Monte Carlo Non-Linear Flow modes studies with AMP Daniel Noel Supervised by: Naghmeh Mohammadi 2 July - 31 August 218 1 Introduction Heavy-ion collisions at the Large Hadron Collider (LHC) generate such high temperatures and energies that it is proposed that quarks and gluons become deconfined. hey would exist in a new state of matter known as quark-gluon plasma (QGP). Studying the properties of this QGP offers a novel way of studying quantum chromodynamics (QCD) without confinement and with the quarks at their bare masses. Following its production, the QGP expands hydrodynamically. As it expands, the temperature and energy density decrease leading to hadronisation of all the partons. he resulting hadron gas continues to expand with elastic and inelastic rescattering occurring between the hadrons. he inelastic collisions can change the hadron content of the medium. his continues until chemical freeze out, whereby inelastic scattering stops and so the particle yields are fixed. Further expansion leaves the medium so dilute that not even elastic scattering can occur, this is known as kinetic freeze out. Finally, the particles are detected by the detector. he hydrodynamic evolution of the system can be described using flow harmonics (v n ) which describe the anisotropic distribution of particles in the QGP. hese relate to the initial state anisotropy of the collisions. he simplest overlap region for a non-central collision is given by an ellipse. his is described by v 2, the second flow harmonic, and is the dominant contribution to the anisotropic flow. Higher order flow harmonics are due to event by event fluctuations of the participating nuclei in addition to the geometry of the collision. For example, there can be triangular or quadrangular collision regions which lead to the third and fourth flow harmonics respectively. hese higher order harmonics measure smaller spatial scales and so are more sensitive to initial conditions and the transport properties of the system. he lower order flow harmonics (n = 2 and 3) show a linear response to the spatial anisotropy. However, the higher order flow harmonics (n > 3) have non-linear contributions from the lower flow harmonics[1]. hese non-linear contributions are proportional to products of lower flow harmonics. he magnitude of the total flow modes (v 2, v 3, v 4, v 5 ) for charged pions, kaons and protons have been investigated by ALICE [2]. At low p values (< 2.5 GeV) there is a mass ordering, with the lower mass particles having higher v n. his is due to radial flow, whereby the system collectively expands with all particles having similar velocities. So, the heavier particles, on average, have higher momenta and so have a greater depletion in the lower p bins. At intermediate p values (2.5 < p < 6 GeV) particles group according to the number of constituent quarks. his particle type (meson and baryon) grouping is due to quark coalescence being the dominant particle production mechanism [3]. hese features of the flow modes are reproduced by the the Monte Carlo (MC) generator A Multi- Phase ransport Model (AMP) [2]. Whether these features are present in the non-linear flow modes V 4,22 and V 5,32 is investigated using ALICE run 2 data at s NN = 5.2 ev. hen, the modelling of these non-linear modes is considered using AMP. his report begins with an overview of anisotropic flow and how this relates to the flow harmonics. he analysis of the run 2 data and AMP data is then presented. 1
2 Anisotropic Flow and Flow Harmonics In a collision of two heavy nuclei the impact parameter is unknown, so instead the centrality is used to quantify how the nuclei collide. his is expressed as a percentage, with lower values indicating the collision has a lower impact parameter and so is more central. In an ideal noncentral collision, the overlap region resembles and ellipsoid and the eccentricity of this ellipsoid in the transverse plane can be quantified according to equation 1. Where X and Y are the coordinates of the participating nucleons with respect to the reaction plane. denotes an average over all participants in an event. he QGP has a very low viscosity, so the spatial anisotropy is transformed to momentum space anisotropy. his momentum space anisotropy is called elliptic flow (v 2 ). ɛ = < Y 2 X 2 > < Y 2 + X 2 > v 2 = < p2 x p 2 y > < p 2 x + p 2 y > (1) Due to event by event fluctuations in the participating nucleons, anisotropic flow has higher harmonics. hese harmonics can be obtained from the Fourier expansion