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Quark-Gluon Plasma – Introduction to Experiments Part - 1

Quark-Gluon Plasma – Introduction to Experiments Part - 1. Tapan Nayak VECC, Kolkata nayak@veccal.ernet.in nayak@cern.ch. Early universe. High Temperature. quark gluon plasma. critical point ?. T c. By increasing the collision energy. Temperature. colour superconductor.

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Quark-Gluon Plasma – Introduction to Experiments Part - 1

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  1. Quark-Gluon Plasma – Introduction to Experiments Part - 1 Tapan Nayak VECC, Kolkata nayak@veccal.ernet.in nayak@cern.ch ICHIC-Goa School

  2. Early universe High Temperature quark gluon plasma critical point ? Tc By increasing the collision energy Temperature colour superconductor hadrongas nucleon gas nuclei CFL r0 Neutron stars vacuum High baryon density baryon density The QCD Phase diagram • Deconfinement • Chiral symmetry restoration ICHIC-Goa School

  3. Why do we expect in a phase transition from hadronic phase to quark-gluon plasma? e/T4 Quark-gluon plasma Hadronic matter T TC Hagedorn Limiting Temperature e is energy density and T is temperature. In hadronic phase both pions and nucleons are regarded as elementary particles, and the system would have a limiting temperature, called the Hagedorn temperature (QM ’84 proceedings). This is analogous to the boiling temperature of water. At around 100deg C even if heat supplied is more, most of the heat energies are used to forming bubbles and not increasing the kinetic energies of water molecules. Similarly in hadronic matter most energies are used to forming pion bubbles. The boilng temp is of the order of pion mass. On the other hand, q-q interactions become weaker as the inter-quark distance becomes shorter (asymptotic freedom). The system behaves like free quarks and gluons. Therefore Stephan-Boltzmann law holds and there is no limiting temperature. Thus we expect a phase transition at T~TC. ICHIC-Goa School

  4. TC ~ 170 15 MeV eC ~ 0.7-1.2 GeV/fm3 e0 ~ 0.16 GeV/fm3 QCD EoS from Lattice Stephan Boltzman limits for a free Quark Gluon gas Energy Density/ (Temperature)4 T/Tc F. Karsch, Prog. Theor. Phys. Suppl. 153, 106 (2004) Recent Lattice results seem to give a value of Tc to be 190 MeV ICHIC-Goa School

  5. QCD EoS from Experiments • Energy Density from experiments: Bjorken estimation • Temperature from pT spectra of emitted particles (for example: pT spectra of f We can get some idea about the: (1) Effective degrees of freedom (thermodynamic degeneracy) at a (2) Time (t) at which matter comes to approximate thermal equilibrium and starts to behave like a hydrodynamic fluid. • Problems arise in accessing Initial conditions: • Initial Energy densities • Initial Temperatures ICHIC-Goa School

  6. pR2 Initial Energy Density – Bjorken estimation Bjorken 1983 Boost invariant hydrodynamics: t : proper time y : rapidity h : pseudo-rapdity ET: transverse energy Nch : Number of charged particles mT : transverse mass R: effective transverse radius ICHIC-Goa School

  7. 3. Rapidity distribution of transverse energy 2a. pT distributions and temperature • Pseudorapidity distribution of charged particles and photons 2b. Estimation of mean transverse mass, <mT> 4. Source size, R from HBT measurements Initial Energy Density and Temperature and T ICHIC-Goa School

  8. Kinematics: What is Rapidity? • In non-relativistic physics the Galileo law of summation of velocities is valid: • v2 = v1 + v (non-rel), • where v1 and v2 are the velocities measured in reference frames one of which moves at a velocity v with respect to the other. • In relativistic physics instead of the above, the Einstein law of summation of velocities is valid: • v2 = (v1 + v) / (1+v1v/c2)(relativistic) • This is non-additive one. This is inconvenient as difference in velocities of two particles depends on the choice of the moving reference frame. • To retain the property of additivity a new kinematic quantity – the rapidity (y) is introduced in relativistic kinematics . By definition: • y = ½ ln (c+v)/(c-v) • And with this, one can show that: y2 = y1 + y (relativistic) • Thus the difference yA – yB in rapidities of two particles in same in all moving reference frame. ICHIC-Goa School

