Global polarization of hyperons in Au+Au collisions at = 200 GeV
Global polarization of hyperons has been measured to be of the order of a few tenths of a percent in Au+Au collisions at = 200 GeV, with no significant difference between and . These new results reveal the collision energy dependence of the global polarization together with the results previously observed at = 7.7 – 62.4 GeV and indicate noticeable vorticity of the medium created in non-central heavy-ion collisions at the highest RHIC collision energy. The signal is in rough quantitative agreement with the theoretical predictions from a hydrodynamic model and from the AMPT (A Multi-Phase Transport) model. The polarization is larger in more peripheral collisions, and depends weakly on the hyperon’s transverse momentum and pseudorapidity within . An indication of the polarization dependence on the event-by-event charge asymmetry is observed at the level, suggesting a possible contribution to the polarization from the axial current induced by the initial magnetic field.
Nucleus-nucleus collisions at the Relativistic Heavy Ion Collider and at the Large Hadron Collider produce a state of partonic matter, the Quark-Gluon Plasma (QGP), that is expected to have existed in nature right after the Big Bang Yagi et al. (2005). Various experimental observations together with sophisticated theoretical calculations indicate that the QGP behaves as a nearly perfect liquid, i.e. a fluid with the lowest ratio of shear viscosity to entropy density () Heinz and Snellings (2013); Voloshin et al. (2010); Gale et al. (2013).
One of the most important observables in heavy-ion experiments is the azimuthal anisotropic flow that is usually quantified by the Fourier coefficients of the azimuthal distribution of the final-state particles relative to the collision symmetry planes. The first-order coefficient, called the directed flow, is argued to be sensitive to the equation of state of the matter, and could serve as a possible signature of the QGP phase transition Csernai and Rhrich (1999); Brachmann et al. (2000); L. Adamczyk et al. (STAR Collaboration) (2014). The second-order coefficient, elliptic flow, offers strong evidence for the fluid-like behavior of the created matter. Furthermore, the higher-order coefficients are found to provide additional constraints on and the initial conditions. In spite of a successful description of the flow observables for by hydrodynamic models, none of the theoretical models can describe quantitatively the directed flow. This indicates that the current models still lack an important ingredient in the description of relativistic heavy-ion collision dynamics. The initial condition in the longitudinal direction would play an important role for the directed flow and vorticity Boek and Wyskiel (2010); Becattini et al. (2015).
Several theoretical models suggest that the large angular momentum carried by two colliding nuclei Z. T. Liang and X. N. Wang (2005); Becattini et al. (2008) can be transferred to the created system. As a consequence, the spin of particles composing the system might be globally polarized along the direction of the system angular momentum, due to spin-orbit coupling. Such a global polarization can be measured experimentally with hyperons via parity-violating weak decays, in which the daughter baryon is preferentially emitted in the direction of the hyperon spin. If the parent hyperon is an antiparticle, the daughter baryon tends to be emitted in the opposite direction to the parent spin.
The angular distribution of daughter baryons in the hyperon decays is given by
where is the hyperon decay constant, is the hyperon polarization, and is the angle between the momentum of daughter baryon and the polarization vector in the hyperon rest frame. Since the angular momentum of the system is perpendicular to the reaction plane (a plane defined by the impact parameter vector and the beam direction), the polarization of hyperons can be measured via the azimuthal distribution of daughter baryons with respect to the reaction plane in the hyperon rest frame, similar to anisotropic flow measurements Voloshin et al. (2010).
The STAR Collaboration performed the first global polarization measurements of hyperons in Au+Au collisions at = 62.4 and 200 GeV in 2007 B. I. Abelev et al. (STAR Collaboration) (2007). These results were consistent with zero within large statistical uncertainties. More recently, the STAR Collaboration has reported a non-zero signal for the global polarization in Au+Au collisions at lower energies ( = 7.7-39 GeV) L. Adamczyk et al. (STAR Collaboration) (2017), with a possible difference between and polarizations that may indicate the effect of the spin alignment by the initial magnetic field. These results can be qualitatively described by hydrodynamic and transport models I. Karpenko and F. Becattini (2017); H. Li, L. Pang, Q. Wang, and X. Xia (2017). The global polarization seems to decrease with increasing collision energy, and those models predict a finite signal (0.2%) at the top RHIC energy, = 200 GeV. It is thus important to measure the global polarization signal at = 200 GeV with all available statistics, in order to enhance understanding of the role of vorticity in heavy-ion collisions. It is likely related to other observables such as directed flow, elliptic flow, and the source tilt of the system measured via femtoscopy Becattini et al. (2008, 2015); Lisa et al. (2000). Ref. Baznat et al. (2018) explains the observed global polarization as a result of the axial charge separation due to the Chiral Vortical Effect Kharzeev et al. (2016). Furthermore, precise measurements of the difference in the polarization between and provide constraints on the magnitude and the lifetime of the magnetic field in heavy-ion collisions Becattini et al. (2017).
