Measuring K$^0_{\rm S}$K$^{\rm{\pm}}$ interactions using pp collisions at $\sqrt{s}=7$ TeV

We present the first measurements of femtoscopic correlations between the K$^0_{\rm S}$ and K$^{\rm \pm}$ particles in pp collisions at $\sqrt{s}=7$ TeV measured by the ALICE experiment. The observed femtoscopic correlations are consistent with final-state interactions proceeding solely via the $a_0(980)$ resonance. The extracted kaon source radius and correlation strength parameters for K$^0_{\rm S}$K$^{\rm -}$ are found to be equal within the experimental uncertainties to those for K$^0_{\rm S}$K$^{\rm +}$. Results of the present study are compared with those from identical-kaon femtoscopic studies also performed with pp collisions at $\sqrt{s}=7$ TeV by ALICE and with a K$^0_{\rm S}$K$^{\rm \pm}$ measurement in Pb-Pb collisions at $\sqrt{s_{\rm NN}}=2.76$ TeV. Combined with the Pb-Pb results, our pp analysis is found to be compatible with the interpretation of the $a_0(980)$ having a tetraquark structure instead of that of a diquark.

Measuring K 0 S K ± interactions using pp collisions at √ s = 7 TeV

Abstract
We present the first measurements of femtoscopic correlations between the K 0 S and K ± particles in pp collisions at √ s = 7 TeV measured by the ALICE experiment.The observed femtoscopic correlations are consistent with final-state interactions proceeding solely via the a 0 (980) resonance.The extracted kaon source radius and correlation strength parameters for K 0 S K − are found to be equal within the experimental uncertainties to those for K 0 S K + .Results of the present study are compared with those from identical-kaon femtoscopic studies also performed with pp collisions at √ s = 7 TeV by ALICE and with a K 0 S K ± measurement in Pb-Pb collisions at √ s NN = 2.76 TeV.Combined with the Pb-Pb results, our pp analysis is found to be compatible with the interpretation of the a 0 (980) having a tetraquark structure instead of that of a diquark.

Introduction
Recently, by using Pb-Pb collisions at √ s NN = 2.76 TeV, the ALICE experiment [1] has published the first-ever study of K 0 S K ± femtoscopy [2].K 0 S K ± femtoscopy differs from identical-kaon femtoscopy, for which a number of studies exist in the literature [3][4][5][6], in that the only pair interaction expected is a final-state interaction (FSI) through the a 0 (980) resonance.It was found in that Pb-Pb study that the FSI in K 0 S K ± proceeds solely through the a 0 (980) resonance, i.e. with no competing non-resonant channels, and the extracted kaon source parameters agree with published results from identical-kaon studies in Pb-Pb collisions.These results were found to be compatible with the interpretation of the a 0 resonance as a tetraquark state rather than a diquark state [2,[7][8][9].A recent theoretical calculation has shown that the ALICE Pb-Pb results can indeed be described by a model based on the four-quark model [10].