  9. Heavy-ion Collision pT pT pT p|| p|| p|| ytarget Projectile ybeam Target dn/dy β y Pseudorapidity: Kinematics: y, h etc. Before After ytarget ybeam dn/dy y ICHIC-Goa School

  10. Zero-degreeCalorimeter Centrality Selection: participants vs. Spectators The collision geometry (i.e. the impact parameter) determines the number of nucleons that participate in the collision “Spectators” “Spectators” “Participants” • Many quantities scale with Npart • or a combination of Npart and • number of collisions, Ncoll: • Transverse Energy • Particle Multiplicity • Particle Spectra Detectors at 90o ICHIC-Goa School

  11. PHOBOS BRAHMS RHIC PHENIX STAR AGS TANDEMS Relativistic Heavy Ion Collider (RHIC)Brookhaven National Laboratory (BNL), Upton, NY v = 0.99995c = 186,000 miles/sec Au + Au at 200 GeV Animation M. Lisa ICHIC-Goa School

  12. Time Projection Chamber Magnet Coils Silicon Tracker SVT & SSD TPC Endcap & MWPC FTPCs Endcap Calorimeter Beam Beam Counters Barrel EM Calorimeter Central Trigger Barrel & TOF STAR Experiment at RHIC Not Shown: pVPDs, ZDCs, and FPDs PMD 4.2 meters TPC is at the heart of STAR ICHIC-Goa School

  13. Gas: P10 ( Ar-CH4 90%-10% ) @ 1 atm Voltage : - 28 kV at the central membrane 135 V/cm over 210 cm drift path 420 CM TPC Gas Volume & Electrostatic Field Cage Self supporting Inner Field Cage:Al on Kapton using Nomex honeycomb; 0.5% rad length ICHIC-Goa School

  14. Pixel Readout of a Pad Plane Sector A cosmic ray + deltaelectron 3 sigma threshold ICHIC-Goa School

  15. sNN = 130, 200 GeV Gold Gold (center-of-mass energy per nucleon-nucleon collision) Au on Au Event at RHIC Two-track separation 2.5 cm Momentum Resolution < 2% Space point resolution ~ 500 mm Rapidity coverage –1.8 < h < 1.8 1000’s of particles ICHIC-Goa School

  16. Hadron identification: STAR Collaboration, nucl-ex/0309012 Particle ID: Time Projection Chamber: 45 padrow, 2 meters (radius), s(dE/dx)8%, -1<<1 Multi-gap Resistive Plate Chamber TOFr: 1 tray (~1/200), s(t)=85ps ICHIC-Goa School

  17. Resonance K*(892) (770) f0(980) (1020) (1232) (1520) (1385) Decay channel K  K K p  p K  Branching Ratio % ~100 ~100 dominant 49.2 >99 22.5 88.2 Width [MeV] 50.7 150 40 to 100 4.46 ~120 15.6 35.8 Life time [fm/c] 4 1.3 40 ~1.75 13 5.6 ICHIC-Goa School

  18. f from K+ K- pairs dn/dm background subtracted m inv dn/dm K+ K- pairs same event dist. mixed event dist. m inv Particle ID using Topology & Combinatorics Secondary vertex: Ks p + p L  p + p X  L + p W  L + K g  e++e- Ks p + + p - f  K + + K - L  p + p - r  p + + p - “kinks” K  +  ICHIC-Goa School

  19. Particle Multiplicity and Pseudorapidity distributions ICHIC-Goa School

  20. 0-3% 15-20 35-40 dNch/dh (dNch/dh)/(½Npart) PHOBOS: nucl-ex/0106006 h Shapes of dNch/dh versus h (Ös = 130) PHOBOS: 3% most central collisions<Nch> = 4200  470 ICHIC-Goa School

