Summary of Professional Accomplishments. Radosław Ryblewski

Transcription

1 Summary of Professional Accomplishments Radosław Ryblewski Kraków, October 18, 2016

2 Contents 1 Personal Data Name and surname Diplomas awarded, scientific and artistic degrees, including name, place, and year of awarding as well as title of doctoral thesis Employment in research institutions Indicated scientific accomplishment Title of the scientific accomplishment List of publications which constitute the indicated scientific accomplishment Percentage contribution of co-authors in publications [H1-H12] (according to their statements) Description of the scientific objective of the publications [H1- H12] as well as results obtained including a discussion of their potential application Scientific objective of the series of papers Abbreviations Notation Introduction Production, thermalization and hydrodynamization of matter in the early stages of heavy-ion collisions ([H1-H2]) Testing hydrodynamic formalisms in the kinetic theory framework ([H3-H5]) Role of the transport coefficients in the second-order viscous fluid hydrodynamics ([H6-H8]) The signatures of anisotropy in the early stages of evolution of matter in heavy-ion collisions ([H9-H12]) Detailed description of publications [H1-H12] Podsumowanie Other scientific achievements List of publications from the Journal Citation Reports (JCR) database After Ph.D. graduation Before Ph.D. graduation List of other publications After Ph.D. graduation

3 3.2.2 Before Ph.D. graduation Joint studies, research documentation and expert s reports Bibliometric information Number of publications and aggregate impact factor (IF) according to Journal Citation Reports (JCR) list (as of the year of publication) Number of citations according to Web of Science database Hirsch index according to Web of Science database Management or participation in international and national research projects International and Polish scientific prizes and awards Presentations at scientific conferences and seminars After Ph.D. graduation Before Ph.D. graduation Poster sessions Participation in European programs and other international and national programs Participation in organizing committees of international and domestic scientific conferences Prizes and awards Participation in research consortia and networks Management of projects carried out in cooperation with scholars from other Polish and foreign centers and in cooperation with businesses Participation in editorial committees and scientific councils of magazines Membership in international and domestic scientific organizations and academic associations Teaching and popularizing achievements and information on international cooperation Teaching achievements and achievements in popularization of science Popular science talks Topical courses Active participation in the organization of popular science events Supervision of Ph.D. candidates and undergraduate students Supervision of undergraduate students

4 4.4 Internships in foreign and domestic research and academic centers Expertise reports or other elaborations for various institutions (public administration; self-governmental administration, public service institutions, business) Participation in expert teams and contest juries Reviewing of international and national projects and publications submitted to international and national journals

5 1 Personal Data 1.1 Name and surname Radosław Ryblewski 1.2 Diplomas awarded, scientific and artistic degrees, including name, place, and year of awarding as well as title of doctoral thesis 2012 Ph.D. in physical sciences (with distinction), Institute of Nuclear Physics Polish Academy of Sciences, Kraków, Title of the Ph.D. dissertation: Collective phenomena in the early stages of relativistic heavy-ion collisions, supervisor: prof. dr hab. Wojciech Florkowski M.Sc. in Physics, Institute of Physics, Jan Kochanowski University, Kielce, Title of the M.Sc. thesis: Hydrodynamika poprzecznie stermalizowanych czastek masywnych w relatywistycznych zderzeniach ciezkich jonów (Hydrodynamics of Transversally Thermalized Massive Particles in Relativistic Heavy-Ion Collisions), supervisor: prof. dr hab. Wojciech Florkowski. 1.3 Employment in research institutions 06/2012-now Adiunct, Department of Theory of Structure of Matter, Institute of Nuclear Physics Polish Academy of Sciences, Kraków. 09/ /2014 Postdoctoral Research Associate, Physics Department, Kent State University, Kent, Ohio, United States. 03/ /2012 Assistant, Department of Theory of Structure of Matter, Institute of Nuclear Physics Polish Academy of Sciences, Kraków. 10/ /2012 Ph.D. student, International Ph.D. Studies, Institute of Nuclear Physics Polish Academy of Sciences, Kraków. 4

6 2 Indicated scientific accomplishment 2.1 Title of the scientific accomplishment In accordance with Article 16, Clause 2 of the Act of March 14, 2003 on Scientific Degrees and Titles as well as Degrees and Titles in the Arts (Journal of Acts No. 65, item 595, with subsequent amendments) the indicated scientific accomplishment is in the form of a series of 12 research papers [H1-H12] under the common title: Role and description of the non-equilibrium dynamics of matter in the relativistic heavy-ion collisions 2.2 List of publications which constitute the indicated scientific accomplishment [H1] R. Ryblewski, W. Florkowski, Equilibration of anisotropic quark-gluon plasma produced by decays of color flux tubes, Physical Review D 88 (2013) 3, (IF 5 year = 4.046, citations: 8). My contribution to the article was to perform part of analytic calculations, write full version of the program solving evolution equations for fields and particles, perform all numerical simulations and take part in preparing the manuscript. I estimate my contribution at 60%. [H2] [H3] R. Ryblewski, Thermalization of parton spectra in the colour-flux-tube model, Journal of Physics G - Nuclear and Particle Physics 43 (2016) 9, (IF 5 year = N/A, citations: 0). W. Florkowski, R. Ryblewski, M. Strickland, Anisotropic hydrodynamics for rapidly expanding systems, Nuclear Physics A 916 (2013), (IF 5 year = 1.774, citations: 41). 5