The argument given in Ref. [2] for a tetraquark a 0 being compatible with the Pb-Pb K 0 S K ± result stated above is based on two factors: 1) the kaon source geometry, and 2) an empirical selection rule (For the sake of simplicity of notation, "a 0 " will be used for the remainder of this paper to represent "a 0 (980).").For factor 1), the production cross section of the a 0 resonance in a reaction channel such as K 0 K − → a − 0 should depend on whether the a − 0 is composed of du or dssu quarks, the former requiring the annihilation of the ss pair and the latter being a direct transfer of the valence quarks from the kaons to the a − 0 .Since the femtoscopic size of the 0-10% most central Pb-Pb collision is measured to be 5-6 fm, the large geometry in these collisions is favorable for the direct transfer of quarks to the a 0 , whereas not favorable for the annihilation of the strange quarks due to the short-ranged nature of the strong interaction.For factor 2), the direct transfer of the valence quarks from the kaons to the a − 0 is favored since this is an "OZI superallowed" reaction [9].The OZI rule can be stated as "an inhibition associated with the creation or annihilation of quark lines" [9].Thus, the annihilation of the strange quarks is suppressed by the OZI rule.Both of these factors favor the formation of a tetraquark a 0 and suppress the formation of a diquark a 0 .As a result of this, if the a 0 were a diquark, one would expect competing non-resonant channels present and/or no FSI at all, i.e. free-streaming, of the kaon pair thus diluting the strength of the a 0 resonant FSI.The fact that this is not seen to be the case in Pb-Pb collisions favors the tetraquark a 0 interpretation.
The geometry of the kaon source is seen to be an important factor in the argument given above, i.e. the large kaon source seen in Pb-Pb collisions suppresses the annihilation of the strange quarks in the kaon pair and enhances the direct transfer of quarks to the a 0 .It is interesting to speculate on the dependence of the strength of the a 0 resonant FSI on the size of the kaon source, particularly for a very small source of size ∼ 1 fm that would be obtained in pp collisions [4,5].For a kaon source of size ∼ 1 fm, the kaons in a produced kaon pair would be overlapping with each other at the source, thus giving a geometric enhancement of the strange-quark annihilation channel that could compete with, or even dominate over, the OZI rule suppression of quark annihilation.Thus we might expect that the tetraquark a 0 resonant FSI could be diluted or completely suppressed by competing non-resonant annihilation channels that could open up, whereas a diquark a 0 resonant FSI, which was not seen to be suppressed by either geometry or the OZI rule in Pb-Pb, would not be diluted.A femtoscopic measurement of K 0 S K ± correlations in pp collisions should be able to measure the strength of the a 0 FSI to test this.
In this Letter, femtoscopic correlations with the particle pair combinations K 0 S K ± are studied for the first time in pp collisions at √ s = 7 TeV by the ALICE experiment.The physics goals of the present K 0 S K ± femtoscopy study are the following: 1) show to what extent the FSI through the a 0 resonance describes the correlation functions, 2) study the K 0 and K 0 sources to see if there are differences in the source parameters, 3) compare the results of the extracted kaon source parameters from the present study with the published results from Pb-Pb collisions and identical kaon results from pp collisions, and 4) see if the results from this pp study are compatible with a tetraquark a 0 as suggested from the Pb-Pb study.

