Strange particle production in pp collisions at √s = 0.9 and 7 TeV

: The spectra of strange hadrons are measured in proton-proton collisions, recorded by the CMS experiment at the CERN LHC, at centre-of-mass energies of 0.9 and 7 TeV. The K 0 s , Lambda, andXi − particlesandtheirantiparticlesarereconstructedfromtheirdecaytopologiesandtheproductionratesaremeasuredasfunctionsofrapidityandtransversemomentum.TheresultsarecomparedtootherexperimentsandtopredictionsofthePY THIAMonteCarloprogram.ThetransversemomentumdistributionsarefoundtodiffersubstantiallyfromthePY THIAresultsandtheproductionratesexceedthepredictionsbyuptoafactorofthree. Strange particle production in pp collisions at √s Abstract: The spectra of strange hadrons are measured in proton-proton collisions, recorded by the CMS experiment at the CERN LHC, at centre-of-mass energies of 0.9 and 7 TeV. The K 0S , Λ, and Ξ − particles and their antiparticles are reconstructed from their decay topologies and the production rates are measured as functions of rapidity and transverse momentum, p T . The results are compared to other experiments and to predictions of the Pythia Monte Carlo program. The p T distributions are found to diﬀer substantially from the Pythia results and the production rates exceed the predictions by up to a factor of three.


Introduction
Measurements of particle yields and spectra are an essential step in understanding protonproton collisions at the Large Hadron Collider (LHC). The Compact Muon Solenoid (CMS) Collaboration has published results on spectra of charged particles at centre-of-mass energies of 0.9, 2.36, and 7 TeV [1,2]. In this analysis the measurement is extended to strange mesons and baryons (K 0 S , Λ, Ξ − ) 1 at centre-of-mass energies of 0.9 and 7 TeV. The investigation of strange hadron production is an important ingredient in understanding the nature of the strong force. The LHC experiments ALICE and LHCb have recently reported results on strange hadron production at √ s = 0.9 TeV [3,4]. In addition to results at √ s = 0.9 TeV, we also present results at √ s = 7 TeV, opening up a new energy regime in which to study the strong interaction. As the strange quark is heavier than up and down quarks, production of strange hadrons is generally suppressed relative to hadrons containing only up and down quarks. The amount of strangeness suppression is an important component in Monte Carlo (MC) models such as Pythia [5] and hijing/bb [6]. Because the threshold for strange quark production in a quark-gluon plasma is much smaller than in a hadron gas, an enhancement in strange particle production has frequently been suggested as an indication of quark-gluon plasma formation [7]. This effect would be further enhanced in baryons with multiple strange quarks. While a quark-gluon plasma is more likely to be found in collisions of heavy nuclei, the enhancement of strange quark production in high 1 Particle-conjugate states are implied throughout this paper.
-1 -JHEP05(2011)064 energy pp collisions would be a sign of a collective effect, according to some models [8,9]. In contrast, recent Regge-theory calculations indicate little change in the ratio of K 0 S to charge particle production with increasing collision energy [10,11]. Thus, these measurements can be used to constrain theories, provide input for tuning of Monte Carlo models, and serve as a reference for the interpretation of strangeness production results in heavy-ion collisions.
Minimum bias collisions at the LHC can be classified as elastic scattering, inelastic single-diffractive dissociation (SD), inelastic double-diffractive dissociation, and inelastic non-diffractive scattering. The results presented here are normalized to the sum of doublediffractive and non-diffractive interactions, referred to as non-single-diffractive (NSD) interactions [1,2]. This choice is made to most closely match the event selection and to compare with previous experiments, which often used similar criteria. The K 0 S , Λ, and Ξ − are long-lived particles (cτ > 1 cm) and can be identified from their decay products originating from a displaced vertex. The particles are reconstructed from their decays: K 0 S → π + π − , Λ → pπ − , and Ξ − → Λπ − over the rapidity range |y| < 2, where the rapidity is defined as y = 1 2 ln E+p L E−p L , E is the particle energy, and p L is the particle momentum along the anticlockwise beam direction. For each particle species, we measure the production rate versus rapidity and transverse momentum p T , the average p T , the central production rate dN dy | y≈0 , and the integrated yield for |y| < 2 per NSD event. We compare our measurements to results from Monte Carlo models and lower energy data.