7 My contribution to the article was to check analytic calculations, write the program solving kinetic and hydrodynamic equations, perform all numerical simulations and take part in preparing the manuscript. I estimate my contribution at 50%. [H4] W. Florkowski, R. Ryblewski, M. Strickland, Testing viscous and anisotropic hydrodynamics in an exactly solvable case, Physical Review C 88 (2013) 2, (IF 5 year = 3.551, citations: 54). My contribution to the article was to perform part of analytic calculations, perform all numerical simulations and take part in preparing the manuscript. I estimate my contribution at 50%. [H5] W. Florkowski, E. Maksymiuk, R. Ryblewski, M. Strickland, Exact solution of the (0+1)-dimensional Boltzmann equation for a massive gas, Physical Review C 89 (2014) 5, (IF 5 year = 3.439, citations: 27). My contribution to the article was to suggest general concept of the article, perform part of analytic calculations, consult writing of the numerical code solving transport equations, check and correct numerical results and take part in preparing the manuscript. I estimate my contribution at 35%. [H6] G. S. Denicol, W. Florkowski, R. Ryblewski, M. Strickland, Shear-bulk coupling in nonconformal hydrodynamics, Physical Review C 90 (2014) 4, (IF 5 year = 3.439, citations: 21). My contribution to the article was to perform analytic calculations concerning anisotropic hydrodynamics, write all numerical codes, perform all numerical simulations and take part in preparing the manuscript. I estimate my contribution at 50%. [H7] A. Jaiswal, R. Ryblewski, M. Strickland, Transport coefficients for bulk viscous evolution in the relaxation time approximation, Physical Review C 90 (2014) 4,

8 (IF 5 year = 3.439, citations: 15). My contribution to the article was to suggest general concept of the article, perform analytic calculations concerning anisotropic hydrodynamics, write all numerical codes, perform all numerical simulations and take part in preparing the manuscript. I estimate my contribution at 55%. [H8] W. Florkowski, A. Jaiswal, E. Maksymiuk, R. Ryblewski, M. Strickland, Relativistic quantum transport coefficients for second-order viscous hydrodynamics, Physical Review C 91 (2015) 5, (IF 5 year = 3.057, citations: 8). My contribution to the article was to formulate general concept of the article, perform part of analytic calculations (including kinetic coefficients), write the numerical code solving evolution equations, check numerical results and take part in preparing the manuscript. I estimate my contribution at 50%. [H9] R. Ryblewski, M. Strickland, Dilepton production from the quark-gluon plasma using (3+1)-dimensional anisotropic dissipative hydrodynamics, Physical Review D 92 (2015) 2, (IF 5 year = 3.805, citations: 5). My contribution to the article was to formulate general concept of the article, perform all analytic calculations, write the numerical code determining QGP evolution in (3+1) dimensions in the framework of anisotropic hydrodynamics and extracting dilepton spectra based on the medium evolution and production rate, perform numerical simulations and take part in preparing the manuscript. I estimate my contribution at 80%. [H10] L. Bhattacharya, R. Ryblewski, M. Strickland, Photon production from a non-equilibrium quark-gluon plasma, Physical Review D 93 (2016) 6, (IF 5 year = N/A, citations: 0). 7

9 My contribution to the article was to prepare the numerical code solving anisotropic hydrodynamics (ahydro) evolution equations and modify the numerical code solving evolution equations of viscous fluid hydrodynamics (AZHYDRO) in order to compare the results, check analytic calculations and numerical results and take part in preparing the manuscript. I estimate my contribution at 40%. [H11] B. Krouppa, R. Ryblewski, M. Strickland, Bottomonia suppression in 2.76 TeV Pb-Pb collisions, Physical Review C 92 (2015) 6, (IF 5 year = 3.057, citations: 1). My contribution to the article was to suggest general concept of the article, coordinate, consult and check numerical calculations, provide and modify the numerical code solving anisotropic hydrodynamics evolution equations and take part in preparing the manuscript. I estimate my contribution at 40%. [H12] W. Florkowski, R. Ryblewski, M. Strickland, Chromoelectric oscillations in a dynamically evolving anisotropic background, Physical Review D 86 (2012) 8, (IF 5 year = 4.170, citations: 12). My contribution to the article was to perform part of analytic calculations, prepare the code solving evolution equations of anisotropic hydrodynamics and color mean field, perform all numerical simulations and take part in preparing the manuscript. I estimate my contribution at 60% Percentage contribution of co-authors in publications [H1-H12] (according to their statements) H1 H2 H3 H4 H5 H6 H7 H8 H9 H10 H11 H12 L. Bhattacharya 30 G.S. Denicol 20 W. Florkowski A. Jaiswal B. Krouppa 25 E. Maksymiuk R. Ryblewski M. Strickland

10 2.3 Description of the scientific objective of the publications [H1-H12] as well as results obtained including a discussion of their potential application Scientific objective of the series of papers The main objective of the listed series of papers was to determine the role of the early non-equilibrium stages of evolution of matter produced in ultra-relativistic heavy-ion collisions in the process of understanding properties of strong interactions and to find hydrodynamic formalisms adequate for their description. In order to realize the main objective the analysis of the following problems was performed: Study the production, thermalization and hydrodynamization rate of the matter produced in heavy-ion collisions in the framework of colorflux tube model (see Section 2.3.5). Develop tools for testing precision of various hydrodynamic formalisms in the description of the non-equilibrium stages of evolution of matter in heavy-ion collisions (see Section 2.3.6). Find the proper form of the transport coefficients in the second-order viscous fluid hydrodynamics and investigate their role in the description of dissipative corrections (see Section 2.3.7). Determine the impact of momentum-space anisotropies on the observables measured in heavy-ion collisions (see Section 2.3.8). In Sections a detailed presentation of the current state of the art in the aforementioned problems and, motivated by it, main objectives and results of the papers [H1-H12] were presented. Section contains detailed description of the papers [H1-H12]. 9