Description of experiment and data selection
The ALICE experiment and its performance in the LHC Run 1 (2009 − 2013) are described in Ref. [1] and Ref. [11,12], respectively.About 370 × 10 6 minimum-bias 7 TeV pp collision events taken in 2010 were used in this analysis.Events were classified using the measured amplitudes in the V0 detectors, which consist of two arrays of scintillators located along the beamline and covering the full azimuth [13,14].Charged particles were reconstructed and identified with the central barrel detectors located within a solenoid magnet with a field strength of B = ±0.5 T. Charged particle tracking was performed using the Time Projection Chamber (TPC) [15] and the Inner Tracking System (ITS) [1].The ITS allowed for high spatial resolution in determining the primary (collision) vertex.A momentum resolution of less than 10 MeV/c was typically obtained for the charged tracks of interest in this analysis [16].The primary vertex was obtained from the ITS, the position of the primary vertex being constrained along the beam direction (the "z-position") to be within ±10 cm of the center of the ALICE detector.In addition to the standard track quality selections [16], the selections based on the quality of track fitting and the number of detected tracking points in the TPC were used to ensure that only well-reconstructed tracks were taken in the analysis [11,15,16].
Particle identification (PID) for reconstructed tracks was carried out using both the TPC and the Timeof-Flight (TOF) detectors in the pseudorapidity range |η| < 0.8 [11,12].For the PID signal from both detectors, a value was assigned to each track denoting the number of standard deviations between the measured track information and calculated values (N σ ) [6,11,12,16].For TPC PID, a parametrized Bethe-Bloch formula was used to calculate the specific energy loss dE/dx in the detector expected for a particle with a given mass and momentum.For PID with TOF, the particle mass was used to calculate the expected time-of-flight as a function of track length and momentum.This procedure was repeated for four "particle species hypotheses", i.e. electron, pion, kaon and proton, and, for each hypothesis, a different N σ value was obtained per detector.

Kaon selection
The methods used to select and identify individual K 0 S and K ± particles are the same as those used for the ALICE K 0 S K 0 S [4] and K ± K ± [5] analyses from √ s = 7 TeV pp collisions.These are now described below.

