Beam Energy Scan at RHIC & Search for Signatures of Phase Transition and Critical Point in z-scaling approach M. Tokarev JINR, Dubna, Russia in collaboration with Yu.Panebratsev, I.Zborovský , A.Kechechyan, A.Alakhverdyants, A.Aparin BLTP, Seminar, 11.04.12, Dubna M.Tokarev
Contents Introduction BES at RHIC z- Scaling (ideas, definitions, properties,…) Self-similarity of hadron production in pp & AA Energy loss in pp & AA Signatures of phase transition & Critical Point Conclusions M.Tokarev
Motivation “Scaling” and “Universality” are concepts developed to understanding critical phenomena. Scaling means that systems near the critical points exhibiting self-similar properties are invariant under transformation of a scale. According to universality, quite different systems behave in a remarkably similar fashion near the respective critical points. Critical exponents are defined only by symmetry of interactions and dimension of the space. H.Stanley, G.Barenblatt ,… Dense, strongly-coupled matter and an almost perfect liquid with partonic collectivity has been created in HIC at RHIC. Experimental study of phase structure of QCD matter started ... STAR, PHENIX, PHOBOS, BRAHMS - White papers - Nucl. Phys. A757 (2005) USA-NSAC 2007 Long-range plan M.Tokarev
Self-similarity principle The self-similarity of a pattern means that it is similar to a part of itself. Physical description in terms of self-similarity parameters constructed as suitable combinations of some physical quantities. Self-similarity parameters (Re, Π , M ,…): Hydrodynamics Point explosion Aerodynamics Re=dU / =r(Et 2 / M=v/c d-diameter r-radius of the front wave v - velocity of medium U-velocity of the fluid c – velocity of sound E-energy of the explosion -density of the fluid t-elapsed time -density of the environment -viscosity of the fluid M.Tokarev
Thermodynamic potentials a a Scaled temperature ( , ) ( , ) G p p G p Gibbs potential G(T,p) a a ( , ) ( , ) F V F V ( ) / Helmholtz potential F(T,V) V T T T c c a a ( , ) ( , ) Internal energy U(S,V) U S V U S V S V Ferromagnetics a Enthalpy E(S,p) a ( , ) ( , ) E S p p E S p S p H V M If one of the thermodynamic potentials is a generalized homogeneous function, then all thermodynamic potentials are GHPs. Scaled density vs. scaled temperature Compressibility vs. scaled pressure Data collapse All curves of this family can be “collapsed” onto a single curve. M.Tokarev
Critical exponents Fluid systems Magnetic systems Scaled temperature ~| | c ' ( ) / T T T ~| | c V H c c ~| | ' ~| | M L G H compressibility ~| | K ' ~| | T T 2 1 G 2 G K c T T 2 V p specific heat H 2 T T 2 H G G c T G M p 2 magnetization T H H p T 2 1 G 2 1 G susceptibility p V T p T 2 V H nsion T Dynamic properties Transport of number of particles, energy, charge,… Critical exponents α , β , γ , δ , … define Transport coefficients the behavior of physics quantities a ( thermal conductivi ty ) ~ , 0 close to the Critical Point b ( shear viscosity ) ~ , 0 c ( bulk viscosity ) ~ , 0 M.Tokarev
Discontinuity of specific heat near a Critical Point Heat capacity of liquid 3 He Specific heat of liquid 4 He Superfluid transition Critical Point Critical Point 3 . 35 T C K 5 . 19 T K C H.E. Stanley, 1971 H. Choi et al., PRL 96, 125301 (2006) Near a critical point the singular part of thermo-dynamic potentials is a Generalized Homogeneous Function (GHF). The Gibbs potential is GHF of . a a ( , ) p ( , ) ( , ) G p p G p 2 2 ( / ) ( ) / c T G T ~| | T T T c V V V c c Critical exponents define the behavior of thermodynamical quantities close to the Critical Point. M.Tokarev
Defects influence upon phase transition Ferroelect ric cristals Defects smear phase transitions BaTiO 3 4 KNaC H O H O 4 4 6 2 Ferroelectric crystal ( ) CH NH COOH H SO 2 2 3 2 4 ( ) CH NH COOH H SO 2 2 3 2 4 Susceptibility Ionizing irradiatio n e Specific heat 450 energy KeV Ionizing irradi ation 11 2 3 . 5 10 /( sec) flux e cm 0 1 Doze MR Critical Point 0 49 . 2 T C C Modification of crystal properties due to directed implantation of impurities or ionizing irradiation Anomalies of the properties in the region of the phase transitions B.A.Strukov, Phase transitions,…(1996) M.Tokarev