11 2.3.2 Abbreviations AdS/CFT - Anti de Sitter/conformal field theory BE - Boltzmann equation BNL - Brookhaven National Laboratory CE - Chapmann Enskog CERN - European Organization for Nuclear Research CGC - color glass condensate DIS - deep inelastic scattering DNMR - Denicol Niemi Molnar Rischke EKT - effective kinetic theory EOS - equation of state HIC - heavy-ion collisions IS - Israel Stewart LHC - Large Hadron Collider lqcd - lattice QCD LTE - local thermal equilibrium NS - Navier Stokes QCD - quantum chromodynamics QGP - quark-gluon plasma RHIC - Relativistic Heavy-Ion Collider RS - Romatschke Strickland RTA - relaxation-time approximation SLAC - Stanford Linear Accelerator Center SPS - Super Proton Synchrotron sqgp - strongly-interacting QGP wqgp - weakly-interacting QGP Notation snn - collision energy in the center of mass system of reference g µν - metric tensor, g µν = diag(1, 1, 1, 1) x µ - space-time coordinates, x µ = (t, x, y, z) p µ - four-momentum, p µ = (E p, p T sin φ p, p T cos φ p, p L ) u µ - four-velocity, u µ = γ(1, v x, v y, v z ) τ - proper time, τ = t 2 z 2 τ 0 - initial proper time of the hydrodynamic evolution τ eq - RTA relaxation time 10

12 τ π, τ Π - relaxation times for the viscous corrections π µν and Π Q s - saturation scale Λ QCD - QCD scale α - fine-structure constant α s - strong interaction coupling constant g - strong interaction coupling parameter, g = 4πα s η - shear viscosity, η = η/s ζ - bulk viscosity m - quasiparticle mass T - temperature P, P L, P T - equilibrium pressure, longitudinal pressure, transverse pressure s - entropy density n - particle density ε - energy density c s - speed of sound f(x, p) - single-particle phase-space distribution function ξ - (RS) anisotropy parameter λ - (RS) transverse-momentum scale µν - projection operator, µν g µν u µ u ν µ - projected gradient, µ µν ν A µν µν αβ Aαβ - symmetrizing operator, µν αβ ( µ α ν β + µ β ν α)/2 µν αβ /3 θ - expansion scalar θ µ u µ T µν - energy-momentum tensor π µν - shear-stress tensor, π µν T µν Π - bulk pressure, Π (P + µν T µν /3) ω µν - vorticity tensor, ω µν ( µ u ν ν u µ )/2 σ µν - shear tensor, σ µν µ u ν 11

13 2.3.4 Introduction One of the greatest achievements of modern physics was the confirmation of the parton structure of hadrons, suggested earlier by Feynmann, in the deep-inelastic scattering (DIS) of electrons on protons at SLAC in This observation irreversibly revolutionized the high-energy physics opening the way to establishing the quantum chromodynamics (QCD) as the fundamental theory of strong interactions and the key element of the Standard Model of particle physics. Quantum chromodynamics, apart from explaining in a natural way the hadron structure in the low energy limit as bound states of partons (quarks and gluons) by refering to the phenomenon of confinement, was also predicting new phenomena in the high energy limit, in particular, asymptotic freedom, for which Gross, Politzer and Wilczek were distinguished with the Nobel Prize in According to their theory in the high temperature and/or density limit the interactions between partons become arbitrarily weak and quarks and gluons may be regarded as the proper degrees of freedom. It is believed that this new state of matter, called the quark-gluon plasma (QGP), might have existed in the early Universe, where the temperatures exceeded million times the temperature of the center of the Sun, and still exists in the inner cores of neutron stars, where the energy density exceeds ten times the density of proton. The existence of both, the confinement and the asymptotic freedom, phenomena entailed a number of speculations about the QCD phase diagram. While the physical properties of QGP, in principle, should follow from QCDbased theoretical considerations i.e. the lattice QCD (lqcd) simulations, their experimental verification in a systematic and controlled way is much more involved. In the 1980s, together with the construction of modern accelerators, it was proposed that the creation of QGP may be possible in the ultra-relativistic collisions of nuclei of heavy elements, where the matter has opportunity to reach the thermodynamic limit. A number of indirect signatures of the creation of a new state of matter were observed already at SPS in CERN, however only the systematic research program at RHIC in BNL and at the LHC in CERN after 2000 was able to confirm these observations. Nowadays the vast majority of data collected in these experiments in the broad range of energy ( s NN GeV/c) confirms production of QGP. Precise determination of its physical properties is recently a subject of intense studies. 12