CMS experiment and collected data
CMS is a general purpose experiment at the LHC [12]. The silicon tracker, lead-tungstate crystal electromagnetic calorimeter, and brass-scintillator hadron calorimeter are all immersed in a 3.8 T axial magnetic field while muon detectors are interspersed with flux return steel outside of the 6 m diameter superconducting solenoid. The silicon tracker is used to reconstruct charged particle trajectories with |η| < 2.5, where the pseudorapidity is defined as η = − ln tan θ 2 , θ being the polar angle with respect to the anticlockwise beam. The tracker consists of layers of 100×150 µm 2 pixel sensors at radii less than 15 cm and layers of strip sensors, with pitch ranging from 80 to 183 µm, covering radii from 25 to 110 cm. In addition to barrel and endcap detectors, CMS has extensive forward calorimetry including a steel and quartz-fibre hadron calorimeter (HF), which covers 2.9 < |η| < 5.2. The data presented in this paper were collected by the CMS experiment in spring 2010 from proton-proton collisions at centre-of-mass energies of 0.9 and 7 TeV during a period in which the probability for two collisions in the same bunch crossing was negligible and the bunch crossings were well separated.
The online selection of events required activity in the beam scintillator counters at 3.23 < |η| < 4.65 in coincidence with colliding proton bunches. The offline selection required deposits of at least 3 GeV of energy in each end of the HF [1], preferentially selecting NSD events. A primary vertex reconstructed in the tracker was required and beam-halo and other beam-related background events were rejected as described in ref. [1]. The data selected with these criteria contain 9.08 and 23.86 million events at 0.9 and 7 TeV, corresponding to approximate integrated luminosities of 240 and 480 µb −1 , respectively. To determine the acceptance and efficiency, minimum-bias Monte Carlo samples were generated at both centre-of-mass energies using Pythia 6.422 [5] with tune D6T [13]. These events were passed through a CMS detector simulation package based on Geant 4 [14].

Strange particle reconstruction
Ionization deposits recorded by the silicon tracker are used to reconstruct tracks. To maximize reconstruction efficiency, we use a combined track collection formed from merging tracks found with the standard tracking described in ref. [15] and the minimum bias tracking described in ref.
[1]. Both tracking collections use the same basic algorithm; the differences are in the requirements for seeding, propagating, and filtering tracks.
As described in ref. [15], the K 0 S and Λ (generically referred to as V 0 ) reconstruction combines pairs of oppositely charged tracks; if the normalized χ 2 of the fit to a common vertex is less than 7, the candidate is kept. The primary vertex is refit for each candidate, removing the two tracks associated with the V 0 candidate. The next two paragraphs describe the selection of candidates for measurement of V 0 and Ξ − properties, respectively. Selection variables are measured in units of σ, the calculated uncertainty including all correlations.
To remove K 0 S particles misidentified as Λ particles and vice versa, the K 0 S (Λ) candidates must have a corresponding pπ − (π + π − ) mass more than 2.5σ away from the world-average Λ(K 0 S ) mass. The production cross sections we measure are intended to represent the prompt production of K 0 S and Λ, including strong and electromagnetic decays. However, V 0 particles can also be produced from weak decays and from secondary nuclear interactions. These unwanted contributions are reduced by requiring that the V 0 momentum vector points back to the primary vertex. This is done by requiring the 3D distance of closest approach of the V 0 to the primary vertex to be less than 3σ. To remove generic prompt backgrounds, the 3D V 0 vertex separation from the primary vertex must be greater than 5σ and both V 0 daughter tracks must have a 3D distance of closest approach to the primary vertex greater than 3σ. With the above selection, the background level for low transverse-momentum Λ candidates remains high. Therefore, additional cuts are applied to Λ candidates with p T < 0.6 GeV/c: • 3D separation between the primary and Λ vertices > 10σ (instead of > 5σ), • transverse (2D) separation between the pp collision region (beamspot) and Λ vertex > 10σ (instead of no cut), where the uncertainty is dominated by the Λ vertex, and • 3D impact parameter of the pion and proton tracks with respect to the primary vertex > (7 − 2|y|)σ (instead of > 3σ) where y is the rapidity of the Λ candidate. The rapidity dependence is a consequence of the observation that, for the low transverse momentum candidates, large backgrounds dominate at small rapidity, while low efficiency characterizes the large rapidity behaviour.