K 0
S selection The K 0 S particles were reconstructed from the decay K 0 S → π + π − , with the daughter π + and π − tracks detected in the TPC, ITS and TOF detectors.The secondary vertex finder used to locate the neutral kaon decays employed the "on-the-fly" reconstruction method [16], which recalculates the daughter track momenta during the original tracking process under the assumption that the tracks came from a decay vertex instead of the primary vertex.Pions with p T > 0.15 GeV/c were accepted (since for lower p T track finding efficiency drops rapidly) and the distance of closest approach to the primary vertex (DCA) of the reconstructed K 0 S was required to be less than 0.3 cm in all directions.The required N σ values for the pions were N TPC σ < 3 (for all momenta) and N TOF σ < 3 for p > 0.8 GeV/c.An invariant mass distribution for the π + π − pairs was produced and the K 0 S was defined to be resulting from a pair that fell into the invariant mass range 0.480 < m π + π − < 0.515 GeV/c 2 , corresponding to ±4.7σ , where σ = 3.7 MeV/c 2 is the width of a Gaussian fit to the invariant mass distribution.

K ± selection
Charged kaon tracks were detected using the TPC and TOF detectors, and were accepted if they were within the range 0.14 < p T < 1.2 GeV/c in order to obtain good PID.The determination of the momenta of the tracks was performed using tracks reconstructed with the TPC only and constrained to the primary vertex.In order to reduce the number of secondary tracks (for instance the charged particles produced in the detector material, particles from weak decays, etc.), the primary charged kaon tracks were selected based on the DCA, such that the DCA transverse to the beam direction was less than 2.4 cm and the DCA along the beam direction was less than 3.2 cm.If the TOF signal were not available, the required N σ values for the charged kaons were N TPC σ < 2 for p T < 0.5 GeV/c, and the track was rejected for p T > 0.5 GeV/c.If the TOF signal were also available and p T > 0.5 GeV/c: The K 0 S K ± experimental pair purity was estimated from a Monte Carlo (MC) study based on PYTHIA [17] simulations with the Perugia2011 tune [18], and using GEANT3 [19] to model particle transport through the ALICE detectors.The purity was determined from the fraction of the reconstructed MC simulated pairs that were identified as actual K 0 S K ± pairs input from PYTHIA.The pair purity was estimated to be ∼ 83% for all kinematic regions studied in this analysis.The single-particle purities for K 0 S and K ± particles used in this analysis were estimated to be ∼ 92% and ∼ 91%, respectively.
3 Analysis methods

Experimental Correlation Functions
This analysis studies the momentum correlations of K 0 S K ± pairs using the two-particle correlation function, defined as where A(k * ) is the measured distribution of pairs from the same event, B(k * ) is the reference distribution of pairs from mixed events, and k * is the magnitude of the momentum of each of the particles in the pair rest frame (PRF), where and m K 0 (E K 0 ) and m K ± (E K ± ) are the rest masses (total energies) of the K 0 S and K ± , respectively.The denominator B(k * ) was formed by mixing K 0 S and K ± particles from each event with particles from ten other events [2].The vertices of the mixed events were constrained to be within 2 cm of each other in the z-direction.Two-track effects, such as the merging of two real tracks into one reconstructed track and the splitting of one real track into two reconstructed tracks, is an important issue for femtoscopic studies.This analysis dealt with these effects using the following method.For each kaon pair, the distance between the K 0 S pion daughter track and the same-charged K ± track was calculated at up to nine points throughout the TPC (every 20 cm from 85 cm to 245 cm) and then averaged.Comparing pairs from the same event to those from mixed events, one observes a splitting peak for an average separation of < 11 cm.To correct for this, this analysis demanded that the same-charge particles from each kaon pair must have an average TPC separation of at least 13 cm.Mixed-event tracks were normalized by subtracting the primary vertex position from each used track point.distribution.The mean k T values for these three bins were 0.66, 0.49 and 1.17 GeV/c, respectively.The raw K 0 S K + correlation functions for these three bins compared with those generated from PYTHIA simulations with the Perugia2011 tune and using GEANT3 to model particle transport through the ALICE detectors are shown in Fig. 1.The raw K 0 S K − correlation functions look very similar to these.It is seen that although PYTHIA qualitatively describes the trends of the baseline of the data, it does not describe it quantitatively such that it could be used to model the baseline directly.Instead, for the present analysis the strategy for dealing with the baseline was to describe it with several functional forms to be fitted to the experimental correlation functions and to use PYTHIA to test the appropriateness of the proposed baseline functional forms.
Three functional forms for the baseline were tested with PYTHIA: quadratic, Gaussian and exponential, given by where a, b and c are fit parameters.Fig. 2 shows fits of Eq. ( 4), Eq. ( 5) and Eq. ( 6) to the PYTHIA correlation functions shown in Fig. 1 for the three k T ranges used in this analysis.As seen, all three functional forms do reasonably well in representing the PYTHIA correlation functions.Thus, all three forms were used in fitting the experimental correlation function and the different results obtained will be used to estimate the systematic uncertainty due to the baseline estimation.Of course there are an infinite number of functions one could try to represent the baseline, but at least the three that were chosen for this work are simple and representative of three basic functional forms.
Correlation functions were corrected for momentum resolution effects using PYTHIA calculations.Two correlation functions were generated with PYTHIA: one in terms of the generator-level k * and one in terms of the simulated detector-level k * .Because PYTHIA does not incorporate final-state interactions, simulated femtoscopic weights were determined using a 9th-order polynomial fit in k * to the experimental correlation function for the k T range considered.When filling the same-event distributions, i.e.A(k * ) in Eq. 1, kaon pairs were individually weighted by this 9th-order fit according to their k * .Then, the ratio of the "ideal" correlation function to the "measured" one (for each k * bin) was multiplied to the data correlation functions before the fit procedure.This correction mostly affected the lowest k * bins, increasing the extracted source parameters by ∼ 2%.

