ ratio keeps rising slowly as a function of or saturates.
Protons and antiprotons in Table 4 have been corrected for feed down (mainly from ), while the results from the STAR Collaboration are not. The proton spectra measured by PHENIX, on the other hand, have a lower -cut of 0.6 GeV/. This makes a direct comparison with RHIC data difficult.
Figure 17 shows a comparison of the measured pion, kaon and proton spectra with several tunes of the PYTHIA event generator Sjostrand:2006za () and with PHOJET Engel:1995sb (). The PYTHIA CSC 306 Moraes:306AIN () tune provides a very poor description of the particle spectra for all species. Similar deviations were already seen for the unidentified charged hadron spectra Aamodt:2010my (). The other PYTHIA tunes, Perugia0 perugia () and D6T D6T (), and PHOJET give a reasonable description of the charged pion spectra, but show large deviations in the kaon and proton spectra. The measured kaon -spectrum falls more slowly with increasing than the event generators predict. A similar trend is seen for the proton spectra, except for PYTHIA tune D6T, which describes the proton spectra reasonably well.
The upper panel of Figure 18 shows the -dependence of the K/ and also the measurements by the E735 Alexopoulos:1993wt () and STAR Collaborations :2008ez (). It can be seen that the observed increase of K/ with does not depend strongly on collision energy.
A comparison with event generators shows that at 1.2 GeV/, the measured K/ ratio is larger than any of the model predictions. It is interesting to note that while the spectra in the CSC tune are much steeper than the other tunes, the -dependence of the K/ ratio is very similar. In the models, the amount of strangeness production depends on the production ratios of gluons and the different quark flavours in the hard scattering and on the strangeness suppression in the string breaking. The latter could probably be tuned to better describe the data. A similar disagreement between measured strangeness production and PYTHIA predictions was found at RHIC energies Heinz:2007ci ().
In the bottom panel of Figure 18, the measured p/ ratio is compared to results at = 200 GeV from the PHENIX Collaboration Adler:2006xd (). Both measurements are feed-down corrected. At low , there is no energy-dependence of the p ratio visible, while at higher GeV/, the p/ ratio is larger at = 900 GeV than at = 200 GeV energy.
Event generators seem to separate into two groups, one with high p/ ratio (PYTHIA CSC and D6T), which agree better with the data and one group with a lower p/ ratio (PHOJET and PYTHIA Perugia0), which are clearly below the measured values. These comparisons can be used for future tunes of baryon production in the event generators.
We present the first analysis of transverse momentum spectra of identified hadrons, , , K, K, p, and in pp collisions at = 900 GeV with the ALICE detector. The identification has been performed using the d/d of the inner silicon tracker, the d/d in the gas of the TPC, the kink topology of the decaying kaons inside the TPC and the time-of-flight information from TOF. The combination of these techniques allows us to cover a broad range of momentum.
Agreement in the K/ ratio is seen when comparing to p
collisions at the Tevatron and SpS. Comparing our results
with a similar measurement from the STAR Collaboration using pp
collisions at = 200 GeV the shape of the spectra shows an
increase of the hard component, but we observe only a slight
increase of the mean -values. Whether the fraction of strange
to non-strange particles rises
with increasing remains open until data at 7 TeV become available.
The ALICE collaboration would like to thank all its engineers and technicians for their invaluable contributions to the construction of the experiment and the CERN accelerator teams for the outstanding performance of the LHC complex.
The ALICE collaboration acknowledges the following funding agencies for their support in building and running the ALICE detector:
Department of Science and Technology, South Africa;
Calouste Gulbenkian Foundation from Lisbon and Swiss Fonds Kidagan, Armenia;
Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq), Financiadora de Estudos e Projetos (FINEP), Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP);
National Natural Science Foundation of China (NSFC), the Chinese Ministry of Education (CMOE) and the Ministry of Science and Technology of China (MSTC);
Ministry of Education and Youth of the Czech Republic;
Danish Natural Science Research Council, the Carlsberg Foundation and the Danish National Research Foundation;
The European Research Council under the European Community’s Seventh Framework Programme;
Helsinki Institute of Physics and the Academy of Finland;
French CNRS-IN2P3, the ‘Region Pays de Loire’, ‘Region Alsace’, ‘Region Auvergne’ and CEA, France;
German BMBF and the Helmholtz Association;
Hungarian OTKA and National Office for Research and Technology (NKTH);
Department of Atomic Energy and Department of Science and Technology of the Government of India;
Istituto Nazionale di Fisica Nucleare (INFN) of Italy;
MEXT Grant-in-Aid for Specially Promoted Research, Japan;
Joint Institute for Nuclear Research, Dubna;
National Research Foundation of Korea (NRF);
CONACYT, DGAPA, México, ALFA-EC and the HELEN Program (High-Energy physics Latin-American–European Network);
Stichting voor Fundamenteel Onderzoek der Materie (FOM) and the Nederlandse Organisatie voor Wetenschappelijk Onderzoek (NWO), Netherlands;
Research Council of Norway (NFR);
Polish Ministry of Science and Higher Education;
National Authority for Scientific Research - NASR (Autoritatea Naţională pentru Cercetare Ştiinţifică - ANCS);
Federal Agency of Science of the Ministry of Education and Science of Russian Federation, International Science and Technology Center, Russian Academy of Sciences, Russian Federal Agency of Atomic Energy, Russian Federal Agency for Science and Innovations and CERN-INTAS;
Ministry of Education of Slovakia;
CIEMAT, EELA, Ministerio de Educación y Ciencia of Spain, Xunta de Galicia (Consellería de Educación), CEADEN, Cubaenergía, Cuba, and IAEA (International Atomic Energy Agency);
Swedish Reseach Council (VR) and Knut Alice Wallenberg Foundation (KAW);
Ukraine Ministry of Education and Science;
United Kingdom Science and Technology Facilities Council (STFC);
The United States Department of Energy, the United States National Science Foundation, the State of Texas, and the State of Ohio.
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