Measuring K0SK± interactions using Pb–Pb collisions at √sNN=2.76TeV
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This is an electronic reprint of the original article. This reprint may differ from the original in pagination and typographic detail. Author(s): Title: Year: Version: Please cite the original version: All material supplied via JYX is protected by copyright and other intellectual property rights, and duplication or sale of all or part of any of the repository collections is not permitted, except that material may be duplicated by you for your research use or educational purposes in electronic or print form. You must obtain permission for any other use. Electronic or print copies may not be offered, whether for sale or otherwise to anyone who is not an authorised user. Measuring K0SK± interactions using Pb–Pb collisions at √sNN=2.76TeV ALICE Collaboration ALICE Collaboration. (2017). Measuring K0SK± interactions using Pb–Pb collisions at √sNN=2.76TeV. Physics Letters B, 774, 64-77. https://doi.org/10.1016/j.physletb.2017.09.009 2017
Physics Letters B 774 (2017) 64–77 Contents lists available at ScienceDirect Physics Letters B www.elsevier.com/locate/physletb Measuring K0 SK±interactions using Pb–Pb collisions at √sNN =2.76 TeV .ALICE Collaboration a r t i c l e i n f o a b s t r a c t Article history: Received 22 May 2017 Received in revised form 24 August 2017 Accepted 4 September 2017 Available online 8 September 2017 Editor: L. Rolandi We present the first ever measurements of femtoscopic correlations between the K0 Sand K±particles. The analysis was performed on the data from Pb–Pb collisions at √sNN =2.76 TeV measured by the ALICE experiment. The observed femtoscopic correlations are consistent with final-state interactions proceeding via the a0(980)resonance. The extracted kaon source radius and correlation strength parameters for K0 SK−are found to be equal within the experimental uncertainties to those for K0 SK+. Comparing the results of the present study with those from published identical-kaon femtoscopic studies by ALICE, mass and coupling parameters for the a0resonance are tested. Our results are also compatible with the interpretation of the a0having a tetraquark structure instead of that of a diquark. ©2017 The Author. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP3. 1. Introduction Identical boson femtoscopy, especially of identical charged pions, has been used extensively over the years to study experimentally the space–time geometry of the collision region in highenergy particle and heavy-ion collisions [1]. Identical-kaon femtoscopy studies have also been carried out, recent examples of which are the ones with Au–Au collisions at √sNN =200 GeV by the STAR Collaboration [2] (K0 SK0 S) and with pp at √s=7TeV and Pb–Pb collisions at √sNN =2.76 TeV by the ALICE Collaboration [3–5] (K0 SK0 Sand K±K±). The pair-wise interactions between the identical kaons that form the basis for femtoscopy are for K±K±quantum statistics and the Coulomb interaction, and for K0 SK0 Squantum statistics and the final-state interaction through the f0(980)/a0(980)threshold resonances. One can also consider the case of non-identical kaon pairs, e.g. K0 SK±pairs. Besides the non-resonant channels which may be present, e.g. non-resonant elastic scattering or free-streaming of the kaons from their freeze-out positions to the detector, the other only pair-wise interaction allowed for a K0 SK±pair at freeze out from the collision system is a final-state interaction (FSI) through the a0(980)resonance. The other pair-wise interactions present for identical-kaon pairs are not present for K0 SK±pairs because: a) there is no quantum statistics enhancement since the kaons are not identical, b) there is no Coulomb effect since one of the kaons is uncharged, and c) there is no strong FSI through the f0reso- E-mail address: [email protected]. nance since the kaon pair is in an I=1 isospin state, as is the a0, whereas the f0is an I=0state. Another feature of the K0 SK±FSI through the a0resonance is, due to the a0having strangeness S=0 and the K0 Sbeing a linear combination of the K0and K0, K0 S=1 √2K0+K0,(1) only the K0K+pair from K0 SK+and the K0K−pair from K0 SK−have S=0 and thus can form the a0resonance. This allows the possibility to study the K0and K0sources separately since they are individually selected by studying K0 SK−and K0 SK+pairs, respectively. An additional consequence of this feature is that only 50% of either the K0 SK−or K0 SK+detected pairs will pass through the a0resonance. This is taken into account in the expression for the model used to fit the correlation functions. On the other hand, the natural requirement that the source sizes extracted from the K0 SK±femtoscopy agree with those obtained for the K0 SK0 Sand K±K±systems allows one to study the properties of the a0resonance itself. This is interesting in its own right since many studies discuss the possibility that the a0, listed by the Particle Data Group as a diquark light unflavored meson state [6], could be a four-quark state, i.e. a tetraquark, or a “K–K molecule” [7–12]. For example, the production cross section of the a0resonance in a reaction channel such as K0K−→a− 0should depend on whether the a− 0is composed of duor dssuquarks, the former requiring the annihilation of the ss pair and the latter being a direct transfer of the quarks in the kaons to the a− 0. The http://dx.doi.org/10.1016/j.physletb.2017.09.009 0370-2693/©2017 The Author. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP3.