In this paper, we present results of the global polarization of and hyperons in Au+Au collisions at = 200 GeV using the data recorded by the STAR experiment in the years 2010, 2011, and 2014. The total dataset is about 150 times larger than the dataset analyzed in the previous search by STAR for hyperon polarization in Au+Au collisions at = 200 GeV B. I. Abelev et al. (STAR Collaboration) (2007). We present the results as functions of the collision centrality, the hyperon’s transverse momentum, and pseudorapidity. We also present comparisons with available theoretical calculations. Furthermore, we present the dependence of the polarization on the event-by-event charge asymmetry, to study a possible relation between the polarization and axial current induced by the initial magnetic field Voloshin (2017).
Ii STAR Experiment
The STAR detector is composed of central barrel detectors used for tracking and particle identification, and trigger detectors located in the forward and backward directions. Charged tracks were measured using the time projection chamber (TPC) M. Anderson et al. (2003), which covers the full azimuth and a pseudorapidity range of . Momenta of charged particles were determined via trajectories of reconstructed tracks and a primary vertex was reconstructed by extrapolating the tracks back to the origin. The TPC also allows particle identification based on the ionization energy loss, , in the TPC gas (Ar 90% + CH 10%).
The time-of-flight detector (TOF) W. J. Llope (STAR Collaboration) (2012) is installed outside the TPC, covering the full azimuth and a pseudorapidity range of . The timing resolution of the TOF system with a start time from the vertex position detectors (VPD) W. J. Llope et al. (STAR Collaboration) (2014) is 100 ps. The TOF extends the capability of particle identification provided by the TPC up to GeV/.
The Zero Degree Calorimeters (ZDC) C. Adler, A. Denisov, E. Garcia, M. Murray, H. Strobele, and S. White (2001) and the VPD were used to determine a minimum-bias trigger. The ZDCs are located at forward (west) and backward (east) angles, , and measure the energy deposit of spectator neutrons. The VPD consists of two identical sets of detectors located at forward and backward rapidities and surrounds the beam pipe, covering a pseudorapidity range of . The VPD also provides the start time of collisions and the position of the collision vertex along the beam direction.
Iii Data Analysis
The analysis is based on the data for Au+Au collisions at = 200 GeV taken in the years 2010, 2011, and 2014 with a minimum-bias trigger. The collision vertex along the beam direction was required to be within 30 cm of the center of the TPC for 2010 and 2011 data and to be within 6 cm for 2014 data. In the 2014 data the narrower vertex selection was required to ensure a good acceptance for the Heavy Flavor Tracker (HFT) installed prior to 2014 run Schambach et al. (2014); Contin et al. (2016) (Note that the HFT was not used in this analysis). Additionally, the difference between the vertex positions along the beam direction determined by the TPC and the VPD was required to be less than 3 cm, to reduce the beam-induced background. The vertex position in the transverse plane was limited to be within 2 cm from the beam line. These selection criteria yielded two hundred million events using the 2010 dataset, three hundred fifty million events using the 2011 dataset, and one billion events using the 2014 dataset. The collision centrality was determined based on the measured multiplicity of charged tracks within , and this was matched to a Monte Carlo Glauber simulation in the same way as in previous studies L. Adamczyk et al. (STAR Collaboration) (2012). The effect of the trigger efficiency was taken into account in the analysis.
