The effects of the Coulomb interaction on charged pion production in Au+Au collisions at RHIC-BES energies are studied. From pT spectra of charged pions measured with STAR experiment, the negative-to-positive pion ratios as a

function of transverse momentum are obtained. Based of these pion ratio the finalstate Coulomb interaction can be investigated. The “Coulomb kick” (a momentum change due to Coulomb interaction) and initial pion ratio for RHIC-BES energies (7.7 GeV, 11.5 GeV, 19.6 GeV, 27 GeV and 39 GeV) and various centrality classes are obtained. The energy and centrality dependence of the Coulomb kick is presented.

These results are connected with the kinetic freeze-out dynamics

Calin, M.

Esanu, T.

Jipa, A.

Lazanu, I.

Ristea, C.

Ristea, O.

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DOI 10.1393/ncc/i2019-19084-yColloquia: EuNPC 2018IL NUOVO CIMENTO 42 C (2019) 84New results on Coulomb interaction effects in relativistic heavyion collisionsO. Ristea(1), C. Ristea(1)(2), A. Jipa(1), I. Lazanu(1), T. Esanu(1)(3)and M. Calin(1)(1) University of Bucharest, Faculty of Physics - Bucharest-Magurele, Romania(2) Institute of Space Sciences - Bucharest-Magurele, Romania(3) Horia Hulubei National Institute for Nuclear Physics and Engineering - Bucharest-Magurele,Romaniareceived 5 February 2019Summary. — The effects of the Coulomb interaction on charged pion productionin Au+Au collisions at RHIC-BES energies are studied. From pT spectra of chargedpions measured with STAR experiment, the negative-to-positive pion ratios as afunction of transverse momentum are obtained. Based of these pion ratio the final-state Coulomb interaction can be investigated. The “Coulomb kick” (a momentumchange due to Coulomb interaction) and initial pion ratio for RHIC-BES energies(7.7 GeV, 11.5 GeV, 19.6 GeV, 27 GeV and 39 GeV) and various centrality classes areobtained. The energy and centrality dependence of the Coulomb kick is presented.These results are connected with the kinetic freeze-out dynamics.1. – IntroductionIn heavy-ion collisions, the difference in shape between the positive and negative piontransverse momentum spectra at low pT can be used to study the Coulomb final-stateinteraction [1-4]. The produced charged particles are moving in a Coulomb field generatedby the net positive charge of the stopped participant protons. Due to their small massand large multiplicities, the charged pions are the particles strongest affected by thisCoulomb field and their final momentum is changed. The strength of the Coulomb fielddepends on the degree of the baryon stopping produced in the collision.The Coulomb effects on charged pion production in Au+Au collisions at RHIC-BESenergies were studied using an analytic model developed in [5, 6]. The model assumesthat, due to Coulomb interaction, on average, a charged pion will receive a momentumchange or “Coulomb kick”, ±pc for π± respectively:(1) pc ≡ |pT − pT,0| ∼= 2e2dN chdy1RfCreative Commons Attribution 4.0 License (http://creativecommons.org/licenses/by/4.0) 12 O. RISTEA et al.where pT is the final transverse momentum, pT,0 is the transverse momentum at thermalfreeze-out, dN ch/dy is the net positive charge distribution and Rf is the thermal freeze-out radius. The π−/π+ ratio is described by the following equation:(2)π−π+=〈π−π+〉pT + pcpT − pcexp(m−T − m+TT)where 〈π−/π+〉 is the initial pion ratio, m±T =√m2 + (pT ± pc)2 and T is the thermalfreeze-out temperature.2. – ResultsThe pion ratios were obtained from the pT spectra produced in Au+Au collisions atRHIC-BES energies (√sNN = 7.7 GeV, 11.5 GeV, 19.6 GeV, 27 GeV and 39 GeV) atmidrapidity and measured by STAR experiment [7]. The uncertainties on pion ratios wereobtained using the experimental point-to-point uncertainties on the STAR pT spectra.Figure 1 shows the π−/π+ ratios as a function of transverse momentum for the mostcentral Au+Au collisions (0-5% centrality). For all energies, at low pT values, an increaseof the pion ratio above unity is observed, however, as the beam energy increases, theasymmetry between π− and π+ production is much less significant. These ratios werefitted with Eq. 2, where the Coulomb kick, pc and initial pion ratio, 〈π−/π+〉, arethe free fit parameters. The thermal freeze-out temperature is fixed parameter and istaken from [7]. The fit range was chosen in the low pT range because in this region theCoulomb interaction is stronger. By increasing the fit range, the fit quality decreases(χ2/dof increases).The Coulomb momentum as a function of the center of mass energy is presented inthe left panel of Fig. 2. Black points are obtained from STAR-BES data and coloredpoints are AGS and SPS results from [5]. The errors on pc are obtained from the fitsand are statistical. The pc decreases with the increase of the energy showing that theCoulomb interaction is stronger at lower energies. If the two colliding nuclei are fullystopped, the net positive charge in the fireball is large, generating a strong electric fieldFig. 