ALICE Collaboration / Physics Letters B 774 (2017) 64–77 65 results from K0 SK−femtoscopy might be sensitive to these two different scenarios. In this Letter, results from the first study of K0 SK±femtoscopy are presented. This has been done for Pb–Pb collisions at √sNN = 2.76 TeV measured by the ALICE experiment at the LHC [13]. The physics goals of the present K0 SK±femtoscopy study are the following: 1) show to what extent the FSI through the a0resonance describes the correlation functions, 2) study the K0and K0sources to see if there are differences in the source parameters, and 3) test published a0mass and coupling parameters by comparisons with published identical kaon results [5]. 2. Description of experiment and data selection The ALICE experiment and its performance in the LHC Run 1 (2009–2013) are described in Ref. [13] and Ref. [14,15], respectively. About 22 ×106Pb–Pb collision events with 0–10% centrality class taken in 2011 were used in this analysis (the average centrality in this range is 4.9% due to a slight trigger inefficiency in the 8–10% range). Events were classified according to their centrality using the measured amplitudes in the V0 detectors, which consist of two arrays of scintillators located along the beamline and covering the full azimuth [16]. Charged particles were reconstructed and identified with the central barrel detectors located within a solenoid magnet with a field strength of B =0.5T. Charged particle tracking was performed using the Time Projection Chamber (TPC) [17] and the Inner Tracking System (ITS) [13]. The ITS allowed for high spatial resolution in determining the primary (collision) vertex. Tracks were reconstructed and their momenta were obtained with the TPC. A momentum resolution of less than 10 MeV/cwas typically obtained for the charged tracks of interest in this analysis. 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, the track selections based on the quality of track reconstruction fit and the number of detected tracking points in the TPC were used to ensure that only well-reconstructed tracks were taken in the analysis [14,15]. Particle identification (PID) for reconstructed tracks was carried out using both the TPC and the Time-of-Flight (TOF) detector in the pseudorapidity range |η| <0.8[14,15]. For each PID method, avalue was assigned to each track denoting the number of standard deviations between the measured track information and calculated values (Nσ) [5,14,15]. For TPC PID, a parametrized Bethe–Bloch formula was used to calculate the specific energy loss dE/dxin 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”—electron, pion, kaon and proton—, and, for each hypothesis, a different Nσvalue was obtained per detector. 2.1. Kaon selection The methods used to select and identify individual K0 Sand K± particles are the same as those used for the ALICE Pb–Pb K0 SK0 Sand K±K±analyses [5]. These are now described below. 2.1.1. K0 Sselection The K0 Sparticles were reconstructed from the decay K0 S→ π+π−, with the daughter π+and π−tracks detected in the TPC and TOF detectors. Pions with pT>0.15 GeV/cwere accepted (since for lower pTtrack finding efficiency drops rapidly) and the distance of closest approach to the primary vertex (DCA) of the reconstructed K0 Swas required to be less than 0.3 cm in all directions. The required Nσvalues for the pions were NσTPC <3 and NσTOF <3for p >0.8 GeV/c. An invariant mass distribution for the π+π−pairs was produced and the K0 Swas defined to be resulting from a pair that fell into the invariant mass range 0.480 <mπ+π−<0.515 GeV/c2. 2.1.2. K±selection Charged kaon tracks were also detected using the TPC and TOF detectors, and were accepted if they were within the range 0.14 <pT<1.5GeV/c. In order to reduce the number of secondaries (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 Nσvalues for the charged kaons were NσTPC <2for pT<0.5 GeV/c, and the track was rejected for pT>0.5 GeV/c. If the TOF signal were also available and pT>0.5GeV/c: NσTPC <3 and NσTOF <2(0.5 <pT<0.8 GeV/c), NσTOF <1.5(0.8 <pT<1.0GeV/c), NσTOF <1(1.0 <pT< 1.5GeV/c). K0 SK±experimental pair purity was estimated from a Monte Carlo (MC) study based on HIJING [18] simulations 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 K0 SK±pairs input from HIJING. The pair purity was estimated to be 88% for all kinematic regions studied in this analysis. 3. Analysis methods 3.1. Experimental correlation functions This analysis studies the momentum correlations of K0 SK±pairs using the two-particle correlation function, defined as C(k∗)=A(k∗)/B(k∗)(2) 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), k∗=(s−m2 K0−m2 K±)2−4m2 K0m2 K± 4s(3) where, s=m2 K0+m2 K±+2EK0EK±−2 pK0· pK±(4) and mK0(EK0) and mK±(EK±) are the rest masses (total energies) of the K0 Sand K±, respectively. The denominator B(k∗)was formed by mixing K0 Sand K±particles from each event with particles from ten other events. The vertexes of the mixed events were constrained to be within 2 cm of each other in the z-direction. A centrality constraint on the mixed events was found not to be necessary for the narrow centrality range, i.e. 0–10%, used in this analysis. Correlation functions were obtained separately for two different magnetic field orientations in the experiment and then either averaged or fit separately, depending on the fitting method used (see below). Correlation functions were measured for three overlapping/nonexclusive pair transverse momentum (kT=|pT,1+pT,2|/2) bins: all kT, kT<0.675 and kT>0.675 GeV/c. The mean kTvalues for these three bins were 0.675, 0.425 and 0.970 GeV/c, respectively.