iii.1 Event plane determination
As an experimental estimate of the reaction plane, the first-order event plane was determined by the ZDCs that are equipped with Shower Maximum Detectors (SMD) C. Adler, A. Denisov, E. Garcia, M. Murray, H. Strobele, and S. White (2001); J. Adams et al. (STAR Collaboration) (2006); B. I. Abelev et al. (STAR Collaboration) (2008). The ZDCs measure the energy deposited by spectator neutrons, and the SMDs measure the centroid of the hadronic shower caused by the interaction between spectator neutrons and the ZDC. Since the spectator neutrons are deflected outward from the centerline of the collisions Voloshin and Niida (2016), we can determine the direction of the angular momentum of the system (see Ref. Adamczyk et al. (2017) for more details). The event plane resolution was estimated by the two-subevent method Poskanzer and Voloshin (1998). Figure 1 shows the event plane resolution for the year 2011 data as an example. The resolution reaches a maximum of 0.39 around 30%-40% centrality for the combined plane of ZDC-SMD east and west. The resolution is consistent between 2010 and 2011 data and is better by 5% for 2014 data compared to that for 2011.
iii.2 Track selection
Charged tracks reconstructed from the TPC hit information were selected with the following requirements to assure good quality. The number of hit points used in the reconstruction was required to be greater than 14. The ratio of the number of hit points used to the maximum possible number of hit points (45 for a track traversing the entire TPC but could be smaller depending on trajectory) was required to be larger than 0.52. Tracks corresponding to GeV/ and were used in this study.
hyperons were identified via decay channels and . These decay modes account for (63.90.5)% of all decays C. Patrignani et al. (Particle Data Group) (2016). The daughter particles of and , i.e. charged pions and protons, were identified by using information from the TPC and time-of-flight information from the TOF detector, like in our previous publication Adamczyk et al. (2017). Charged pions and protons were selected by requiring the track to be within three standard deviations (3) from their peaks in the normalized distribution. If the track had TOF hit information, a constraint based on the square of the measured mass was required. If the TOF information was not available, an additional cut based on was applied, requiring pions (protons) to be 3 away from the proton (pion) peak in the normalized distribution.
The invariant mass, , was calculated using candidates for the daughter tracks. To reduce the combinatorial background, selection criteria based on the following decay topology parameters were used:
Distance of the closest approach (DCA) between daughter tracks and the primary vertex,
DCA between reconstructed trajectories of () candidates and the primary vertex,
DCA between two daughter tracks,
Decay length of () candidates.
Furthermore () candidates were required to point away from the primary vertex. Cuts on the decay topology were adjusted, depending on the collision centrality, to account for the variation of the combinatorial background with centrality. The background level relative to the () signal in the mass region falls below 30% at maximum in this analysis. Finally, and with GeV/ and were analyzed in this study.
Figure 2 shows the invariant mass distributions for and in the 30%-40% centrality bin as an example. The combinatorial background under the peak was estimated by fitting the off-peak region with a linear function, and by the event mixing technique Adamczyk and others (STAR Collaboration) (2013), shown in Fig. 2 as solid and broken lines, respectively.
iii.4 Polarization measurement
As mentioned in Sec. I, the global polarization can be measured via analysis of the azimuthal distribution of daughter protons in the rest frame relative to the reaction plane. As mentioned in Sec. III.1, the first-order event plane determined by the spectator fragments was used in this analysis as an estimator of the reaction plane. The sideward deflection of the spectators allows us to know the direction of the initial angular momentum. Taking into account the experimental resolution of the event plane, the polarization projected onto the direction of the system global angular momentum can be obtained by B. I. Abelev et al. (STAR Collaboration) (2007):
where are the decay parameters of () and (), C. Patrignani et al. (Particle Data Group) (2016). The angle denotes the azimuthal angle of the daughter proton in the rest frame. The Res() is the resolution of the first-order event plane. Two different techniques were used to extract the polarization signal : the invariant mass method and the event plane method, both of which are often used in flow analyses N. Borghini and J. Y. Ollitrault (2004); Voloshin et al. (2010).
In the invariant mass method N. Borghini and J. Y. Ollitrault (2004); Adamczyk and others (STAR Collaboration) (2013), the mean value of the sine term in Eq. (2) was measured as a function of the invariant mass. Since the particles and background cannot be separated on an event-by-event basis, the observed polarization signal is the sum of the signal and background:
where is the background fraction at the invariant mass . The term is the polarization signal for (), where , and the term is the background contribution, which is in general expected to be zero, but could be non-zero, for example, due to misidentification of particles or errors in track reconstruction. The data were fitted with Eq. (3) to extract the polarization signal. Since the shape of the background as a function of invariant mass is unknown, two assumptions concerning the background contribution were tested: a linear function over () and zero background contribution (, ). Figure 3 shows the observed as a function of the invariant mass . Since the daughter proton tends to be emitted in the direction of the parent hyperon spin, and in the opposite direction for antiparticles, the for shows negative values around its mass region as shown in Fig. 3(b), while it is positive for as in Fig. 3(a). We found that results from these two background assumptions give consistent results within uncertainties, and the difference was incorporated in the systematic uncertainty as described in the following section.