14 2.3.5 Production, thermalization and hydrodynamization of matter in the early stages of heavy-ion collisions ([H1-H2]) The study of the physical properties of QGP through the heavy-ion collisions (HIC) is complicated by the fact, that the information about its space-time evolution is accessible only indirectly through the measurement of four-momenta of the particles in the final state, when the matter is already cold and practically non-interacting. As a result, in order to understand the QGP dynamics it is required to model all stages of evolution of matter in the collision, in particular, the early non-equilibrium one which precedes the proper QGP phase. However, assuming that the matter quickly reaches the state relatively close to the local thermal equilibrium (LTE), and the interactions are strong enough to uphold this state, its further soft-mode evolution may be described in the framework of standard 1 relativistic dissipative fluid mechanics, commonly known as relativistic viscous fluid hydrodynamics. The main advantage of such a method is to exchange, in general highly complicated, microscopic description of a system of many particles and fields with the effective one based on a few macroscopic variables satisfying, in particular, equations following from the fundamental conservation laws. In this way the information about the system dynamics at the microscopic level reduces to the knowledge of its thermodynamic properties encoded in the equation of state (EOS) and its dissipative phenomena characterised by the transport coefficients. A detailed analysis of the experimental data on the particles fluctuations and correlations at RHIC and the LHC suggests, that, in contrast to the earlier expectations, the created matter is, in practice, a strongly-coupled system (sqgp) which undergoes collective (hydrodynamic) expansion from the earliest moments after the collision (τ h 1 fm/c). In this context the main goal is to understand the production mechanisms of the matter and the thermalization 2 processes in the early stages of the collision. This knowledge is essential to tell if, and how the produced matter reaches vicinity of the LTE state in such a short time, and, in consequence, if and at which moment the hydrodynamic description is applicable. In practice, early thermalization seems to be hard to understand at the 1 By standard in this context we mean dissipative hydrodynamic formalisms based on the assumption of the vicinity of LTE state. They are also called hydrodynamics of viscous fluids. As the case of the formalism called anisotropic hydrodynamics [1 11] shows this requirement is not a necessary condition for construction of a consistent dissipative hydrodynamic formalism. 2 Thermalization is understood as the process of reaching the state very close to LTE. 13

15 microscopic level [P10]. In the light of the successes of the early hydrodynamic description it leads to a paradox known as the early thermalization puzzle. The latter is one of the most important problems of the HIC physics of the last decade. Within the HIC models which in the early stages of the evolution include presence of strong color fields the produced matter is initially locally strongly anisotropic in the momentum space, which results in the longitudinal pressure which is much smaller than the transverse pressure 3 (P L P T ) [12 15]. Moreover, even if the matter was already created in the LTE state its rapid longitudinal expansion together with relatively slow transverse expansion leads to generation of significant dissipative corrections, which quickly drive the system far from the LTE state [16]. As a result, until recently, the early thermalization in HIC was only explained with the exponential increase of the color-field instabilities in the anisotropic medium 4 [17 22]. Nevertheless, recently one can see a significant progress in this respect. Due to the non-perturbative character of interactions in sqgp there is increasing interest in HIC models which employ the Maldacena AdS/CFT correspondence [23]. Their results indicate that the thermalization is not only unnecessary for the hydrodynamic description to be applicable, but probably it is not realised at all in HIC [24 27]. It means that instead of thermalization it is enough to reach the state called by Heller et al. hydrodynamization of the system [25]. In this case deviations from LTE state are well described within the viscous fluid hydrodynamics with the use of the dissipative corrections. In the high-energy limit the early stages of evolution of matter may be also described using models based on the saturation effects [28, 29], such as color glass condensate (CGC) model [30 32], or glasma model [33]. These models, using Yang Mills classical field theory methods predict that in the early stages of evolution (τ Q 1 s ) in the process of collision of two color-excited nuclei the system of strong color fields oriented mainly along the beam direction [33] is generated. Results obtained by Epelbaum et al. [34] and Berges et al. [35] in the framework of models including first-order resummation of CGC show that moderate increase of the strong coupling constant (g 0.5, α s 0.02) leads to sufficient hydrodynamization of the system in a relatively short time (τ h 1 fm/c). Similar conclusions were drawn by Kurkela et al. [36] who used effective kinetic theory (EKT) with the initial conditions taken from the simulations done within CGC. Qualitatively similar description of the early stages of evolution of matter 3 The transverse T and longitudinal L direction is defined with respect to the direction of the beam of colliding ions. 4 Henceforth, the adjective anisotropic will always refer to the anisotropy in the momentum space measured locally. 14

16 in HIC to CGC/glasma may be also obtained using so called color-flux-tube model [37 48], where the color field dynamics is treated in the Abelian dominance approximation [49 53], while the particles are produced through the decay of color fields described within the Schwinger tunnelling mechanism [37 39, 54 56]. This model, originally used to describe the parton production in the e + e reactions, compared to CGC/glasma, contains a number of simplifications, for instance neglecting presence of the color magnetic fields, it has however a virtue of being solvable analytically. The main objective of Refs. [H1-H2] was to study the rate of production, thermalization and hydrodynamization of the QGP created in the color-fluxtube model through the analysis of evolution of the pressure ratio P L /P T 5 [H1] and the spectra of produced partons [H2]. The results obtained for the values of shear viscosity η to entropy density s ratio extracted from the hydrodynamic fits to the experimental data η bound η 3 η bound (where η η/s, and η bound = 1/(4π) being the lower bound of the η obtained within AdS/CFT correspondence [57]) show that despite the lack of early thermalization large differences between P L and P T are well described using the dissipative corrections within viscous fluid hydrodynamics. The latter observations may indicate the early hydrodynamization in HIC, and are in line with the ones obtained in the framework of AdS/CFT correspondence [24 27], CGC/glasma [34, 35] and EKT [36] quoted above. One should stress that the study presented in Ref. [H1] were one of the first which in a straightforward manner related the thermalization/hydrodynamization rate of QGP with its transport properties ( η), and the only ones which used the color-fluxtube model in the context of the thermalization/hydrodynamization of QGP in HIC. Results on the pressure anisotropy obtained in the framework of color-flux-tube model may serve in future, for instance, as initial conditions for hydrodynamic models simulations or the background for electromagnetic emissions from QGP Testing hydrodynamic formalisms in the kinetic theory framework ([H3-H5]) In the light of the arguments presented in Section and due to the simplicity of the hydrodynamic description the fluid dynamical modelling play an important role in the theoretical description of the collective evolution of 5 Due to the imposed Bjorken symmetry P L and P T are the only independent pressure components in the analysed problem. 15