66 ALICE Collaboration / Physics Letters B 774 (2017) 64–77 Fig. 1. Examples of raw K0 SK+correlation functions for the three kTbins with linear fits to the baseline at large k∗. Statistical uncertainties are shown. Fig. 1 shows sample raw K0 SK+correlation functions for these three bins for one of the magnetic field orientations. One can see the main feature of the femtoscopic correlation function: the suppression due to the strong final-state interactions for small k∗. In the higher k∗region, the effects of the a0appear to not be present and thus could be used as a reference, i.e. “baseline”, for the a0-based model fitted to C(k∗)in order to extract the source parameters. Also shown in the figure are linear fits to the baseline for large k∗. The effects on C(k∗)by the a0resonance are mostly seen in the k∗<0.2 GeV/cregion, where the width of the a0region reflects the size of the kaon source (see equations below). Correlation functions were corrected for momentum resolution effects using HIJING calculations. HIJING was used to create two correlation functions: one in terms of the generator-level k∗and one in terms of the simulated detector-level k∗. Because HIJING does not incorporate final-state interactions, weights were calculated using a 9th-order polynomial fit in k∗to an experimental correlation function and were used when filling the same-event distributions. These weights were calculated using 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 several percent. 3.2. Final-state interaction model The K0 SK±correlation functions were fit with functions that include a parameterization which incorporates strong FSI. It was assumed that the FSI arises in the K0 SK±channels due to the near-threshold resonance, a0(980). 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. [2] for more details on this parameterization). Using an equal emission time approximation in the PRF [20], the elastic K0 SK±transition is written as a stationary solution − 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 a plane wave and an outgoing spherical wave, − k∗( r∗)=e−i k∗· r∗+f(k∗)eik∗r∗ r∗,(5) where f(k∗)is the s-wave K0K−or K0K+scattering amplitude whose contribution is the s-wave isovector a0resonance (see Eq. (11) in Ref. [2]), Table 1 The a0masses and coupling parameters, all in GeV (taken from Ref. [2]). Reference ma0γa0K¯ Kγa0πη Martin [7] 0.974 0.333 0.222 Antonelli [8] 0.985 0.4038 0.3711 Achasov1 [9] 0.992 0.5555 0.4401 Achasov2 [9] 1.003 0.8365 0.4580 f(k∗)=γa0→KK m2 a0−s−i(γa0→KKk∗+γa0→πηkπη).(6) In Eq. (6), ma0is the mass of the a0resonance, and γa0→KK and γa0→πη are the couplings of the a0resonance to the K0K−(or K0K+) and πη channels, respectively. Also, s =4(m2 K0+k∗2)and kπη denotes the momentum in the second decay channel (πη) (see Table 1). The correlation function due to the FSI is then calculated by integrating − k∗( r∗)in the Koonin–Pratt equation [22,23] C( k∗)=d3 r∗S( r∗)− k∗( r∗) 2 ,(7) where S( r∗)is a one-dimensional Gaussian source function of the PRF relative distance r∗with a Gaussian width Rof the form S( r∗)∼e− r∗ 2/(4R2).(8) Equation (7) can be integrated analytically for K0 SK±correlations with FSI for the one-dimensional case, with the result C(k∗)=1+λα1 2 f(k∗) R 2 +2Rf(k∗) √πRF1(2k∗R) −If(k∗) RF2(2k∗R),(9) where F1(z)≡√πe−z2erfi(z) 2z;F2(z)≡1−e−z2 z.(10) In the above equations αis the fraction of K0 SK±pairs that come from the K0K−or K0K+system, set to 0.5 assuming symmetry in K0and K0production [2], Ris the radius parameter from the spherical Gaussian source distribution given in Eq. (8), and λis the correlation strength. The correlation strength is unity in the ideal case of pure a0-resonant FSI, perfect PID, a perfect Gaussian kaon source and the absence of long-lived resonances which decay into kaons. Note that the form of the FSI term in Eq. (9) differs from
ALICE Collaboration / Physics Letters B 774 (2017) 64–77 67 the form of the FSI term for K0 SK0 Scorrelations (Eq. (9) of Ref. [2]) by a factor of 1/2due to the non-identical particles in K0 SK±correlations and thus the absence of the requirement to symmetrize the wavefunction given in Eq. (5). As seen in Eq. (6), the K0K−or K0K+s-wave scattering amplitude depends on the a0mass and decay couplings. In the present work, we have taken the values used in Ref. [2] which have been extracted from the analysis of the a0→πη spectra of several experiments [7–10], shown in Table 1. The extracted a0mass and decay couplings have a range of values for the various references. Except for