The resulting mass distributions of K 0 S and Λ candidates from the 0.9 and 7 TeV data are shown in figures 1 and 2. The π + π − mass distribution is fit with a double Gaussian (with a common mean) signal function plus a quadratic background. The pπ − mass distribution  is fit with a double Gaussian (common mean) signal function and a background function of the form Aq B , where q = M pπ − − (m p + m π − ), M pπ − is the pπ − invariant mass, and A and B are free parameters. The fitted K 0 S (Λ) yields at √ s = 0.9 and 7 TeV are 1.4×10 6 (2.8×10 5 ) and 6.5×10 6 (1.5×10 6 ), respectively.
To reconstruct the Ξ − , charged tracks of the correct sign are combined with Λ candidates. The χ 2 probability of the fit to a common vertex for the Λ and the charged track must be greater than 5%. In this fit, the Λ candidate is constrained to have the correct world-average mass [16]. The primary vertex is refit for each Ξ − candidate, removing all tracks associated with the Ξ − . The Ξ − candidates must then pass the following selection criteria: • 3D impact parameter with respect to the primary vertex > 2σ for the proton track from the Λ decay, > 3σ for the π − track from the Λ decay, and > 4σ for the π − track from the Ξ − decay, • invariant mass from the π + π − hypothesis for the tracks associated with the Λ candidate at least 20 MeV/c 2 away from the world-average K 0 S mass, • 3D impact parameter of the Ξ − candidate with respect to the primary vertex < 3σ, • 3D separation between Λ vertex and primary vertex > 10σ, and • 3D separation between Ξ − vertex and primary vertex > 2σ.
The mass distributions of Ξ − candidates from the √ s = 0.9 and 7 TeV data are shown in figure 3. The Λπ − mass is fit with a double Gaussian (with a common mean) signal function and a background function of the form Aq 1/2 + Bq 3/2 , where q = M Λπ − − (m Λ + m π − ) and M Λπ − is the Λπ − invariant mass. The fitted Ξ − yields at √ s = 0.9 and 7 TeV are 6.2×10 3 and 3.4×10 4 , respectively.

Efficiency correction
The efficiency correction is determined from a Monte Carlo simulation which is used to measure the effects of acceptance and the efficiency for event selection (including the trigger) and particle reconstruction. The Monte Carlo samples are reweighted to match the -5 -

JHEP05(2011)064
observed track multiplicity in data, as this has been shown to be an important component of the trigger efficiency [1,2]. This is referred to as track weighting. The efficiency correction also accounts for the other decay channels of the strange particles that we do not attempt to reconstruct, such as K 0 S → π 0 π 0 . The efficiency is given by the number of reconstructed particles divided by the number of generated particles, subject to two modifications. Firstly, the efficiency correction is used to account for candidates from SD events. As the results are normalized to NSD events, candidates from SD events which pass the event selection must be removed. This is done by defining the efficiency as the number of reconstructed candidates in all events divided by the number of generated candidates in NSD events. Secondly, the efficiency is modified to account for the small contribution of reconstructed non-prompt strange particles which pass the selection criteria. This is only an issue for the Λ particles which receive contributions from Ξ and Ω decays. Since these non-prompt Λ particles are present in both the MC and data, we modify the efficiency to remove this contribution by calculating the numerator using all of the reconstructed strange particles and the denominator with only the prompt generated strange particles. As the MC fails to produce enough Ξ particles (see section 6), the non-prompt Λ's are weighted more than prompt Λ's in the efficiency calculation.
The results of this analysis are presented in terms of two kinematic distributions: transverse momentum and rapidity. For all modes, |y| is divided into 10 equal size bins from 0 to 2 and p T is divided into 20 equal size bins from 0 to 4 GeV/c plus one bin each from 4 to 5 GeV/c and 5 to 6 GeV/c. In addition, the V 0 modes also have 6-8 GeV/c and 8-10 GeV/c p T bins. All results are for particles with |y| < 2.