17 matter in HIC. Hydrodynamics as an effective theory may be formulated in a general way by referring to the fundamental physical principles (conservation laws, thermodynamic principles etc.) and symmetries. However, in order to gain knowledge about the EOS and transport coefficients, one has to refer to some fundamental microscopic theory. In the vast majority of cases one uses kinetic theory for that purpose 6. Traditionally viscous fluid hydrodynamics is formulated in the form of gradient expansion around the LTE state, which in the kinetic theory approach, is expressed through the expansion of the single-particle phase-space distribution function f(x, p) around equilibrium distribution function f eq (x, p). Hydrodynamics of the perfect fluid thus appears in the zeroth order of this expansion. Based on the uncertainty principle of the quantum mechanics [58] it is known however that all the fluids in Nature undergo dissipation effects [57]. Formulation of the relativistic hydrodynamics including these phenomena is however non-trivial and unfortunately ambiguous. Including them in the first order of the expansion through the naive relativistic generalisation of the Navier Stokes (NS) [59] theory leads to a number of complications, including causality violation. This problem was solved in the next order of the expansion in the framework of second-order viscous fluid hydrodynamics known as Israel Stewart (IS) theory [60 63]. Within IS theory dissipative corrections are treated as independent variables, which evolve towards universal attractor of NS equations according to their respective time scales given by the relaxation times. Despite many successes in describing the experimental data the IS theory suffers from a few problems. As it was noted above, the formal condition of applicability of viscous fluid hydrodynamics are small perturbations of the LTE state. In the light of the strong local anisotropies ( δf f eq, where δf f f eq ) predicted by microscopic models (see results of papers [H1-H2], Section 2.3.5), suggests that in some cases the predictions of IS theory may be questionable. Strong anisotropies are also a potential source of technical problems connected with overestimation of dissipative corrections as well as the conceptual ones related to the non-physical results caused by the corrections. In particular one often observes negative pressures in the system, negative values of the distribution function, or lack of reproducing free-streaming limit when η. Moreover, the IS theory may be obtained in various ways, in each case resulting, in general, in a different form of evolution equations and transport coefficients. Determination of the QGP 6 In the case of conformal systems it is also possible to use predictions obtained within AdS/CFT correspondence, however the latter does not give direct information about the microscopic dynamics of the system in the form of a distribution function. 16

18 properties through the transport coefficients (including viscosity) based on the hydrodynamic fits to the experimental data is thus biased with some systematic error related to their definition within the evolution equations. In the light of above problems there is a large interest in finding the hydrodynamic formalisms, whose applicability would be justified in the early stages of evolution of matter in HIC. Among potential solutions of these problems in the framework of viscous fluid hydrodynamics one should mention i.e. Denicol Niemi Molnar Rischke (DNMR) formalism 7 [64, 65] based on the systematic expansion in Knudsen number and inverse Reynolds number, the gradient expansion based on the iterative solution of the Boltzmann equation known as the Chapmann Enskog (CE) method [66, 67], or the third-order hydrodynamics [68, 69]. In the recent years efficacy of the alternative hydrodynamic approaches was also presented, in particular, of the anisotropic hydrodynamics (ahydro) [1 11] based on the reorganisation of the hydrodynamic expansion around anisotropic distribution( function of the Romatschke Strickland (RS) form f RS (p, x) = p2 ) f eq + ξ(x) p 2 L /λ(x) (where ξ is anisotropy parameter, while λ is transverse-momentum scale) [70], or the generalisation of this approach through the inclusion of the additional perturbative corrections (vahydro) [71 73]. In the light of the broad range of the aforementioned formalisms it is esssential to have some exact solution allowing for comparing their efficacy. Due to the fact that most of the hydrodynamic formalisms are based on the kinetic theory equations a reasonable starting point is to obtain exact solutions of the relativistic Boltzmann equation (BE) p µ µ f = C(f). (1) In general solving Eq. (1) is highly-complicated. Fortunately most of the methods mentioned above are based on the relaxation time approximation (RTA) [74], in which case the collisional kernel has the form C(f) = p µ u µ δf/τ eq, (2) where τ eq denotes relaxation time of the system. The remaining part of the presented considerations is restricted to the case where the collisional kernel of Eq. (1) has the form of Eq. (2). 7 The DNMR formalism is also commonly referred to as 14-moment Grad approximation, however hereafter we will consequently avoid this term, since strictly speaking 14-moment Grad approximation is just a special case of the method worked out by the authors of the paper [65]. 17