the Martin reference [7], which extracts the a0values from the reaction 4.2 GeV/cincident momentum K−+p →+(1385)π−ηusing a two-channel Breit– Wigner formula, the other references extract the a0values from the radiative φ-decay data, i.e. φ→π0ηγ , from the KLOE collaboration [24]. These latter three references apply a model that assumes, after taking into account the φ→π0ρ0→π0ηγ background process, that the φdecays to the π0ηγ final state through the intermediate processes φ→K+K−γ→a0γor φ→K+K−→ a0γ, i.e. the “charged kaon loop model” [9]. The main difference between these analyses is that the Antonelli reference [8] assumes a fixed a0mass in the fit of this model to the π0ηdata, whereas the Achasov1 and Achasov2 analyses [9] allow the a0 mass to be a free parameter in the two different fits made to the data. It is assumed in the present analysis that these decay couplings will also be valid for K0K−and K0K+scattering due to isospin invariance. Correlation functions were fitted with all four of these cases to see the effect on the extracted source parameters. 3.3. Fitting methods In order to estimate the systematic errors in the fitting method used to extract Rand λusing Eq. (9), two different methods, judged to be equally valid, have been used to handle the effects of the baseline: 1) a separate linear fit to the “baseline region,” followed by fitting Eq. (9) to the correlation function divided by the linear fit to extract the source parameters, and 2) a combined fit of Eq. (9) and a quadratic function describing the baseline where the source parameters and the parameters of the quadratic function are fitted simultaneously. The source parameters are extracted for each case from both methods and averaged, the symmetric systematic error for each case due to the fitting method being one-half of the difference between the two methods. Both fitting methods will now be described in more detail. 3.3.1. Linear baseline method In the “linear baseline method,” for the all kT, kT<0.675 and kT>0.675 GeV/cbins the a0regions were taken to be k∗<0.3, k∗<0.2 and k∗<0.4GeV/c, respectively. In the higher k∗region it was assumed that effects of the a0were not present and thus can be used as a reference, i.e. “baseline”, for the a0-based model fitted to C(k∗), which was averaged over the two magnetic field orientations used in the experiment, to extract the source parameters. For the three kTbins, linear fits were made in the k∗ranges 0.3–0.45, 0.2–0.45 and 0.4–0.6GeV/c, respectively, and the correlation functions were divided by these fits to remove baseline effects extending into the low-k∗region. These ranges were taken to define the baselines since the measured correlation functions were found to be linear here. For larger values of k∗the correlation functions became non-linear. The baseline was studied using HIJING MC calculations which take into account the detector characteristics as described earlier. The C(k∗)distributions obtained from HIJING do not show suppressions at low k∗as seen in Fig. 1 but rather show linear distributions over the entire ranges in k∗ shown in the figure. HIJING also shows the baseline becoming nonlinear for larger values of k∗, as seen in the measurements. The MC generator code AMPT [25] was also used to study the baseline. AMPT is similar to HIJING but also includes final-state rescattering effects. AMPT calculations also showed linear baselines in the k∗ranges used in the present analysis, becoming non-linear for larger k∗. Both HIJING and AMPT qualitatively show the same direction of changes in the slopes of the baseline vs. kTas seen in the data, but AMPT more accurately described the slope values themselves, suggesting that final-state rescattering plays a role in the kTdependence of the baseline slope. The systematic uncertainties on the extracted source parameters due to the assumption of linearity in these k∗regions were estimated from HIJING to be less than 1%. Fig. 2 shows examples of K0 SK+and K0 SK−correlation functions divided by linear fits to the baseline with Eq. (9) using the Achasov2 parameters. One can see the main feature of the femtoscopic correlation function: the suppression due to the strong final-state interactions for small k∗. As seen, the a0FSI parameterization gives an excellent representation of the “signal region” of the data, i.e. the suppression of the correlation functions in the k∗ range 0 to about 0.15 GeV/c. 3.3.2. Quadratic baseline method In the “quadratic baseline method,” Rand λare extracted assuming a quadratic baseline function by fitting the product of a quadratic function and the Lednicky equation, Eq. (9), to the raw correlation functions for each of the two magnetic field orientations used in the experiment, such as shown in Fig. 1, i.e., Cfit raw(k∗)=a(1−bk∗+ck∗2)C(k∗)(11) where C(k∗)is given by Eq. (9), and a, band care fit parameters. Eq. (11) is fit to the same k∗ranges as shown in Fig. 1, i.e. 0–0.45 GeV/cfor all kTand kT<0.675 GeV/c, and 0–0.6GeV/cfor kT>0.675 GeV/c. The fits to the experimental correlation functions are found to be of similar good quality as seen for the linear baseline method fits shown in Fig. 2. 