Final-state interaction model
The final-state interaction model used in the present pp collision analysis follows the same principles as the ones used for the ALICE Pb-Pb collision analysis [2].The measured K 0 S K ± correlation functions were fit with formulas that include a parameterization which incorporates strong FSI.It was assumed that the FSI arises in the K 0 S K ± channels due to the near-threshold resonance, a 0 .This parameterization was introduced by R. Lednicky and is based on the model by R. Lednicky and V.L. Lyuboshitz [20,21] (see also Ref. [3] for more details on this parameterization).
Using an equal emission time approximation in the PRF [20], the elastic K 0 S K ± transition is written K 0 S K ± interaction using pp collisions ALICE Collaboration as a stationary solution Ψ − k * ( r * ) of the scattering problem in the PRF.The quantity r * represents the emission separation of the pair in the PRF, and the − k * subscript refers to a reversal of time from the emission process.At large distances this has the asymptotic form of a superposition of an incoming plane wave and an outgoing spherical wave, where f (k * ) is the s-wave K 0 K − or K 0 K + scattering amplitude whose contribution is the s-wave isovector a 0 resonance (see Eq. ( 11) in Ref. [3]) and In Eq. ( 8), m a 0 is the mass of the a 0 resonance, and γ a 0 →KK and γ a 0 →πη are the couplings of the a 0 resonance to the K 0 K − (or K 0 K + ) and πη channels, respectively.Also, s = 4(m 2 K 0 + k * 2 ) and k πη denotes the momentum in the second decay channel (πη) (see Tab. 1).
The correlation function due to the FSI is then calculated by integrating Ψ − k * ( r * ) in the Koonin-Pratt equation [22,23], where S( r * ) is a one-dimensional Gaussian source function of the PRF relative distance | r * | with a Gaussian width R of the form Equation 9 can be integrated analytically for K 0 S K ± correlations with FSI for the one-dimensional case, with the result where In the above equations α is the fraction of K 0 S K ± pairs that come from the K 0 K − or K 0 K + system, set to 0.5 assuming symmetry in K 0 and K 0 production [3], R is the radius parameter from the spherical Gaussian source distribution given in Eq. ( 10), and λ is the correlation strength.The correlation strength is unity in the ideal case of pure a 0 -resonant FSI, perfect PID, a perfect Gaussian kaon source and the absence of long-lived resonances which decay into kaons.The term ∆C is a calculated correction factor that takes into account the deviation of the spherical wave assumption used in Eq. ( 7) in the inner region of the short-range potential (see the Appendix in Ref. [3]).Its effect on the extracted source parameters is to increase them by ∼ 14%.Note that the form of the FSI term in Eq. ( 11) differs from the form of the FSI term for K 0 S K 0 S correlations (Eq.( 9) of Ref. [3]) by a factor of 1/2 due to the non-identical particles in K 0 S K ± correlations and thus the absence of the requirement to symmetrize the wavefunction given in Eq. (7).
As seen in Eq. ( 8), the K 0 K − or K 0 K + s-wave scattering amplitude depends on the a 0 mass and decay couplings.From the ALICE Pb-Pb collision K 0 S K ± study [2], it was found that source parameters extracted with the "Achasov2" parameters of Ref. [7] agreed best with the identical kaon measurements, K 0 S K ± interaction using pp collisions ALICE Collaboration Reference m a 0 γ a 0 K K γ a 0 πη Achasov2 [7] 1.003 0.8365 0.4580  The experimental K 0 S K ± correlation functions, calculated using Eq. ( 1), were fit with the expression where C baseline (k * ) is Eq. ( 4), Eq. ( 5) or Eq. ( 6).
The fitting strategy used was to carry out a 5-parameter fit of Eq. ( 13) to the K 0 S K ± experimental correlation functions to extract R, λ , a, b and c for each of the k T ranges, for each of the three baseline functional forms, and for the two k * fit ranges, (0.0-0.6 GeV/c) and (0.0-0.8 GeV/c), giving six R and six λ parameter values for each k T range and charge state.These six values were then averaged and the variance calculated to obtain the final values for the parameters and an estimate of the combined systematic uncertainties from the baseline assumptions and fit range, respectively.
Figure 3 shows sample correlation functions divided by the quadratic baseline function with fits of Eq. ( 13) for K 0 S K ± and the k * fit range (0.0 − 0.6 GeV/c) for the three k T bins.The fits using the other baseline assumptions and to the wider range of (0.0 − 0.8 GeV/c) are similar in quality.The χ 2 /ndf for the fits lie in the range ∼ 1 − 2. Statistical (lines) and the quadratic sum of the statistical and systematic (boxes) uncertainties are shown.The systematic uncertainties were determined by varying cuts on the data (See the discussion of the "cut systematic uncertainty" in the section below on "Systematic Uncertainties for more details.").Fig. 4 shows sample raw correlation functions for K 0 S K + for the three k T bins and the quadratic baseline function, Eq. 4, that was fit corresponding to the 5-parameter fits of Eq. 13 to the K 0 S K + data presented in Fig. 3. Statistical uncertainties on the fit parameters were obtained by constructing the 1σ λ vs. R contour and taking the errors to be at the extreme extents of the contour.This method gives the most conservative estimates of the statistical uncertainties.
The Achasov2 a 0 FSI parameterization coupled with the various baseline assumptions gives a good representation of the signal region of the data, i.e. reproducing the enhancement in the k * region 0.0− 0.1 GeV/c and the small dip in the region 0.1 − 0.3 GeV/c.A good representation of the signal region was also seen to be the case for the Pb-Pb analysis with the Achasov2 parameterization, which has a qualitatively different k * dependence of the correlation function that is dominated by a dip at low k * (Compare present Fig. 3 with Fig. 2 from Ref. [2]).The enhancement seen for the small-R system at low k * is expected from Eq. ( 11) as a consequence of the first term in the brackets that goes as 1/R 2 .This demonstrates the ability of Eq. ( 11) to describe the FSI in both the small and large size regimes as going through the a 0 resonance.