The efficiency correction for the V 0 modes uses a two-dimensional binning in p T and |y|. Thus, the data are divided into 240 bins in the |y|, p T plane. The invariant mass histograms in each bin are fit to a double Gaussian signal function (with a common mean) and a background function. In bins with few entries, a single Gaussian signal function is used. For the Λ sample, some bins are merged due to sparse populations in |y|, p T space. The merging is performed separately when measuring |y| and p T such that the merging occurs across p T and |y| bins, respectively. The efficiency from MC is evaluated in each bin and applied to the measured yield to obtain the corrected yield. The twodimensional binning used for the V 0 efficiency correction greatly reduces problems arising from remaining differences in production dynamics between the data and the simulation. The much smaller sample of Ξ − candidates prevents the use of 2D binning. Thus, the data are divided into |y| bins to measure the |y| distribution and into p T bins to measure the p T distribution. However, the MC spectra do not match the data. Therefore, each Monte Carlo Ξ − particle is weighted in p T (|y|) to match the distribution in data when measuring the efficiency versus |y| (p T ). Thus, the MC and data distributions are forced to match in the variable over which we integrate to determine the efficiency. We refer to this as kinematic weighting. The efficiencies for all three particles are shown versus |y| and p T in figure 4. The efficiencies (for particles with |y| < 2) include the acceptance, event selection, reconstruction and selection, and also account for other decay channels. The increase in efficiency with p T is due to the improvement in tracking efficiency as track p T increases and to the selection criteria designed to remove prompt decays. The slight decrease at high p T is  Figure 4. Total efficiencies, including acceptance, trigger and event selection, reconstruction and particle selection, and other decay modes, as a function of |y| (left) and p T (right) for K 0 S , Λ, and Ξ − produced promptly in the range |y| < 2. Error bars come from MC statistics. due to particles decaying too far out to have reconstructed tracks. While there is no centreof-mass energy dependence on the efficiency versus p T , particles produced at √ s = 7 TeV have a higher average-p T , resulting in a higher efficiency when plotted versus rapidity.
As a check on the ability of the Monte Carlo simulation to reproduce the efficiency, the (well-known) K 0 S , Λ, and Ξ − lifetimes are measured. For the K 0 S measurement, the data are divided into bins of p T and ct, where ct is calculated as ct = cmL/p where m, L, and p are, respectively, the mass, decay length, and momentum of the particle. In each bin the data is corrected by the MC efficiency and the corrected yields summed in p T to obtain the ct distribution. Due to smaller sample sizes, the Λ and Ξ − yields are only measured in bins of ct. Using the kinematic weighting technique, the MC efficiency in each bin of ct is calculated with the p T spectrum correctly weighted to match data. The corrected lifetime distributions, shown in figure 5, display exponential behaviour. The vertex separation requirements result in very low efficiencies and low yields in the first lifetime bin and are thus expected to have some discrepancies. An actual measurement of the lifetime would remove this issue by using the reduced proper time, where one measures the lifetime relative to the point at which the particle had a chance to be reconstructed. The measured values of the lifetimes are also reasonably consistent with the world averages [16] (shown in figure 5) considering that only statistical uncertainties are reported and that this is not the optimal method for a lifetime measurement.
To convert the efficiency corrected yields to per event yields requires the true number of NSD events, which is obtained by correcting the number of selected events for the event selection inefficiency. The event selection includes both the online trigger and offline selection described in section 2. The event selection efficiency is determined in two ways. In the default method, it is calculated directly from the Monte Carlo simulation (appropriately weighted by the track multiplicity to reproduce the data). In the alternative method, the event selection efficiency versus track multiplicity is derived from the Monte Carlo. Then, each measured event is weighted by the inverse of the event selection efficiency based on its number of tracks. The number of events divided by the number of weighted events gives the event selection efficiency. However, since the event selection requires a primary vertex, no events will have fewer than two tracks. Therefore, the Monte Carlo is also used to determine the fraction of NSD events which have fewer than two tracks and the event selection efficiency is adjusted to include this effect. In both methods, the event selection efficiency accounts for unwanted SD events which pass the event selection. The numerator in the efficiency ratio contains all selected events, including single-diffractive events, while the denominator contains all NSD events.

Systematic uncertainties
The systematic uncertainties, reported in table 1, are divided into two categories: normalization uncertainties, which only affect the overall normalization, and point-to-point uncertainties, which may also affect the shape of the p T and |y| distributions.
The list below summarizes the source and evaluation of the point-to-point systematic uncertainties.