1. – The π−/π+ ratios produced in most central Au+Au collisions (0-5% centrality) at√sNN = 7.7 GeV, 11.5 GeV, 19.6 GeV, 27 GeV and 39 GeV, as a function of pT . Data arefrom [7]. The red lines are the fits with Eq. 2.NEW RESULTS ON COULOMB INTERACTION EFFECTS IN HEAVY-ION COLLISIONS 3 [GeV]NN s0 10 20 30 40 [MeV/c]cp5101520AuAu BESAuAu AGSPbPb SPS [GeV]NN s10 20 30 40R1.11.21.3Fig. 2. – Left: The Coulomb kick as a function of beam energy. The lines are the fits with threefunctions described in the text. Right: Initial pion ratio as a function of energy.that will influence the charged pions produced in collision. As the energy increases, iethe nuclei become more transparent and the net-positive charge in central interactionregion decreases, as fewer of the original nucleons are stopped at midrapidity. Thereforethe Coulomb effects are less significant.We used three functions to describe this energy dependence. Fit functions, parametersand χ2/dof are given in Table I. The power-law function seems to describe better theenergy dependence of the Coulomb kick (red - f1, black - f2 and blue - f3).At thermal freeze-out, the ratio of the yields of π− and π+ is considered as initialpion ratio. After thermal freeze-out, the final-state Coulomb interaction modifies the pTspectra, the positive pions being accelerated and negative pions being deccelerated bythe net positive charge, resulting the detected (final) spectra.The energy dependence of the initial pion ratio is shown in Fig. 2 (right). The errorson the initial pion ratio are obtained from the fits and are statistical. The 〈π−/π+〉values decrease with the increase of the energy. At low energies, due to contributionsfrom Δ resonances and isospin conservation, 〈π−/π+〉 values are larger than unity. Withincreasing energy the ratios decrease towards unity, indicating that the pion productionmechanisms are changing and pion pair production dominates.Figure 3 (left panel) shows the Coulomb kick as a function of collision centralityexpressed as Npart (the number of participating nucleons) in Au+Au at 7.7 GeV, 11.5GeV and 19.6 GeV. The errors on pc are obtained from the fits and are statistical. TheNpart values and associated errors were taken from [7]. The pc values increase in morecentral collisions for all energies because the overlap volume is larger and therefore a moreintense positive charge generates a stronger Coulomb field in the interaction region. Forall centrality classes the largest values of pc are at 7.7 GeV, due to large baryon stoppingat midrapidity at this energy. As the energy increases, the degree of baryon stoppingTable I. – The fit functions used to describe the energy dependence of the Coulomb kick.Function a b χ2/doff1 = a + b ln√sNN 32.98±1.08 -7.04±0.38 10.11f2 = a (√sNN )b 61.66 ± 5.01 -0.56±0.03 4.25f3 = a + b√sNN 19.62 ± 0.41 -0.34±0.02 28.234 O. RISTEA et al.partN0 100 200 300 [MeV/c]cp01020AuAu 7.7 GeVAuAu 11.5 GeVAuAu 19.6 GeVpartN0 100 200 300 [fm]fR0246810AuAu 7.7 GeVAuAu 11.5 GeVAuAu 19.6 GeVFig. 3. – Left: The centrality and energy dependence of the Coulomb kick. Right: The thermalfreeze-out radius as a function of collision centrality.reduces and consequently the Coulomb interaction. For semi-central and peripheralAu+Au collisions at√sNN = 27 GeV and 39 GeV the pion ratios show no significantenhancement at low pT and the information related to the Coulomb interaction fromthese data could not be obtained.From Eq. 1, using the pc values, the thermal freeze-out radius was obtained. ThedN ch/dy = dNp/dy − dN p̄/dy values were taken from [7], where dNp/dy and dN p̄/dyare the rapidity densities for protons and antiprotons, respectively. The Rf uncertaintieswere obtained using the experimental uncertainties of STAR dNp/dy and dN p̄/dy dataand pc uncertainties from the fits with Eq. 2. The energy and centrality dependenceof the freeze-out radius is shown in right panel of Fig. 3. From 7.7 GeV to 19.6 GeVthe freeze-out radius shows no energy dependence. Rf increases in more central Au+Aucollisions indicating the formation of a larger system.3. – ConclusionsThe π−/π+ ratios produced in Au+Au collisions at RHIC-BES energies were used tostudy the Coulomb interaction between the charged pions and the net-positive charge inthe fireball at midrapidiy. The Coulomb interaction effects are stronger in central colli-sions and at lower beam energies. The initial pion ratio decreases with energy suggestinga change in the pion production mechanisms and the increased role of pair productionmechanism at higher energies. The size of the system at freeze-out Rf increases in morecentral collisions and is not changing with energy for the energy range considered here.∗ ∗ ∗This work was supported by IFA, RO-FAIR program, project number 09-FAIR/16.09.2016.REFERENCES[1] E802 Collaboration, Phys. Rev. C, 57 (1998) 466.[2] E877 Collaboration, Phys. Rev. C, 62 (2000) 024901.[3] NA44 Collaboration, Phys. Lett. B, 372 (1996) 339.[4] WA98 Collaboration, Eur. Phys. J C, 48 (2006) 343.[5] Barz H. W. et al., Phys. Rev. C, 57 (1998) 2536.[6] Heiselberg H., Nucl. Phys. A, 638 (1998) 479C.[7] STAR Collaboration, Phys. Rev. C, 96 (2017) 044904.

New results on Coulomb interaction effects in relativistic heavy ion collisions

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New results on Coulomb interaction effects in relativistic heavy ion collisions

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