Extracted R and λ parameters
The results for the extracted average R and λ parameters and the statistical and systematic uncertainties on these for the present analysis of K 0 S K ± femtoscopy from 7 TeV pp collisions are shown in Tab. 2. The statistical uncertainties given are the averages over the 6 fits for each case.As can be seen, R and λ for K 0 S K + agree within the statistical uncertainties with those for K 0 S K − in all cases.
Correlation functions divided by one of the baseline functions with fits from Eq. ( 13) for K 0 S K + and K 0 S K − and k * fit range (0.0-0.6 GeV/c) for the three k T bins and the quadratic baseline function assumption.Statistical (lines) and the quadratic sum of the statistical and systematic (boxes) uncertainties are shown.For k * > 0.05 GeV/c, the systematic uncertainties become negligible and the boxes are no longer shown.

Systematic uncertainties
Table 2 shows the total systematic uncertainties on the extracted R and λ parameters.As is seen, for most cases the total systematic uncertainty is larger than the statistical uncertainty.The total systematic uncertainty is broken down in Tab. 2 into two main contributions, the "fit systematic uncertainty" and the "cut systematic uncertainty", and is the quadratic sum of these.The fit systematic uncertainty is the combined systematic uncertainty due to the various baseline assumptions and varying the k * fit range, as described earlier.The cut systematic uncertainty is the systematic uncertainty related to the various cuts made in the data analysis.To determine this, single particle cuts were varied by ∼ 10%, and the value chosen for the minimum separation distance of same-sign tracks was varied by ∼ 20%.Taking the upper-limit values of the variations to be conservative, this led to additional errors of 4% for R and 8% for λ .As seen in the table, the fit systematic uncertainty dominates over the cut systematic uncertainty in all cases, demonstrating the large uncertainties in determining the non-femtoscopic baseline in pp collisions.The "total quadratic uncertainty" is the quadratic sum of the "statistical uncertainty" column and the "total systematic uncertainty" column.In this section comparisons of the present results for R and λ with K 0 S K ± measurements from ALICE 2.76 TeV Pb-Pb collisions for 0− 10% centrality [2], and with identical-kaon measurements from ALICE 7 TeV pp collisions [4,5] are presented.Since it is seen in Tab. 2 that the extracted parameters for K 0 S K + agree within the statistical uncertainties with those for K 0 S K − in all cases, these are averaged over weighted by the statistical uncertainties in the following figures Figure 5 shows the comparison with the ALICE Pb-Pb collision K 0 S K ± measurements.The λ parameters have been divided by the pair purity for each case.It is seen that R for 0 − 10% centrality Pb-Pb is ∼ 5 fm, and is significantly larger than the R ∼ 1 fm measured for pp collisions.This is expected since R reflects the geometric size of the interaction region of the collision.It is somewhat surprising that λ for pp collisions is seen to be significantly less than that for Pb-Pb collisions.There are two main factors effecting the value of the λ parameter: 1) the degree to which a Gaussian fits the correlation function and 2) the effect of long-lived resonances diluting the kaon sample.For 1), it is seen in Fig. 3 for pp Figure 5: R and λ parameters extracted in the present analysis from K 0 S K ± femtoscopy averaged over K 0 S K + and K 0 S K − , along with a comparison with K 0 S K ± results from ALICE 2.76 TeV Pb-Pb collisions for 0 − 10% centrality [2].The quadratic sum of the statistical and systematic uncertainties is plotted for all results as boxes and the statistical uncertainties are given as lines.and in Fig. 2 of Ref. [2] for Pb-Pb that the Gaussian function used in the Ledincky equation, Eqs. 10 and 11, fits both colliding systems well, minimizing the effect of 1).For 2), the K * decay (Γ ∼ 50 MeV) has the largest influence on diluting the kaon sample, and it is unlikely that the multiplicity ratio of K/K * changes dramatically in going from 2.76 TeV to 7 TeV.From these arguments we might naively expect λ to be similar in the pp and Pb-Pb cases.
In order to properly compare the present results with the ALICE pp collision identical-kaon measurements, we must take the weighted average (weighted by their statistical uncertainties) over the multiplicity bins used in Refs.[4,5] since our present results are summed over all multiplicity.Figure 6 shows the comparison between the present results for R and λ and measurements from the identical-kaon femtoscopy in 7 TeV pp collisions.The R values are seen to agree between the present analysis and the identical kaon analyses within the uncertainties.The λ parameters for the identical kaons are seen to scatter in a wide range between values of 0.3 − 0.7, whereas the K 0 S K ± values are seen to lie in the narrower range of 0.25 − 0.30.
In order to clarify the comparison between the λ values from K 0 S K ± and the identical-kaon results, the weighted average (weighted by the quadratic sum of the statistical and systematic uncertainties) over the identical kaon values is plotted as a blue band in Fig. 6, the width of the band being 2σ , where σ is the weighted average uncertainty of the measurements.As seen, the K 0 S K ± values tend to be somewhat smaller than the average of the identical kaons, as was also the case for the comparison with the λ values from Pb-Pb seen in Fig. 5.