• Kinematic weighting versus 2D binning: The efficiency corrections using the 1D kinematic weighting technique (used for the Ξ − analysis) and the 2D binning technique (used for the V 0 analysis) were compared by measuring the efficiency with both methods on the highest statistics channel (K 0 S at 7 TeV).
• Non-prompt Λ: The contribution of non-prompt Λ decays is varied by a factor of two in the simulation.
• Detached particle reconstruction: Finding that the corrected lifetime distributions are exponential with the correct lifetime is a verification of our understanding of the reconstruction efficiency versus decay length. The systematic uncertainty is taken as the difference between the fitted lifetimes and the world-average lifetimes [16]. While the K 0 S and Λ lifetimes are within 1% of the world-average, a 2% systematic uncertainty is conservatively assigned.
• Mass fits: As an alternative to using a double-Gaussian signal shape, the V 0 invariant mass distributions are fit using a signal shape taken from Monte Carlo.
• Matching versus fitting: The number of reconstructed events, used in the numerator of the efficiency, is calculated in two ways. The truth matching method counts all reconstructed candidates which are matched to a generated candidate, based on the daughter momentum vectors and the decay vertex. The fitting method fits the MC mass distributions to extract a yield. The difference between these two is taken as a systematic.
• Misalignment: The nominal efficiency, obtained using a realistic alignment in the MC, is compared to the efficiency from a MC sample with perfect alignment.
• Beamspot: The location and width of the luminous region of pp collisions (beamspot) is varied in the simulation to assess the effect on efficiency.
• Detector material: The nominal efficiency is compared to the efficiency from a MC simulation in which the tracker was modified. The modification consisted of two parts. First, the mass of the tracker was increased by 5% which is a conservative estimate of the uncertainty. Second, the amounts of the various materials inside the tracker were adjusted within estimated uncertainties to obtain the tracker which maximized the interaction cross section. Both effects were implemented by changing material densities such that the tracker geometry remained the same. The effect is to decrease the efficiency as more particles, both primary and secondary, interact.
• Geant 4 cross sections: The cross sections used by Geant 4 for low energy strange baryons and all antibaryons are known to be overestimated [19]. The size of this effect is evaluated by analyzing Λ-Λ asymmetries.

JHEP05(2011)064
As the trigger efficiency is used to derive the number of NSD events, it only affects the normalization. The normalization systematic uncertainties, most of which come from trigger efficiency uncertainties, are described below.
• Alternative trigger efficiency calculation: The difference between the default and alternative trigger efficiency measurements, described in section 4, is taken as the systematic uncertainty on the method.
• Fraction of SD vs NSD: The change in trigger efficiency when the fraction of singlediffractive events in Monte Carlo is varied by ±50% is taken as the systematic uncertainty on the fraction of SD events. The Pythia 6 MC produces approximately 20% SD events while the fraction in the triggered data is considerably less [1, 2]. As the UA5 experiment measured 15.5% for this fraction at 900 GeV [20], a variation of ±50% is conservative.
• Modelling diffractive events: In addition to the fraction of SD events, the modelling of SD and NSD events may not be correct. The trigger efficiency obtained using the D6T tune is compared with the trigger efficiency from the P0 tune and Pythia 8. In particular, Pythia 8 uses a new Pomeron description of diffraction, modelled after PHO-JET [21,22], which results in a large increase in the track multiplicity of SD events.
• Track weighting: The track weighting of the Monte Carlo primarily affects the trigger efficiency. The track weighting requires a measurement of the track multiplicity distribution in data and MC. The default track multiplicity distribution is calculated from events which pass the trigger, except the primary vertex requirement is not applied. Two variations are considered. First, the track multiplicity distribution is measured from events also requiring a primary vertex. As this requires at least two tracks per event, the weight for events with fewer than two tracks is taken to be the same as the weight for events with two tracks. Second, the track weighting is determined with the primary vertex requirement (as in the first case), but without the HF trigger. The variation is taken as a systematic uncertainty on the track weighting.
• Branching fractions: The results are corrected for other decay channels of K 0 S , Λ, and Ξ − . The branching fraction uncertainty reported by the PDG [16] is used as the systematic uncertainty.