19 The main objective of Refs. [H3-H5] was to obtain exact solutions of the Boltzmann kinetic equation (1) with the collisional kernel treated in the RTA (2) in the special case of (0+1)-dimensional Bjorken flow [75]. The use of these approximations allowed for finding exact analytic formal solution of the Eq. (1), which was subsequently solved numerically to an arbitrary precision. Obtained quasi-analytic exact solutions allowed for the study of the precision of the description of dissipative corrections in various hydrodynamic formalisms (see Refs. [H3-H8]). In particular it made possible to judge the applicability of the aforementioned hydrodynamic formalisms in the case of large values of anisotropy (ξ 0) as predicted by the microscopic models. The main result of the tests performed in Refs. [H3-H5] was the observation of expected (in view of aforementioned arguments) imprecise description within IS theory and the good performance of the ahydro prescription. Obtained exact solutions were also used multiple times as the starting point for construction of other similar exact solutions (see [76, 77] for the case of the so called Gubser flow [78]). One should stress that the exact solutions of BE obtained in Refs. [H3-H5] both deliver a unique tool for testing the numerical codes and algorithms used to solve evolution equations and allow for the straightforward check of the agreement between the hydrodynamic formalisms and underlying kinetic theory Role of the transport coefficients in the second-order viscous fluid hydrodynamics ([H6-H8]) All hydrodynamic formalisms based on the kinetic theory equations employ quasi-particle interpretation of QGP. The latter is based on the asymptotic freedom property of QCD, which suggests that, in the high-temperature limit (T Λ QCD ), QCD may be interpreted as a weakly interacting system of quasi-particles (wqgp) possessing thermal masses m q, q,g (T ) gt [79, 80]. In the temperature range achievable at RHIC and the LHC standard quasi-particle approach breaks down and, in practice, one has to take into account non-perturbative effects in the system. One of the methods of proceeding in this situation is to broaden the range of applicability of quasiparticle interpretation of QGP to the lower temperatures through the usage of lqcd thermodynamic results for entropy in order to determine the temperature dependence of the effective mass m(t ). Existence of the finite masses results in the new scale apart from temperature, which is connected with the conformal symmetry breaking in the system. In the context of the QGP hydrodynamical modelling the latter requires inclusion, apart from the pressure corrections caused by shear viscosity, an additional additional (isotropic) correction caused by the bulk viscosity ζ. 18

20 One can show that the most general form of evolution equations of secondorder viscous fluid hydrodynamics derived based on the Boltzmann kinetic equation (1) have the following structure 8 [65] τ Π Π + Π = ζθ δππ Πθ + λ Ππ π µν σ µν + ϕ 1 Π 2 + ϕ 3 π µν π µν, (3) τ π π µν + π µν = 2ησ µν + 2τ π π µ α ω ν α δ ππ π µν θ τ ππ π µ α σ ν α + λ ππ Πσ µν +ϕ 6 Ππ µν + ϕ 7 π µ α π ν α, (4) where π µν is the shear-stress tensor generated by the shear viscosity, and Π is the bulk pressure generated by the bulk viscosity 9. Coefficients ζ, η and δ ΠΠ, δ ππ, τ ππ, λ Ππ λ ππ multiplying various tensorial structures in Eqs. (3) and (4) are the first- and second-order transport coefficients, respectively, and τ π, τ Π are the relaxation times of the evolved corrections. Transport coefficients are in general complicated functions of mass and temperature and their certain form depends not only on the form of the collisional kernel C(f) but also method/formalism used for deriving Eqs. (3) and (4) from Eq. (1). The quadratic terms ϕ 1 Π 2, ϕ 3 π µν π µν, ϕ 6 Ππ µν, and ϕ 7 π α µ π ν α are present exclusively when the collisional kernel C(f) is non-linear in the distribution function f [81]. In the case of RTA ϕ 1 = ϕ 3 = ϕ 6 = ϕ 7 = 0 [65, 67]. In the case when the system is close to the LTE state, or at late stages of the evolution (τ τ eq ), the dominating contribution to the Eqs. (3) and (4) comes from the first-order terms. In such a case the system dynamics is determined, to a good approximation, by the values of shear and bulk viscosity. However, in the early stages of the evolution when the system is highly anisotropic the second-order terms may have a comparable magnitude and, in consequence, may significantly affect the evolution of the dissipative corrections. It may be important in the context of the results of Ref. [H5], where it was shown that the IS theory fail completely in describing the Π correction. Most importantly, one should stress Eqs. (3) and (4) contain direct couplings (λ Ππ and λ ππ ) between the equations for π µν and Π, which are not present in the original IS theory, and may be responsible for the 8 For simplicity of further considerations we assume from now on that there are no conserved charges in the system. 9 Viscous corrections π µν and Π are defined by symmetric and traceless part of the energy-momentum tensor π µν T µν and traceful part Π (P + µν T µν /3), respectively. We adopt notation where A µν µν αβ Aαβ, with µν αβ ( µ α ν β + µ β ν α)/2 µν αβ /3, and µν g µν u µ u ν. In Eqs. (3)-(4) we also used the definition of the vorticity tensor ω µν ( µ u ν ν u µ )/2, shear tensor σ µν µ u ν, expansion scalar θ µ u µ, and the proper-time derivative ( ) d/dτ. In the above equations u µ is the fluid four-velocity and µ ν µ ν projected gradient. 19