4.4
Implications from the present results for the a 0 to be a tetraquark state The K 0 S K ± FSI is described well by assuming it is due to the a 0 resonance for both pp and Pb-Pb collisions, as seen in Fig. 3 of the present work and in Fig. 2 of Ref. [2].The R parameters extracted from this method are also seen to agree within uncertainties with the identical-kaon measurements for each of these collision systems.For Pb-Pb collisions, it was found that the λ parameters extracted from K 0 S K ± : R and λ parameters extracted in the present analysis from K 0 S K ± femtoscopy averaged over K 0 S K + and K 0 S K − , along with comparisons with identical kaon results from ALICE 7 TeV pp collisions averaged over event multiplicity.The quadratic sum of the statistical and systematic uncertainties is plotted for all results as boxes and the statistical uncertainties are given as lines.Also plotted as a blue band is the weighted average of the identical-kaon values.also agree with the corresponding identical-kaon measurements for Pb-Pb collisions indicating that the FSI between the kaons goes solely through the a 0 resonance.The present pp collision results for λ , which are lower than the corresponding identical-kaon values in pp collisions seen in Fig. 6 and lower than the K 0 S K ± values from Pb-Pb collisions seen in Fig. 5, imply that the FSI for these collisions does not go solely through the a 0 resonance, i.e. non-resonant elastic channels and/or free-streaming are also present.From the arguments given in the Introduction, this is the geometric effect that would be expected in the case of a tetraquark a 0 since competing annihilation channels could open up in the smaller system and compete with the FSI through the a 0 , whereas for a diquark a 0 the FSI should still go solely through the a 0 .The pp collision results are thus compatible with the conclusion from the Pb-Pb collision measurement [2] that favors the interpretation of the a 0 resonance to be a tetraquark state.

Summary
In summary, femtoscopic correlations with the particle pair combinations K 0 S K ± are studied in pp collisions at √ s = 7 TeV for the first time by the LHC ALICE experiment.Correlations in the K 0 S K ± pairs are produced by final-state interactions which proceed through the a 0 resonance.It is found that the a 0 final-state interaction describes the shape of the measured K 0 S K ± correlation functions well.The extracted radius and λ parameters for K 0 S K − are found to be equal within the experimental uncertainties to those for K 0 S K + .Results of the present study are compared with those from identical-kaon femtoscopic studies also performed with pp collisions at √ s = 7 TeV by ALICE and with a recent ALICE K 0 S K ± measurement in Pb-Pb collisions at √ s NN = 2.76 TeV.These comparisons suggest that non-resonant elastic scattering channels are present in pp collisions, unlike in Pb-Pb collisions.It is our conclusion that the present results, in combination with the ALICE Pb-Pb collision measurements, favor the interpretation of the a 0 to be a tetraquark state.

Figure 1 :
Figure 1: Raw K 0 S K + correlation functions for the three k T bins compared with those from PYTHIA.The error bars are statistical.The scale of C(k * ) is arbitrary.

Figure 2 :
Figure 2: Comparisons of fits of three possible baseline functional forms with the PYTHIA correlation functions that were shown in Fig. 1.Fits were made in the k * range 0 − 0.8 GeV/c.The scale of C(k * ) is arbitrary.
thus in the present pp collision study only the Achasov2 parameters are used.These parameters are shown in Tab. 1.

Figure 4 :
Figure 4: Sample raw correlation functions for K 0 S K + showing the fitted quadratic baseline function, Eq. 4. Statistical uncertainties are shown.The scale of C(k * ) is arbitrary.

4. 3
Comparisons with K 0 S K ± results from Pb-Pb collisions at √ s NN = 2.76 TeV and identical-kaon results from pp collisions at √ s = 7 TeV

Figure 6
Figure6: R and λ parameters extracted in the present analysis from K 0 S K ± femtoscopy averaged over K 0 S K + and K 0 S K − , along with comparisons with identical kaon results from ALICE 7 TeV pp collisions averaged over event multiplicity.The quadratic sum of the statistical and systematic uncertainties is plotted for all results as boxes and the statistical uncertainties are given as lines.Also plotted as a blue band is the weighted average of the identical-kaon values.

Table 1 :
The a 0 mass and coupling parameters, all in GeV/c 2 , used in the present study.

Table 2 :
Fit results for average R and λ showing statistical and systematic uncertainties from K 0 S K ± femtoscopy with pp collisions at √ s = 7 TeV.The "[+/-]" in the first column refers to K 0 S K + or K 0 S K − .See the text for the definitions of the various uncertainties.