3.4. Systematic uncertainties Systematic uncertainties on the extracted source parameters were estimated by varying the ranges of kinematic and PID cut values on the data by ±10% and ±20%, as well as from MC simulations. The main systematic uncertainties on the extracted values of Rand λdue to various sources, not including the baseline fitting method, are: a) k∗fitting range: 2%, b) single-particle and pair cuts (e.g. DCA cuts, PID cuts, pair separation cuts): 2%–4% for R and 3%–8% for λ, and c) pair purity: 1% on λ. Combining the individual systematic uncertainties in quadrature, the total systematic uncertainties on the extracted source parameters, not including the baseline fitting method contribution, are in the ranges 3%–5% for Rand 4%–8% for λ. As mentioned earlier, for the two fitting methods, the source parameters are extracted for each case from both methods and averaged, the symmetric systematic error for each case due to the fitting method being one-half of the difference between the two methods. The baseline fitting method systematic error thus obtained is added in quadrature with the systematic errors given above. It is found that the size of the baseline fitting method systematic errors are about 50% larger for Rand of similar magnitude for λas those quoted above for the non-fitting-method systematic errors.
68 ALICE Collaboration / Physics Letters B 774 (2017) 64–77 Fig. 2. Examples of K0 SK+and K0 SK−correlation functions divided by linear fits to the baseline with the Lednicky parameterization using the Achasov2 [9] parameters. Statistical (lines) and the linear sum of statistical and systematic uncertainties (boxes) are shown. 4. Results and discussion Fig. 3 shows sample results for the Rand λparameters extracted in the present analysis from K0 SK±femtoscopy using the Achasov1 parameters. The left column compares K0 SK+and K0 SK− results from the quadratic baseline fit method, and the right column compares results averaged over K0 SK+and K0 SK−for the quadratic baseline fits and the linear baseline fits. As it is usually the case in femtoscopic analyses, the fitted Rand λparameters are correlated. The fitting (statistical) uncertainties are taken to be the extreme values of the 1σfit contours in Rvs. λ. Statistical uncertainties are plotted for all results. It is seen in the figure that the Rand λvalues for K0 SK−have a slight tendency to be larger than those for K0 SK+. Such a difference could result from the K−–nucleon scattering cross section being larger than that for K+–nucleon (see Fig. 51.9 of Ref. [6]), possibly resulting in more final-state rescattering for the K−. Since the difference is not significant once systematic uncertainties are taken into account, K0 SK+ and K0 SK−are averaged over in the final results. The difference in the extracted parameters between the two baseline fitting methods is also seen to be small, and is accounted for as a systematic error, as described earlier. The results for the Rand λparameters extracted in the present analysis from K0 SK±femtoscopy, averaged over the two baseline fit methods and averaged over K0 SK+and K0 SK−, are presented in Table 2 and in Figs. 4 and 5. Fit results are shown for all four parameter sets given in Table 1. Figs. 4 and 5 also show comparisons with identical kaon results for the same collision system and energy from ALICE from Ref. [5]. Statistical and total uncertainties are shown for all results. As shown in Fig. 4, both Achasov parameter sets, with the larger a0masses and decay couplings, appear to give Rvalues that agree best with those obtained from identical-kaon femtoscopy. The Antonelli parameter set appears to give slightly lower values. Comparing the measured Rvalues between K0 SK0 Sand K±K±in Fig. 4 they are seen to agree with each other within the uncertainties. In fact, the only reason for the femtoscopic K0 SK±radii to be different