The systematic uncertainties at the two centre-of-mass energies are found to be essentially the same. The normalization uncertainties and the detached particle reconstruction uncertainty are obtained from the average of the results from the two centre-of-mass energies. The other point-to-point systematic uncertainties are derived from the higher statistics 7 TeV results. The point-to-point systematic uncertainties are measured as functions of p T and |y| and found to be independent of both variables. Therefore, the systematic uncertainties are estimated such that they include approximately 68% of the points (representing a 1σ error). The resulting systematic uncertainties are summarized in table 1.  For the measurements of dN/dy, dN/dy| y≈0 , and dN/dp T , the full systematic uncertainty is applied. For the Λ/K 0 S and Ξ − /Λ production ratio measurements, the largest point-to-point systematic uncertainty of the two particles is used and, among the normalization systematic uncertainties, only the branching fraction correction is considered. Note that for the Ξ − /Λ production ratios, the Λ branching fraction uncertainty cancels in the ratio.

Results
The results reported here are normalized to NSD interactions. The number of NSD raw events (given in section 2) are corrected for the trigger efficiency and the fraction of SD events after the selection. The corrected number of NSD events is 9.95×10 6 and 37.10×10 6 for √ s = 0.9 and 7 TeV, respectively.

JHEP05(2011)064
6.1 Distributions dN/dy and dN/dp T The corrected yields of K 0 S , Λ, and Ξ − , versus |y| and p T are plotted in figure 6, normalized to the number of NSD events. The rapidity distribution is flat at central rapidities with a slight decrease at higher rapidities while the p T distribution is observed to be rapidly falling. The rapidity distributions also show results from three different Pythia models: Pythia 6.422 with the D6T and P0 tunes [13,17] and Pythia 8.135 [18]. Fits to the Tsallis function, described below, are overlaid on the p T distributions.

Analysis of p T spectra
The corrected p T spectra are fit to the Tsallis function [23], as was done for charged particles [1, 2]. The Tsallis function used is: where C is a normalization parameter and T and n are the shape parameters. The results of the fits are shown in table 2. The data points used in the fits include only the statistical uncertainty. The statistical uncertainties on the fit parameters are obtained from the fit. The systematic uncertainties are obtained by varying the cuts and Monte Carlo conditions (tune, material, beamspot, and alignment) in the same way as used to obtain the point-to-point systematic uncertainties on the distributions. The systematic uncertainty on the normalization parameter C also includes the normalization uncertainty given in table 1. The normalized χ 2 indicates good fits to most of the samples. The T parameter can be associated with the inverse slope parameter of an exponential which dominates at low p T , while the n parameter controls the power law behaviour at high p T . While both parameters are necessary, they are highly correlated, with correlation coefficients around 0.9, making it difficult to elucidate information. Nevertheless, it is clear that T increases with particle mass and centreof-mass energy. This indicates a broader low-p T shape at higher centre-of-mass energy and for higher mass particles. In contrast, the high p T power-law behaviour seems to show a much steeper fall off for the two baryons than for the K 0 S . While the power-law behaviour of the baryons does not show any dependence on the centre-of-mass energy, the fall off of the K 0 S particles produced at √ s = 0.9 TeV is steeper than those produced at √ s = 7 TeV. We calculate the average p T directly from the data in the dN/dp T histograms. The Tsallis function fit is used to obtain the correct bin centre and to account for events beyond the measured p T range, both of which are small effects. The statistical uncertainty on the average p T is obtained by finding the standard deviation of p T and dividing by the square root of the equivalent number of background-free events, where the equivalent number of background-free events is given by the square of the inverse of the relative uncertainty on the total number of signal events. The systematic uncertainty is composed of two components added in quadrature. The first component is the same as used in determining the Tsallis function systematic uncertainties (varying the cuts and Monte Carlo conditions). The second component is obtained by using the mean p T of the fitted Tsallis function. The   Table 3. Average p T in units of MeV/c obtained from the appropriate dN/dp T distribution as described in the text. Results from Pythia 6 with tune D6T are also given. In each data column, the first uncertainty is statistical and the second is systematic.
average p T from data and Pythia 6 with the D6T underlying event tune is shown in table 3.
The Pythia values are quite close to the √ s = 7 TeV data and somewhat lower than the √ s = 0.9 TeV data. Although the average p T results from Pythia are relatively close to the data, the Pythia p T distributions are significantly broader than the data distributions. This disagreement can be seen in figure 7, which shows the ratio of Pythia to data for production of K 0 S , Λ, and Ξ − versus transverse momentum. As well as a broader distribution, the Pythia distributions also show significant variation as a function of tune and version.