21 faulty description within IS approach. These couplings are also present in other approaches [82, 83], however their role was ignored till now. The main objective of Refs. [H6-H7] was to determine the role of couplings λ Ππ and λ ππ in the description of the bulk pressure Π and verify the arguments for neglecting them by most of the practitioners. Using exact quasi-analytic solutions of the Boltzmann kinetic equation (see Refs. [H3- H5]) in Refs. [H6-H7] it was shown that more systematic and consistent formulations of viscous fluid hydrodynamics (DNMR formalism [64, 65] and CE method [66, 67]), or the alternative formulation within the anisotropic hydrodynamics [1 11] give significantly better agreement with the kinetic theory equations than the standard IS formalism. Moreover, for the first time it was shown explicite that the systematic inclusion of the second-order transport coefficients in the equations of viscous fluid hydrodynamics is crucial for simultaneous description of the dissipative corrections Π and π µν generated by bulk and shear viscosity, respectively. In particular, an important role of the direct couplings (λ Ππ and λ ππ ) between the evolution equations of these corrections was presented. It was also shown that the terms containing these couplings in some cases may be comparable with the first-order terms. Obtained results are an important step in understanding structure of the hydrodynamic equations based on the kinetic theory. They will allow for much more precise description of the properties of matter in HIC, in particular extraction of its bulk and shear viscosity from the data. They may be also applied to the description of astrophysics objects like the neutron stars. Moreover, in Ref. [H8] using the DNMR and CE formalisms form of the transport coefficients for quantum statistics, and consequently for QGP (assuming it is a superposition of quarks and gluons) was obtained. It was shown that in the assumed model the impact on the plasma evolution resulting from its chemical content is relatively small. Nevertheless, obtained coefficients may be used in the hydrodynamics simulations in future The signatures of anisotropy in the early stages of evolution of matter in heavy-ion collisions ([H9-H12]) The results of the microscopic models of early stages of evolution of matter in HIC clearly suggest that the system produced in these reactions is locally highly anisotropic in the momentum space (see Section and Refs. [H1-H2]). On the other hand, so far, there is no precise model informa- 20

22 tion about space-time evolution of the amplitude of these anisotropies ξ(x), as well as experimental observables, which could be used to verify model predictions 10. In the framework of anisotropic hydrodynamics it was shown [7], that typical hadronic observables are, to some extent, insensitive to the early stages of evolution, mainly due to the fact that they are determined at later times. Electromagnetic signals, i.e. photons and dileptons, are almost perfect observables since they are emitted during the whole evolution of QGP and practically they do not interact with it (α α s ), so that, once produced, they leave the collision area carrying an undisturbed information about the medium at the moment of emission. Originally the studies of the emission of electromagnetic probes were limited to the case of QGP in the LTE state. Together with the development of the theory of viscous fluid hydrodynamics in the last years there were also results of calculations taking into account the impact of the dissipative effects in QGP [85 88] within the δf correction treated in the 14-moment Grad approximation [89]. A potential problem resulting from this method is the incorrect description of the anisotropy in the large transverse momentum range which quite often leads to negative values of the distribution function and problems with determining production probability (see Section and Refs. [H3-H5]). First attempt to solve this problem was to include the anisotropy in the photon and dilepton production in the consistent way (i.e. on the level of the distribution function of the scattering particles as well as in the elements of the scattering matrix) [90], through the usage of the RS distribution function [70]. Original predictions [91, 92] were however based on the simple interpolating model of evolution of the medium in (0+1) dimensions (Bjorken flow). In the recent years it was shown however that the usage of the RS form in the kinetic equations also allows to derive the anisotropic hydrodynamics evolution equations of the medium [1 11], whose predictions, as it was shown in Refs. [H3-H7] are in better agreement with the kinetic theory results than the model used in [91, 92]. In Refs. [H9-H10] the analysis of photon and dilepton production in highly-anisotropic QGP in the leading order of the electromagnetic coupling constant O(α 2 ) was performed. In particular, in the case of dileptons the 10 The results of Ref. [84] indicate that the so called directed flow v 1 is an observable sensitive to the pressure anisotropy in the system in the early stages of evolution, however since there is no precise knowledge about the space-time rapidity dependence of the production of matter the verification of this hypothesis may be difficult. 21

23 production in the annihilation process q q γ l + l was taken into account while in the case of photons the Compton scattering q( q)g q( q)γ and the quark-antiquark annihilation q q gγ processes were included. The study goes significantly beyond the scope of the previous works on the subject [91, 92] employing the realistic anisotropic hydrodynamics model for the evolution of the QGP and performing the calculations in (3+1)-dimensional setup. The main objective of the study was to determine the sensitivity of the produced dilepton and photon spectra to the anisotropy in the system. Obtained results indicate significant (an order of magnitude) sensitivity of the photon spectra in the range of large momenta p T 6 GeV/c (and similarly of dilepton spectra in the range of large momenta and invariant mass) to the value of anisotropy in the system at the beginning of the evolution ξ 0 ξ(τ 0 ) (where τ 0 denotes the initialization time of the hydrodynamic evolution) 11. Obtained results open the possibility to measure the amplitude of anisotropy in the HIC based on the measurement of photon and dilepton spectra in the large momentum/invariant mass range. One of the fundamental physical phenomena occuring in the QGP are the oscillations of the created color fields [40, 50] (see Refs. [H1-H2]). Certain physical properties of the QGP produced in the process of decay of these fields, in particular its anisotropy, have an effect in the modification of the frequency of these oscillations. So far such oscillations were studied assuming certain form of the evolution of the medium. In particular their evolution in the isotropic plasma (ξ(τ) 0) [46] and the anisotropic plasma in the special case of free-streaming medium (ξ(τ) = (1 + ξ 0 )(τ/τ 0 ) 2 1) [19 21] was studied. However, according to the predictions of many microscopic models of the early stages of the plasma evolution, the medium with which the fields interact is initially highly-anisotropic [12 15], while at later stages of the evolution the system undergoes gradual thermalization [24 27, 34, 35], which yields non-trivial non-analytic dependence of ξ(τ). Such a behaviour may have an important impact on the frequency of the aforementioned oscillations, and in consequence, for instance, on the modification of the emission of the electromagnetic radiation in such a system [40]. Indirect observation of such phenomena might be a potential probe of the thermalization/hydrodynamization rate in the system. 11 Due to the lack of precise information on the space-time variation of anisotropy ξ(x) at τ = τ 0 the constant initial value ξ(τ 0 ) = const. was assumed. 22