Although the invariant mass method was used as the default method in this analysis, the event plane method was also tested as a systematic check. In the event plane method, the same procedure as used in flow analyses was utilized Voloshin et al. (2010). First, the number of and was counted in each bin of the hyperon emission azimuthal angle relative to the event plane after the background subtraction, as demonstrated in Fig. 2. Then the yield of and as a function of was fitted with a sine function to obtain the mean sine . The difference in results from the invariant mass and event plane methods is included in the systematic uncertainty.
iii.5 Effect of feed-down
A sizable number of and produced in the collisions are secondary particles – products of heavier particle decays, such as , , and . The parent particles are also polarized. The polarization is transferred from the parent particle to the daughter . The contribution of such feed-down to the measured polarization was studied in Refs. Becattini et al. (2017); I. Karpenko and F. Becattini (2017); H. Li, L. Pang, Q. Wang, and X. Xia (2017) and was found to dilute the polarization of the primary s by 15%–20%. Note that this estimate is model-dependent. In addition, this effect might be smaller in our analysis due to reduction of secondary particles by cuts on the decay topology of . Below, the results are compared to models which does and does not take into account the feed-down effect.
iii.6 Systematic uncertainties
The systematic uncertainties were estimated by varying topological cuts, and comparing the results obtained with different methods for the signal extraction and for the event plane determination. Below we describe each systematic source and provide typical values.
We applied ten different topological cuts and used the standard deviation from the default cut set results as the symmetric systematic uncertainty. The effect from the variation of the topological cuts was found to be 3%.
As described in the previous section, two different techniques were used to extract the polarization signal. We used the result obtained with the invariant mass method as default results, and the difference in the results from the event plane method was included in the systematic uncertainty. The difference in polarization based on different methods was found to be 21%.
The first-order event plane determined by both ZDC-SMDs in the east and west sides was used in this analysis. For a cross check, the event plane determined by each ZDC-SMD on its own was also used in the analysis, although the poorer event-plane resolution resulted in larger statistical uncertainties. The difference between the results was included in the systematic uncertainty (22%).
According to Ref. C. Patrignani et al. (Particle Data Group) (2016), the decay parameter for , , is 0.642 0.013, while for , based on world-average data. If CP is conserved, . In this study, we use and the uncertainty in was incorporated into the systematic uncertainty (2%). Also, the difference from the case using , which we found to be 9.6%, was included in the systematic uncertainty for .
As mentioned in Sec.III.3, the combinatorial background in the invariant mass distributions for and was estimated by a linear function fit and by the event mixing technique as shown in Fig. 2. The difference between the results obtained with the two approaches was included in the systematic uncertainty (1%).
In the invariant mass method, the background contribution in the off-peak region of () mass distribution is unknown, but is supposed to be zero as mentioned in Sec. III.4. We confirmed that the background signal was consistent with zero when increasing the background by applying looser topological cuts. Therefore, the results from the zero-background assumption for the fitting function were used as the final results, and the difference from the non-zero background assumption was included in the systematic uncertainty (13%).
Final systematic uncertainties were calculated by taking the square root of the quadratic sum of the difference between the default condition and each systematic source. We further examined whether or not there is a possible experimental bias in our results. The data for Au+Au collisions in the years 2010 and 2011 were taken with two different polarities of the magnetic field. In order to check the effect of the magnetic field configuration, we divided the data into two groups according to the magnetic field polarity, and confirmed that there was no significant difference between the two groups. Those two groups also correspond to different times of data-taking. Despite changes in the trigger conditions, which had the effect of further improving data-taking during runs, and the associated change in the detector conditions, no significant difference in the polarization results was observed.