Phase Diagram of Strongly Interacting Matter The phase diagram of strongly interacting The phase diagram of water is established nuclear matter is under study Ice III Ice X Ice XIII Phases - ? Phases ( ice I-XV, liquid, vapor ) Phase boundaries -? Phase boundaries Phase transitions - ? Phase transitions Triple Point - ? Triple Point (16) Critical Point - ? Critical Point (2) M.Tokarev
The Relativistic Heavy Ion Collider 3.83 km circumference Two separated rings 120 bunches/ring 106 ns bunch crossing time A+A, p+A, p+p Maximum Beam Energy : 500 GeV for p+p 200A GeV for Au+Au Luminosity Au+Au: 2 x 10 26 cm -2 s -1 p+p : 2 x 10 32 cm -2 s -1 Beam polarizations P=70% Nucleus-nucleus collisions (AuAu, CuCu, dAu, CuAu, UU, … √ s NN =7.7-200 GeV) Polarized proton-proton collisions M.Tokarev
Main goal of investigations in relativistic AA collisions is search for and study new state of nuclear matter …, AGS, SPS, RHIC, LHC, … Central Au-Au s 1/2 =200 GeV 200 GeV Cu+Cu 3-6% Au+Au 35-40% RHIC & STAR …, NICA, FAIR , … High energy-density and very strong interacting matter was created at RHIC. RHIC data on dN ch /d η , v 2 , R CP ,… exhibit scaling laws. What kind of interacting matter is created ? Transition to the new state of matter does not Thermodynamics, hydrodynamics, … manifest abrupt changes in observables. Phase transition, critical point, … “White papers” Self-similarty of created matter, … STAR, PHENIX, PHOBOS & BRAHMS M.Tokarev
The Solenoid Ttracker At RHIC (STAR) M.Tokarev
STAR Detector MTD EMC Barrel MRPC ToF Barrel EMC End Cap FMS BBC Roman Pots TPC FPD Phase 2 computing DAQ1000 COMPLETE Trigger and DAQ FGT Ongoing R&D HFT Upgrades M.Tokarev
Identified Particle Acceptance at STAR Au+Au 7.7 GeV Au+Au 200 GeV Au+Au 39 GeV π K p Homogeneous acceptance for all energies. M.Tokarev
Beam Energy Scan at RHIC Motivation Systematic study of AuAu collisions Search for phase transition and critical point of strongly interacting matter Elliptic & directed flow v 2 , v 1 Azimuthally-sensitive femtoscopy Fluctuation measures: <K/π>, <p/π>, <p T >, <N ch >… Search for turn-off of new phenomena seen at higher RHIC energies Constituent-quark-number scaling of v 2 Hadron suppression in central collisions R AA Ridge ( ∆φ - Δη correlations) Local parity violation STAR Collaboration: An Experimental Exploration of the QCD Phase STAR Note SN0493. Diagram: The Search for the Critcal Point Phys. Rev. C 81, 024911 (2010). and the Onset of Deconfinement Phys.At.Nucl., 2011, V .74, №5, p.769 . arXiv:1007.2613v1 [nucl ‐ ex] M.Tokarev
Beam Energy Scan Program at STAR RHIC - signatures for a phase transition - signatures for a critical point - boundary of phase diagram M.Tokarev
Central Au+Au @ 7.7 GeV Central Au+Au @ 200 GeV event in STAR TPC event in STAR TPC RHIC beam energy scan with Au+Au: √s NN = 7.7, 11.5, 19.6, 27, 39, 62, 130, 200 GeV M.Tokarev
AuAu Beam Energy Scan Program at RHIC STAR Experimental Study of the QCD Phase Diagram AuAu & 7.7 GeV and Search for the Critical Point STAR Note SN0493, Phys. Rev. C 81, 024911 (2010) STAR Run 10,11 Multiplicity distribution √ s NN MB Events B (MeV) (GeV) in Millions 5.0 550 7.7 410 4.3 11.5 300 11.7 19.6 230 35.8 27 151 70 .4 39 112 130.4 62.4 73 67 .3 130 36 200 24 M.Tokarev
Flow of nuclear matter collectivity of partonic degree of freedom M.Tokarev
Directed (v 1 ) & Elliptic (v 2 ) flow in AuAu collisions Fourier expansion of the momenta distribution Coordinate-Space 3 Ψ 1 2 cos ( r ) d N E v n Anisotropy 3 n d p 1 n cos ( ) v n Momentum-Space n r p Anisotropy 1 tan ( ) y p x AuAu & 200 GeV v 1 (y) sensitive to baryon transport, space momentum correlations and QGP formation. v 2 provides the possibility to gain information about the degree of thermalization of the hot, dense medium . The breaking of v 2 number of quark scaling will indicate a transition from partonic to hadronic degrees of freedom. M.Tokarev
NCQ scaling: Au+Au 200 & 39 GeV Flow vs. - energy - centrality - particle mass v2 of light nuclei scaled to the number of constituent quarks (NCQ) of their constituent nucleons, are consistent with NCQ scaled v2 of baryons and mesons NCQ scaling holds good for v2 of light nuclei in Au+Au 39 GeV C.Jena, CPOD 2011, November 7-11, Wuhan, China M.Tokarev
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