from the K0 SK0 Sand K±K±ones would be if the K0 Sand K±sources were displaced with respect to each other. This is not expected because the collision dynamics is governed by strong interactions for which the isospin symmetry applies. The results for the correlation strength parameters λare shown in Fig. 5. The λparameters from K0 SK±and K±K±are corrected for experimental purity [5]. The K0 SK0 Spairs have a high purity of >90%, so the corresponding correction was neglected [5] (see the earlier discussion on purity). Statistical and total uncertainties are shown for all results. The K0 SK±λvalues, with the exception of the Martin parameters, appear to be in agreement with the λvalues for the identical kaons. All of the λvalues are seen to be measured to be about 0.6, i.e. less than the ideal value of unity, which can be due to the contribution of kaons from K∗decay (∼50 MeV, where is the decay width) and from other long-lived resonances (such as the D-meson) distorting the spatial kaon source distribution away from the ideal Gaussian which is assumed in the fit function [26]. One would expect that the K0 SK±λvalues agree with those from the identical kaons if the FSI for the K0 SK±went solely through the a0resonant channel since this analysis should see the same source distribution. In order to obtain a more quantitative comparison of the present results for Rand λwith the identical kaon results, the χ2/ndf is calculated for Rand λfor each parameter set, χ2 ω/ndf =1 ndf 3 i=1 [ωi(K0 SK±)−ωi(KK)]2 σ2 i (12)
ALICE Collaboration / Physics Letters B 774 (2017) 64–77 69 Fig. 3. Sample results for the Rand λparameters extracted in the present analysis from K0 SK±femtoscopy using the Achasov1 parameters. The left column compares K0 SK+ and K0 SK−results from the quadratic baseline fit method, and the right column compares results averaged over K0 SK+and K0 SK−for the quadratic baseline fits and the linear baseline fits. Statistical uncertainties are plotted for all results. Table 2 Fit results for Rand λextracted in the present analysis from K0 SK±femtoscopy averaged over K0 SK+and K0 SK−. Statistical and systematic errors are also shown. Parameters R(fm) or λAll kTkT<0.675 GeV/ck T>0.675 GeV/c Achasov2 R5.17 ±0.16 ±0.41 6.71 ±0.40 ±0.42 4.75 ±0.18 ±0.36 λ0.587 ±0.034 ±0.051 0.651 ±0.073 ±0.076 0.600 ±0.040 ±0.034 Achasov1 R4.92 ±0.15 ±0.39 6.30 ±0.40 ±0.43 4.49 ±0.18 ±0.30 λ0.650 ±0.038 ±0.056 0.723 ±0.087 ±0.091 0.649 ±0.048 ±0.038 Antonelli R4.66 ±0.17 ±0.46 5.74 ±0.36 ±0.26 4.07 ±0.18 ±0.29 λ0.624 ±0.044 ±0.058 0.703 ±0.085 ±0.077 0.613 ±0.052 ±0.037 Martin R3.29 ±0.12 ±0.35 4.46 ±0.25 ±0.20 2.90 ±0.11 ±0.41 λ0.305 ±0.020 ±0.033 0.376 ±0.041 ±0.037 0.296 ±0.021 ±0.030 where ωis either Ror λ, iruns over the three kTvalues, the number of degrees of freedom taken is ndf =3 and σiis the sum of the statistical and systematic uncertainties on the ith K0 SK±extracted parameter (Note that the all kTbin indeed contains the kaon pairs that make up the kT<0.675 GeV/cand kT>0.675 GeV/cbins, but in addition it contains an equal number of new pair combinations between the kaons in the kT<0.675 GeV/cand kT>0.675 GeV/cbins. So for the purposes of this simple comparison, we approximate the all kTbin as being independent.) The linear sum of the statistical and systematic uncertainties is used for σito be consistent with the linear sum of the statistical and systematic uncertainties plotted on the points in Figs. 4 and 5. The quantity ωi(KK)is determined by fitting a quadratic to the identical kaon results and evaluating the fit at the average kTvalues of the K0 SK± measurements. Table 3 summarizes the results for each parameter set and the extracted p-values. As seen, the Achasov2, Achasov1 and Antonelli parameter sets are consistent with the identical kaon results for both Rand λ. The Martin parameter set is seen to have vanishingly small p-values for both Rand λand is thus in clear Table 3 Comparisons of Rand λfrom K0 SK±with identical kaon results. Parameters χ2 R/ndf Rp-value χ2 λ/ndf λp-value λ(K0 SK±) λ(KK) Achasov2 0.456 0.713 0.248 0.863 1.04 ±0.17 Achasov1 0.583 0.626 0.712 0.545 1.14 ±0.20 Antonelli 1.297 0.273 0.302 0.824 1.09 ±0.20 Martin 14.0 0.000 22.2 0.000 0.55 ±0.10 disagreement with the identical kaon results, as can easily be seen by examining Figs. 4 and 5. In order to quantitatively estimate the size of the non-resonant channel present, the ratio λ(K0 SK±) λ(KK)has been calculated for each parameters set, where the average is over the three kTvalues and the uncertainty is calculated from the average of the statistical+systematic uncertainties on the K0 SK±parameters. These values are shown in the last column of Table 3. Disregarding the Martin value, the smallest value this ratio can take within the uncertain-