of the azimuthal (ϕ) distribution of particles, according to equation 2. dn dϕ 1 + 2 n v n cos[n(ϕ Ψ n )] (2) Ψ n is the azimuthal angle of symmetry plane and v n is the flow coefficient of the n th order harmonic respectively. hese can be calculated as v n =< cos[n(ϕ Ψ n )] > (3) where denotes an average over all particles in all events. Figure 1 indicates how the third order harmonic is generated by individual colliding nucleons. Figure 1: he individual nucleons involved in a collision. heir triangular shape leads to the third order flow harmonic, v 3. he non-linear contributions to V 4 and V 5 in equations 4 and 5 are V 4,22 and V 5,32. It has been recently shown [1] that these are uncorrelated with the linear modes so can be isolated. he magnitudes of the linear and non-linear modes can be combined in quadrature to obtain the v n value. Notationally, V n is a vector and v n is the magnitude of this vector. V 4 = χ 4,22 (V 2 ) 2 + V L 4 = V 4,22 + V L 4 (4) V 5 = χ 5,32 V 2 V 3 + V L 5 = V 5,32 + V L 5 (5) Since the symmetry plane angle Ψ n is unknown, the values of v 4,22 and v 5,32 are obtained using particle correlations [2]. he events are split into two sub-events A and B, see Figure 2, to 2
reduce non-flow effects. If the linear and non-linear modes are independent we can calculate these according to [1]: v A 4,22 = cos(4ϕ A 1 2ϕ B 2 2ϕ B 3 ) cos(2ϕ A 1 + 2ϕ A 2 2ϕB 3 2ϕB 4 ) (6) v A 5,32 = cos(5ϕ A 1 3ϕ B 2 2ϕ B 3 ) cos(3ϕ A 1 + 2ϕ A 2 3ϕB 3 2ϕB 4 ) (7) Where ϕ A i and ϕ B i represent the azimuthal angle of the i-th particle in sub-region A and B respectively. Similarly, v n,mk can be calculated for sub-events B and by taking a weighted average of v A n,mk and vb n,mk the overall flow harmonics v 4,22 and v 5,32 are calculated. Figure 2: he two regions A and B used for the sub-event method. When the particle of interest (POI) is in one region, the reference particles are chosen in the other region. 3
3 Run 2 data he data analysis is performed over minimum bias collisions at s NN = 5.2 ev collected in 215 with the ALICE detector. he non-linear flow modes of charged pions, kaons and (anti- )protons are investigated. he tracks selected from PC have an η <.8, and the reference particles have.2 < p < 5 GeV. Overall, after applying the event selection criteria 61 million events are used for the analysis. he centrality distributions of the particles is not uniform. Measurements are performed in 1% centrality percentiles and the results are reported in 1% centrality intervals using the number of events in every 1% centrality percentile as a weight. 3.1 Run 2 data results Figures 3 and 4 show the results for and centrality intervals for charged pions, kaons and (anti-)protons. v 4,22.1.8 v 4,22.1.8.6.6.4.4 1 2 3 4 5 6 1 2 3 4 5 6 Figure 3: he v 4,22 in and central collisions. he data were collected at the ALICE detector at s NN = 5.2 ev. v 5,32.1.8 v 5,32.1.8.6.6.4.4 1 2 3 4 5 6 1 2 3 4 5 6 Figure 4: he v 5,32 in and central collisions. he data were collected at the ALICE detector at s NN = 5.2 ev. Just like the total flow modes v 2, v 3 and v 4, these non-linear modes show a distinctive mass splitting at low p (< 2.5 GeV), with the heavier particles having a depletion in the low p bins. Moreover, there is particle type grouping at intermediate p (2.5 < p < 6 GeV), with the particles grouping based on to how many quarks they contain. 4
4 A Multi-Phase ransport Model (AMP) he MC generator AMP can be run with two main configurations of hadron production. he default version uses the Lund String fragmentation [4]. Whereas, the string melting version uses quark coalescence. Furthermore, an evolution phase of the medium, the hadronic rescattering phase, can be switched on and off. When turned on this gives time for radial flow to develop further. In this analysis, AMP is run with three different settings, see able 1. By comparing the flow modes from each of these settings, the effect of the hadronic rescattering phase (and radial flow) on the mass splitting at low p values can be investigated. Likewise, the effect of quark coalescence for the intermediate p particle type grouping is tested. Hadron Production Hadronic rescattering ALICE MC production String Melting On AMP_LHC13f3c String Melting Off AMP_LHC13f3a Default On AMP_LHC13f3b able 1: he three AMP settings considered, with the ALICE MC production information. 