The relative production versus transverse momentum between different species is shown in figure 8. The N (Λ)/N (K 0 S ) and N (Ξ − )/N (Λ) distributions both increase with p T at low p T , as expected from the higher average p T for the higher mass particles. At higher p T the N (Λ)/N (K 0 S ) distribution drops off while the N (Ξ − )/N (Λ) distribution appears to plateau. This is consistent with the values of the power-law parameter n for these distributions. Interestingly, the collision energy has no observable effect on the level or shape of these production ratios. The Pythia results are superimposed on the same plot. While Pythia reproduces the general features, it differs significantly in the details and shows large variations depending on tune and version. Figure 9 shows a comparison of the CMS p T distributions with results from other recent experiments [3,24,25]. To compare with the CMS results, the CDF, ALICE, and STAR distributions are multiplied by 8πp T , 4, and 8π, respectively. The CDF cross sections are also divided by 49 mb (the NSD cross section used by CDF [25]) to obtain distributions normalized to NSD events, matching the CMS and STAR normalization. The ALICE results are normalized to inelastic events (including single diffractive events). The ALICE and CMS results at 0.9 TeV agree for all three particles. The distributions behave as expected, with higher centre-of-mass energy corresponding to increased production rates and harder spectra. To remove the effect of normalization, figure 10 shows a comparison of Λ to K 0 S and Ξ − to Λ production ratios versus transverse momentum. The CMS results agree with the results from pp collisions at √ s =0.2 TeV from STAR [24] and at √ s =0.9 TeV results from ALICE [3]. These three results show a remarkable consistency across a wide variety of collision energies. In contrast, the CDF values for N (Λ)/N (K 0 S ) [26] are significantly higher than the CMS results while the CDF measurements of N (Ξ − )/N (Λ) [25] are lower, albeit with less significance.
Reducing the p T distributions to a single value, the average p T , we compare the CMS results with earlier results at lower energies in figure 11 [3,24,[26][27][28][29][30][31][32]. The CMS results are in excellent agreement with the recent ALICE measurements at 0.9 TeV. The CMS results continue the overall trend of increasing average p T with increasing particle mass and increasing centre-of-mass energy.

Analysis of production rate
As a measure of the overall production rate in NSD events, dN dy | y≈0 and the total yield for |y| < 2 were extracted and tabulated in table 4. The quantity dN dy | y≈0 is the average value of dN dy over the region |y| < 0.2. The integrated yields for |y| < 2 are obtained by integrating the p T spectra, using the Tsallis function fit to account for particles above the measured p T range.
The central production rates of K 0 S , Λ, and Ξ − are compared to previous results in figure 12. The results show the expected increase in production with centre-of-mass energy with little evidence of a difference due to beam particles. As the ALICE results are normalized to all inelastic collisions, they are expected to be somewhat lower than the CMS results.  [25], ALICE [3], and STAR [24] results show the combined statistical and systematic uncertainties. The CMS, CDF, and STAR results are normalized to NSD events while the ALICE results are normalized to all inelastic events. seen in the comparisons shown in the left panes of figure 6; Pythia underestimates the production of strange particles and the discrepancy grows with particle mass. Table 5 shows a comparison of the production rate of data to Pythia 6 with the D6T tune. The left column shows a large increase in the strange particle production cross section as the centre-of-mass energy increases from 0.9 to 7 TeV. The systematic uncertainties for this ratio are reduced as the same uncertainty affects both samples nearly equally. The results for K 0 S and Λ are consistent with the increase observed in inclusive charged particle production [1, 2] ( 5.  Figure 10. Ratio of Λ to K 0 S production (top) and Ξ − to Λ production (bottom) versus p T . The CMS, ALICE [3], and STAR [24] error bars include the statistical and systematic uncertainties. The CDF error bars include the statistical uncertainties for N (Λ)/N (K 0 S ) [26] and the statistical and systematic uncertainties for N (Ξ − )/N (Λ) [25].  