We also calculated the cumulant terms in a similar way as described in Ref. Abelev and others (STAR Collaboration) (2008); Borghini et al. (2002) and subtracted them from the observed signal to check for a possible detector effect due to non-uniformity in acceptance and a residual detector effect coming from the event plane calibration:
where the double angle brackets indicate an average over particles first, and then an average over events. It was found that the correction terms are negligible and there was no significant difference in the results beyond the current uncertainty due to the correction. Therefore we did not apply this correction to the final results.
The effect of the tracking efficiency was studied using a Geant simulation Abelev and others (STAR Collaboration) (2008) and found to be negligible. Also, the acceptance correction proposed in our previous analysis B. I. Abelev et al. (STAR Collaboration) (2007) was applied. The measured polarization can be written as:
where is an acceptance correction factor defined as
The correction factor was estimated using the experimental data.
The analysis was also performed separately for each data set taken in different years. It was found that the results from the years 2010, 2011, and 2014 were consistent within their uncertainties. Therefore we combined all results, the measured , to improve the statistical significance.
Figure 4 presents the global polarization of and as a function of the collision energy for the 20–50% centrality bin in Au+Au collisions. The results from this analysis are shown together with the results from lower collision energies = 7.7–62.4 GeV L. Adamczyk et al. (STAR Collaboration) (2017). The 2007 result for = 200 GeV B. I. Abelev et al. (STAR Collaboration) (2007) has a large uncertainty and is consistent with zero. Our new results for = 200 GeV with significantly improved statistical precision reveal non-zero values of the polarization signal, 0.277 0.040 (stat) (sys) [%] and 0.240 0.045 (stat) (sys) [%] for and respectively, and are found to follow the overall trend of the collision energy dependence. While the energy dependence of the global polarization was not obvious from the lower energy results, together with the new 200 GeV results, the polarization is found to decrease at higher collision energy. Calculations for primary and all taking into account the effect of feed-down, from a 3+1D viscous hydrodynamic model vHLLE with the UrQMD initial state I. Karpenko and F. Becattini (2017) are shown for comparison. The model calculations agree with the data over a wide range of collision energy, including = 200 GeV within the current accuracy of our experimental measurements. Calculations from a Multi-Phase Transport (AMPT) model predict slightly higher polarization than the hydrodynamic model, but are also in good agreement with the data within uncertainties. Neither of the models accounts for the effect of the magnetic field or predicts significant difference in and polarization due to any other effect, e.g., non-zero baryon chemical potential makes the polarization of particles lower than that of antiparticles, but the effect is expected to be small Fang et al. (2016). Other theoretical calculations Xie et al. (2017); Baznat et al. (2018) such as a chiral kinetic approach with the quark coalescence model Sun and Ko (2017) can also qualitatively reproduce the experimental data. It should be noted that most of the models calculate the spin polarization from the local vorticity at the freeze-out hypersurface. However it is not clear when and how the vorticity and polarization are coupled during the system evolution and how much the hadronic rescattering at the later stage affects the spin polarization.
We also performed differential measurements of the polarization, versus the collision centrality, the hyperon’s transverse momentum, and the hyperon’s pseudorapidity. The vorticity of the system is expected to be smaller in more central collisions because of smaller initial source tilt Boek and Wyskiel (2010); Adamczyk et al. (2017), and/or because the number of spectator nucleons becomes smaller. Therefore, the initial longitudinal flow velocity, which would be a source of the initial angular momentum of the system, becomes less dependent on the transverse direction Becattini et al. (2008). Figure 5 presents the centrality dependence of the polarization. The polarization of and is found to be larger in more peripheral collisions, as expected from an increase in the thermal vorticity Jiang et al. (2016). With the given large uncertainties, it is not clear if the polarization saturates or even starts to drop off in the most peripheral collisions.
Figure 6 shows the polarization as a function of for the 20%–60% centrality bin. The polarization dependence on is weak or absent, considering the large uncertainties, which is consistent with the expectation that the polarization is generated by a rotation of the system and therefore does not have a strong dependence. One might expect a decrease of the polarization at lower due to the smearing effect caused by scattering at the later stage of the collisions, and/or a decrease of polarization at higher because of a larger contribution from jet fragmentation, but it is difficult to discuss such effects given the current experimental uncertainties. Calculations for primary from a hydrodynamic model with two different initial conditions (ICs) F. Becattini and Iu. Karpenko (2018) are compared to the data. The dependence of the polarization slightly depends on the initial conditions, i.e. Glauber IC with the initial tilt of the source Boek and Wyskiel (2010); Becattini et al. (2015) and the initial state from the UrQMD model Karpenko et al. (2015). The UrQMD IC includes a pre-equilibrium phase which leads to the initial flow, but the Glauber IC does not include it, and the initial energy density profile is different between the two ICs, both of which would affect the initial angular momentum. The data are closer to the UrQMD IC, but on average are slightly higher than the calculations.