70 ALICE Collaboration / Physics Letters B 774 (2017) 64–77 Fig. 4. Source radius parameter, R, extracted in the present analysis from K0 SK±femtoscopy averaged over K0 SK+and K0 SK−and the two baseline fit methods (red symbols), along with comparisons with identical kaon results from ALICE [5] (blue symbols). Statistical (lines) and the linear sum of statistical and systematic uncertainties (boxes) are shown. (For interpretation of the colors in this figure, the reader is referred to the web version of this article.) Fig. 5. Correlation strength parameter, λ, extracted in the present analysis from K0 SK±femtoscopy averaged over K0 SK+and K0 SK−and the two baseline fit methods (red symbols), along with comparisons with identical kaon results from ALICE [5] (blue symbols). Statistical (lines) and the linear sum of statistical and systematic uncertainties (boxes) are shown. (For interpretation of the colors in this figure, the reader is referred to the web version of this article.)
ALICE Collaboration / Physics Letters B 774 (2017) 64–77 71 ties is 0.87 (from the Achasov2 parameters) which would thus allow at most a 13% non-resonant contribution. The results of this study presented above clearly show that the measured K0 SK±have dominantly undergone a FSI through the a0 resonance. This is remarkable considering that we measure in Pb– Pb collisions the average separation between the two kaons at freeze out to be ∼5fm, and due to the short-ranged nature of the strong interaction of ∼1fm this would seem to not encourage a FSI but rather encourage free-streaming of the kaons to the detector resulting in a “flat” correlation function. A dominant FSI is what might be expected if the a0would be a four-quark, i.e. tetraquark, state or a “K–K molecule.” There appears to be no calculations in the literature for the tetraquark vs. diquark production cross sections for the interaction KK →a0, but qualitative arguments compatible with the a0being a four–quark state can be made based on the present measurements. The main argument in favor of this is that the reaction channel K0K−→a− 0(K0K+→a+ 0) is strongly favored if the a− 0(a+ 0) is composed of dssu(dssu) quarks such that a direct transfer of the quarks in the kaons to the a− 0(a+ 0) has taken place, since this is an “OZI superallowed” reaction [12]. The “OZI rule” can be stated as “an inhibition associated with the creation or annihilation of quark lines” [12]. Thus, adiquark a0final state is less favored according to the OZI rule since it would require the annihilation of the strange quarks in the kaon interaction. This would allow for the possibility of a significant non-resonant or free-streaming channel for the kaon interaction that would result in a λvalue below the identical-kaon value by diluting the a0signal. As mentioned above, the collision geometry itself also suppresses the annihilation of the strange quarks due to the large separation between the kaons at freeze out. Note that this assumes that the C(k∗)distribution of a non-resonant channel would be mostly “flat” or “monotonic” in shape and not showing a strong resonant-like signal as seen for the a0in Fig. 1 and Fig. 2. This assumption is clearly true in the free-streaming case, which is assumed in Eq. (9) in setting α=0.5due to the non-resonant kaon combinations. A similar argument, namely that the success of the “charged kaon loop model” in describing the radiative φ-decay data favors the a0as a tetraquark state, is given in Ref. [9]. 5. Summary In summary, femtoscopic correlations with K0 SK±pairs have been studied for the first time. This new femtoscopic method was applied to data from central Pb–Pb collisions at √sNN =2.76 TeV by the LHC ALICE experiment. Correlations in the K0 SK±pairs are produced by final-state interactions which proceed through the a0(980) resonance. The a0resonant FSI is seen to give an excellent representation of the shape of the signal region in the present study. The differences between K0K+and K0K−for the extracted R and λvalues are found to be insignificant within the uncertainties of the present study. The three larger a0mass and decay parameter sets are favored by the comparison with the identical kaon results. The present results are also compatible with the interpretation