24 In Ref. [H11], the oscillations of uniform longitudinal color electric field in the dynamically evolving color-neutral anisotropic medium were studied. In the performed analysis the QGP dynamics was described with the (0+1)-dimensional evolution equations of the anisotropic hydrodynamics [1, 2], while the field fluctuations were described by the linearized classical Boltzmann Vlasov transport equations coupled to the Maxwell equations. Interestingly, results obtained for various configurations of the initial anisotropy showed that the oscillations are rather insensitive to the value of anisotropy of the medium. Despite the fact that the light mesons dominate the particle spectrum measured in HIC, due to the Debye screening effect most of the light hadrons undergo disassociation already around the pseudo-critical temperature of the phase transition T c 0.16 GeV/c, which makes them limited source of information about the physical properties of QGP. In this context the bound states of heavy quarks whose mass spectrum may be successfully described within non-relativistic models of the binding potential are promising tool. According to these models one expects sequential suppression of the heavy q q states [93] and quite significant disassociation temperatures T d T c [94]. As a result if analysed comprehensively they may serve as a valuable source of information about the QGP at all stages of the evolution of matter in HIC. In particular bottomonia Υ(1s) may survive in temperatures up to 4T c [94], which, based on the hydrodynamic fits to the experimental data, are easily accessible in the early stages of evolution of matter (τ 0 1 fm/c) in HIC at RHIC and the LHC. As it was shown in Refs. [H1-H2] precise description of the early stage of evolution in HIC requires consistent inclusion of potentially large momentum-space anisotropies (ξ 0 0). As the results of Refs. [H3-H7] show a very good approximation of the space-time evolution of the actual distribution function may be provided by the RS form and, based on it, the kinetic formulation of the anisotropic hydrodynamics [1 11]. The first predictions on the bottomonia Υ(1s) and χ b1 suppression within this framework taking into account the anisotropies in the definition of the binding potential where presented in Refs. [95, 96] using (1+1)-dimensional model of evolution of QGP. In Ref. [H12] the results on the inclusive suppression factor R AA for the Υ(1s) and Υ(2s) states produced in the s NN = 2760 GeV/c Pb-Pb collisions at the LHC were presented. This work is an extension of the 23

25 study performed in Refs. [95, 96] through the usage of the realistic (3+1)- dimensional model of QGP evolution in the framework of anisotropic hydrodynamics. Results obtained in Ref. [H12] for various values of the shear viscosity η { η bound, 3 η bound } show a very good agreement with the CMS and ALICE experimental data. The range of values of η bound is also in a good agreement with the one extracted using the light-hadron correlation data. Presented results are an important argument for the applicability of the used models to the description of the heavy-quarkonia dynamics. 24

26 2.3.9 Detailed description of publications [H1-H12] [H1] R. Ryblewski, W. Florkowski, Equilibration of anisotropic quark-gluon plasma produced by decays of color flux tubes, Physical Review D 88 (2013) 3, The main objective of Ref. [H1] was the analysis of the production, thermalization and hydrodynamization processes in the plasma produced in the color-flux-tube model [37 48]. In the study one used the Abelian dominance approximation for the color fields [49, 51 53], for which the evolution equations for quarks, antiquarks and gluons have the classical Boltzmann Vlasov form. In the evolution equations one additionally introduced terms which describe pair production through the decay of the color electric field according to the Schwinger tunnelling mechanism[37 39, 54 56], as well as introduced the effects of collisions through the inclusion of the RTA collisional terms [74]. In order to include the impact of the color currents induced in the system by the particle production on the value of the mean color field the evolution equations for the particles and Maxwell equations for the fields were solved in the self-consistent way. Aiming at the description of the early stages of the evolution in the analysis the Bjorken [75] symmetry was imposed in the system. The latter assumes the invariance of the system with respect to the Lorentz boosts in the longitudinal direction (beam direction) and the homogeneity of the system in the transverse direction. One should note here that the value of the coupling constant used in the calculations is quite large (g 5.48) which suggests that non-perturbative character of the analysed processes. Similar models to the one used in Ref. [H1] were analysed in the past [97 100], however present work contains a number of new results. In particular, for the first time in the context of thermalization and hydrodynamization one analysed the time evolution of the pressure anisotropy determined by the pressure ratio P L /P T. Moreover, by relating the relaxation time τ eq in the collisional kernels with the shear viscosity η using the Anderson Witting relation τ eq η/t [101], it was possible to relate the resulting thermalization/hydrodynamization rate with the values of η obtained from the hydrodynamic fits to the experimental data. In particular, in the study the values of shear viscosity in the range η η bound, 10 η bound were used. Initial value of the color electric field was chosen in such a way that the maximal effective temperature in the system resulting from the Landau matching condition reached the maximal values expected in the central collisions at 25