Table 4. dN dy | y≈0 and integrated yields (|y| < 2.0) per NSD event from data. In each data column, the first uncertainty is statistical and the second is systematic. crease in particle production from 0.9 to 7 TeV is not well modelled by Pythia 6. Another feature, seen in the right column, is the deficit of strange particles produced by Pythia 6. The deficit of K 0 S particles in the MC, 15% (28%) low at 0.9 (7) TeV, is consistent with the results found in the production of charged particles [1, 2]. However, the deficit is much worse as the mass increases, resulting in a 63% reduction in Ξ − particles in MC compared to data at √ s =7 TeV. While values are only presented for Pythia 6 with the D6T tune, the same features are also evident for the other two Pythia comparisons in the rapidity distribution plots in figure 6.   Figure 11. Average p T for K 0 S (top), Λ (middle), and Ξ − (bottom), as a function of the centre-of-mass energy. The CMS measurements are for |y| < 2. The other results are from UA5 [27][28][29][30][31] (pp collisions covering |y| < 2.5, |y| < 2, and |y| < 3 for K 0 S , Λ, and Ξ − , respectively), E735 [32] (pp collisions using tracks with −0.36 < η < 1.0), CDF [26] (pp collisions covering |η| < 1.0), STAR [24] (pp collisions covering |y| < 0.5), and ALICE [3] (pp collisions covering |y| < 0.75 for K 0 S and Λ and |y| < 0.8 for Ξ − ). Some points have been slightly offset from the true energy to improve visibility. The vertical bars indicate the statistical and systematic uncertainties (when available) summed in quadrature.  Figure 12. The central rapidity production rate for K 0 S (top), Λ (middle), and Ξ − (bottom), as a function of the centre-of-mass energy. The previous results are from UA5 [29,30] (pp), CDF [33] (pp), STAR [24] (pp), and ALICE [3] (pp). The CMS, UA5, and STAR results are normalized to NSD events. The CDF results are normalized to events passing their trigger and event selection defined chiefly by activity in both sides of the detector, at least four tracks, and a primary vertex. The ALICE results are normalized to all inelastic events. Some points have been slightly offset from the true energy to improve visibility. The vertical bars indicate the statistical uncertainties for the UA5 and CDF results and the combined statistical and systematic uncertainties for the CMS, ALICE, and STAR results.

Conclusions
This article presents a study of the production of K 0 S , Λ, and Ξ − particles in proton-proton collisions at centre-of-mass energies 0.9 and 7 TeV. By fully exploiting the low-momentum track reconstruction capabilities of CMS, we have measured the transverse-momentum distribution of these strange particles down to zero. From this sample of 10 million strange particles, the transverse momentum distributions were measured out to 10 GeV/c for K 0 S and Λ and out to 6 GeV/c for Ξ − . We fit these distributions with a Tsallis function to obtain information on the exponential decay at low p T and the power-law behaviour at high p T . All species show a flattening of the exponential decay as the centre-of-mass energy increases. While the baryons show little change in the high-p T region, the K 0 S power-law parameter decreases from 7.8 to 6.9. The average p T values, calculated directly from the data, are found to increase with particle mass and centre-of-mass energy, in agreement with predictions and other experimental results. While the Pythia p T distributions used in this analysis show significant variation based on tune and version, they are all broader than the data distributions.
We have also measured the production versus rapidity and extracted the value of dN/dy in the central rapidity region. The increase in production of strange particles as the centreof-mass energy increases from 0.9 to 7 TeV is approximately consistent with the results for inclusive charged particles. However, as in the inclusive charged particle case, Pythia fails to match this increase. For K 0 S production, the discrepancy is similar to what has been found in charged particles. However, the deficit between Pythia and data is significantly larger for the two hyperons at both energies, reaching a factor of three discrepancy for Ξ − production at √ s = 7 TeV. If a quark-gluon plasma or other collective effects were present, we might expect an enhancement of double-strange baryons to single-strange baryons and/or an enhancement of strange baryons to strange mesons. However, the production ratios N (Λ)/N (K 0 S ) and N (Ξ − )/N (Λ) versus rapidity and transverse momentum show no change with centre-of-mass energy. Thus, the deficiency in Pythia is likely originating from parameters regulating the frequency of strange quarks appearing in colour strings. The variety of measurements presented here can be used to tune Pythia and other models as well as a baseline to understand measurements of strangeness production in heavy-ion collisions.