of the a0resonance as a tetraquark state. This work should provide a constraint on models that are used to predict kaon–kaon interactions [27,28]. It will be interesting to apply K0 SK±femtoscopy to other collision energies, e.g. the higher LHC energies now available, and bombarding species, e.g. proton–proton collisions, since the different source sizes encountered in these cases will probe the interaction of the K0 Swith the K±in different sensitivity ranges (i.e. see the Rdependence in Eq. (9)). Acknowledgements 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 gratefully acknowledges the resources and support provided by all Grid centers and the Worldwide LHC Computing Grid (WLCG) collaboration. The ALICE Collaboration acknowledges the following funding agencies for their support in building and running the ALICE detector: A. I. Alikhanyan National Science Laboratory (Yerevan Physics Institute) Foundation (ANSL), State Committee of Science and World Federation of Scientists (WFS), Armenia; Austrian Academy of Sciences and Nationalstiftung für Forschung, Technologie und Entwicklung, Austria; Ministry of Communications and High Technologies, National Nuclear Research Center, Azerbaijan; Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq), Universidade Federal do Rio Grande do Sul (UFRGS), Financiadora de Estudos e Projetos (Finep) and Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP), Brazil; Ministry of Science & Technology of China (MSTC), National Natural Science Foundation of China (NSFC) and Ministry of Education of China (MOEC), China; Ministry of Science, Education and Sports and Croatian Science Foundation, Croatia; Ministry of Education, Youth and Sports of the Czech Republic, Czech Republic; The Danish Council for Independent Research Natural Sciences, the Carlsberg Foundation and Danish National Research Foundation (DNRF), Denmark; Helsinki Institute of Physics (HIP), Finland; Commissariat à l’Energie Atomique (CEA) and Institut National de Physique Nucléaire et de Physique des Particules (IN2P3) and Centre National de la Recherche Scientifique (CNRS), France; Bundesministerium für Bildung, Wissenschaft, Forschung und Technologie (BMBF) and GSI Helmholtzzentrum für Schwerionenforschung GmbH, Germany; General Secretariat for Research and Technology, Ministry of Education, Research and Religions, Greece; National Research, Development and Innovation Office, Hungary; Department of Atomic Energy Government of India (DAE) and Council of Scientific and Industrial Research (CSIR), New Delhi, India; Indonesian Institute of Science, Indonesia; Centro Fermi – Museo Storico della Fisica e Centro Studi e Ricerche Enrico Fermi and Istituto Nazionale di Fisica Nucleare (INFN), Italy; Institute for Innovative Science and Technology, Nagasaki Institute of Applied Science (IIST), Japan Society for the Promotion of Science (JSPS) KAKENHI and Japanese Ministry of Education, Culture, Sports, Science and Technology (MEXT), Japan; Consejo Nacional de Ciencia y Tecnología (CONACYT), through Fondo de Cooperación Internacional en Ciencia y Tecnología (FONCICYT) and Dirección General de Asuntos del Personal Academico (DGAPA), Mexico; Nederlandse Organisatie voor Wetenschappelijk Onderzoek (NWO), Netherlands; The Research Council of Norway, Norway; Commission on Science and Technology for Sustainable Development in the South (COMSATS), Pakistan; Pontificia Universidad Católica del Perú, Peru; Ministry of Science and Higher Education and National Science Centre, Poland; Korea Institute of Science and Technology Information and National Research Foundation of Korea (NRF), Republic of Korea; Ministry of Education and Scientific Research, Institute of Atomic Physics and Romanian National Agency for Science, Technology and Innovation, Romania; Joint Institute for Nuclear Research (JINR), Ministry of Education and Science of the Russian Federation and National Research Centre Kurchatov Institute, Russia; Ministry of Education, Science, Research and Sport of the Slovak Republic, Slovakia; National Research Foundation of South Africa, South Africa; Centro de Aplicaciones Tecnológicas y Desarrollo Nuclear (CEADEN), Cubaenergía, Cuba, Ministerio de Ciencia e Innovacion and Centro de Investigaciones Energéticas, Medioambientales y Tecnológicas (CIEMAT), Spain; Swedish Research Council (VR) and Knut & Alice Wallenberg Foundation (KAW), Sweden; European Organization for Nuclear Research, Switzerland; National Science and Technology Development Agency (NSDTA), Suranaree