4.1 AMP Results Using 35 million events at s NN = 2.76 ev for each of the 3 AMP settings in table 1, distributions of v 4,22 and v 5,32 are calculated. Figures 5, 6 and 7 show v 4,22 for each of the 3 AMP versions discussed above. Likewise, 8, 9 and 1 show v 5,32 for each of the 3 AMP versions. hese plots are for and centrality intervals for charged pions, kaons and (anti-)protons. For both v 4,22 and v 5,32, the string melting AMP with hadronic rescattering correctly predicts the distinct mass ordering at low p as well as the particle type grouping at intermediate p. he string melting AMP without hadronic rescattering fails to reproduce the mass ordering at low p, indicating that radial flow hasn t fully developed. Moreover, the default setting, without quark coalescence, fails to reproduce the particle type grouping at intermediate p. Overall, both quark coalescence and the hadronic rescattering phase are important for qualitatively recreating the data. he qualitative predictions of string melting AMP with hadronic rescattering are correct. However, there is a large quantitative difference to the data measurements (Figures 3 and 4). he AMP results are shifted towards smaller p values. For example, the p value where the v 4,22 curves for each particle cross is around 2.6 GeV for the data (Figure 3) and is around 1.2 GeV for AMP (Figure 5). his same effect has been seen previously when analysing the total flow modes [2] and can be attributed to AMP having an unrealistically low amount of radial flow. his leads to there being less depletion in the low p bins. 5 Conclusions he non-linear flow modes v 4,22 and v 5,32 are investigated using run 2 ALICE data and AMP Monte Carlo production. hese modes have contributions from (v 2 ) 2 and v 2 v 3 respectively, and so similar characteristic features as the total flow modes are expected. hese features are the mass ordering at low p values and the particle type grouping at intermediate p values, and are found to be present for the non-linear modes too. Moreover, AMP with string melting (quark coalescence) and hadronic rescattering qualitatively models these non-linear flow modes well. Indicating that both quark coalescence and radial flow are important for reproducing the characteristic features. AMP, however, fails to quantitatively reproduce the flow modes, just as it fails to for the total flow modes [2]. his is likewise probably due to a smaller radial flow component with respect to the data. 5
.3 5 v 4,22.35 string melting.3 5 v 4,22.35 string melting.15.15.1.1.5.5.5.5 1 1.5 2 2.5 3.5.5 1 1.5 2 2.5 3 Figure 5: he v 4,22 in and central collisions produced by AMP at s NN = 2.76 ev. String melting and hadronic rescattering were used..3 5 v 4,22.35 string melting with no hadronic rescattering.3 5 v 4,22.35 string melting with no hadronic rescattering.15.15.1.1.5.5.5.5 1 1.5 2 2.5 3.5.5 1 1.5 2 2.5 3 Figure 6: he v 4,22 in and central collisions produced by AMP at s NN = 2.76 ev. String melting with no hadronic rescattering were used..3 5 v 4,22.35 default.3 5 v 4,22.35 default.15.15.1.1.5.5.5.5 1 1.5 2 2.5 3.5.5 1 1.5 2 2.5 3 Figure 7: he v 4,22 in and central collisions produced by AMP at s NN = 2.76 ev. he default (Lund string fragmentation) and hadronic rescattering settings were used. 6
.3 5 v 5,32.35 string melting.3 5 v 5,32.35 string melting.15.15.1.1.5.5.5.5 1 1.5 2 2.5 3.5.5 1 1.5 2 2.5 3 Figure 8: he v 5,32 in and central collisions produced by AMP at s NN = 2.76 ev. String melting and hadronic rescattering were used..3 5 v 5,32.35 string melting with no hadronic rescattering.3 5 v 5,32.35 string melting with no hadronic rescattering.15.15.1.1.5.5.5.5 1 1.5 2 2.5 3.5.5 1 1.5 2 2.5 3 Figure 9: he v 5,32 in and central collisions produced by AMP at s NN = 2.76 ev. String melting with no hadronic rescattering were used..3 5 v 5,32.35 default.3 5 v 5,32.35 default.15.15.1.1.5.5.5.5 1 1.5 2 2.5 3.5.5 1 1.5 2 2.5 3 Figure 1: he v 5,32 in and central collisions produced by AMP at s NN = 2.76 ev. he default (Lund string fragmentation) and hadronic rescattering settings were used. 7
References [1] ALICE Collaboration, Linear and non-linear flow mode in Pb Pb collisions at s NN = 2.76 ev, Phys. Lett. B 773 (217) 68 8. [2] ALICE Collaboration, Higher harmonic flow coefficients of identified hadrons in collisions at s NN = 2.76 ev, JHEP (216) 164. [3] D. Molnar and S. A. Voloshin, Elliptic flow at large transverse momenta from quark coalescence, Phys. Rev. Lett. 91 (23) 9231. [4] B. Nilsson-Almqvist and E. Stenlund, Interactions between hadrons and nuclei: he Lund Monte Carlo-FRIIOF version 1.6, Computer Physics Communications 43 (1987) 387 397. 8