Figure 7 presents the pseudorapidity dependence of the polarization for and . It is consistent with being constant within uncertainties. The vorticity is expected to decrease at large rapidities, but might also have a local minimum at due to complex shear flow structure I. Karpenko and F. Becattini (2017); Jiang et al. (2016); Deng and Huang (2016). Due to baryon transparency at higher collision energy and the event-by-event fluctuations in the participant center-of-mass, such a dependence might be difficult to observe within the acceptance of the STAR detector.
As mentioned in the introduction, the vorticity might be also related to anomalous chiral effects Kharzeev et al. (2016). Similar to the Chiral Magnetic Effect, which is the induction of an electric current along the magnetic field in a medium with non-zero axial charge, an axial current can be generated in the medium with non-zero baryon chemical potential by the system rotation via the Chiral Vortical Effect. On the other hand, the axial current can be generated in the medium with non-zero vector chemical potential by the magnetic field () via the Chiral Separation Effect. Note that points along the magnetic field in the case of (where is the particle electric charge), but is opposite for . Since the directions of the magnetic field and the initial angular momentum of the system are parallel, an additional contribution by to the polarization might be observed, i.e., for (), the spins of particles (antiparticles) in are aligned to the direction of which can contribute to the hyperon polarization. One can test this by studying the dependence of the polarization on the event charge asymmetry, where denotes the number of positively (negatively) charged particles, assuming the relation .
Figure 8 presents the polarization as a function of the event charge asymmetry , where was normalized by its RMS, , to avoid a possible centrality bias, since the width of the distribution becomes wider in peripheral collisions. The results have large uncertainties, but the dependence on seems to be different for and . The data were fitted with a linear function and the extracted slope values are shown in Fig. 8. The observed difference in slopes is a 1–2 effect.
We present the results of global polarization measurements for and hyperons in Au+Au collisions at = 200 GeV. With a 150-fold improvement in statistics compared to the previous measurements, we were able to measure the polarization with better than a tenth of a percent accuracy. Depending on centrality, non-zero signal in the range of 0.1%–0.5% was observed. When the present polarization measurement at 200 GeV, with its relatively small uncertainty, is combined with earlier polarization measurements at lower RHIC energies L. Adamczyk et al. (STAR Collaboration) (2017), the overall trend of an increase with decreasing beam energy is constrained with improved significance. Within the uncertainties these results agree with predictions from a hydrodynamic model (UrQMD+vHLLE) and the AMPT (A Multi-Phase Transport) model. We find no significant difference between and polarization at = 200 GeV within the uncertainties.
The polarization was also studied as functions of the collision centrality, the hyperon’s transverse momentum, and pseudorapidity. The polarization was found to be larger in more peripheral collisions, as expected from theoretical calculations, but no significant dependence on pseudorapidity or transverse momentum was observed. Furthermore, an indication of a polarization dependence on the event-by-event charge asymmetry was observed. This is consistent with a possible contribution to the global polarization from the axial current induced by the initial magnetic field, although the statistical uncertainties need to be improved to reach a definitive conclusion.
Acknowledgements.We thank the RHIC Operations Group and RCF at BNL, the NERSC Center at LBNL, and the Open Science Grid consortium for providing resources and support. This work was supported in part by the Office of Nuclear Physics within the U.S. DOE Office of Science, the U.S. National Science Foundation, the Ministry of Education and Science of the Russian Federation, National Natural Science Foundation of China, Chinese Academy of Science, the Ministry of Science and Technology of China and the Chinese Ministry of Education, the National Research Foundation of Korea, Czech Science Foundation and Ministry of Education, Youth and Sports of the Czech Republic, Department of Atomic Energy and Department of Science and Technology of the Government of India; the National Science Centre of Poland, the Ministry of Science, Education and Sports of the Republic of Croatia, RosAtom of Russia and German Bundesministerium fur Bildung, Wissenschaft, Forschung and Technologie (BMBF) and the Helmholtz Association.
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