  21. Particle production Number of charged particles as a function of pseudorapidity Extrapolation to LHC Au+Au 0-6% centrality => LHC predictions (Pb+Pb at 5.5TeV): 1100-2000 Dec 11, 2007 ICHIC-Goa School DAE Nuclear Physics Symposium, Sambalpur 21

  22. STAR RESULTS Phobos PHENIX BRAHMS WA98 Phobos WA97/NA57 NA49 E917/866 E877 Particle Density (dN/dh) vs. s1/2 Top 5% centrality ICHIC-Goa School

  23. 2a. pT distributions and temperature 2b. Estimation of mean transverse mass, <mT> ICHIC-Goa School

  24. Bose-Einstein fits mt exponential fits K- p+ Identified Particle Spectra Au+Au @ 200GeV p+, p-, K+, K- spectra versus centrality: PRL 92 (2004) 171801 ICHIC-Goa School

  25. ICHIC-Goa School

  26. Nu Xu Pressure, Flow, … • tds = dU + pdV s– entropy; p – pressure; U – energy; V – volume t = kBT, thermal energy per dof • In high-energy nuclear collisions, interaction among constituents and density distribution will lead to: • pressure gradient  collective flow number of degrees of freedom (dof) • Equation of State (EOS) • The thermalization is not required – pressure gradient only depends on thedensity gradient and interactions.  Space-time-momentum correlations! ICHIC-Goa School

  27. ud ss uud sss Hadron Spectra from RHICp+p and Au+Au collisions at 200 GeV 0-5% more central collisions Multi-strange hadron spectra are exponential in their shapes. STAR white papers - Nucl. Phys. A757, 102(2005). ICHIC-Goa School

  28. Freeze-out Systematic At freeze-out: The ‘temperature’ parameters Tfo seem to be around 100 -140 MeV. v2 continuously rise with beam energy. A clear increase in averaged velocity parameters r - increase of the ‘pressure’ in the system at RHIC. When v2 crosses zero, a plateau appears for Tfo and r at beam energy ~ 5 GeV.

  29. Slope Parameter Systematics

  30. STAR: -mesons • 200 GeV A+A collisions: • The multi-strange baryons productions ,  are enhanced in A+A collisions • The -mesonproductions are also enhanced, but may be with different trends • The enhancements are NOT due to Canonical Ensample Suppression! • PRL. 98 (2007) 062301 (nucl-ex/0606014); PRL in print, nucl-ex/ 0703033; nucl-ex/ 0705.2511

  31. Nu Xu Blast Wave Fits: Tfo vs. bT 1) p, K, and p change smoothly from peripheral to central collisions. 2) At the most central collisions, T reaches 0.6c. 3) Multi-strange particles ,  are found at higher Tfo and lower T •  light hadrons move • with higher velocity • compared to strange • hadrons • STAR: NPA715, 458c(03); PRL 92, 112301(04); 92, 182301(04). 200GeV Au + Au collisions ICHIC-Goa School

  32.  -meson Flow: Partonic Flow QM2008: J. Chen; X.B. Wang “-mesons are produced via coalescence of seemingly thermalized quarks in central Au+Au collisions. This observation implies hot and dense matter with partonic collectivity has been formed at RHIC” ICHIC-Goa School

  33. Nu Xu EoS Parameters at RHIC • In central Au+Au collisions at RHIC • - partonic freeze-out: • *Tpfo = 165 ± 10 MeV weak centrality dependence • vpfo ≥ 0.2 (c) • - hadronic freeze-out: • *Tfo = 100 ± 5 (MeV) strong centrality dependence • vfo = 0.6 ± 0.05 (c) • Systematic study are needed to understand the • centrality dependence of the EoS parameters • * Thermalization assumed ICHIC-Goa School

  34. 3. Rapidity distribution of transverse energy ICHIC-Goa School

  35. Measurement of Transverse Energy (ET) Raghunath Sahoo: Ph.D. thesis arXiv:0804.1800 [nucl-ex] Transverse energy (ET) is the energy produced transverse to the beam direction. This is generated due to the initial scattering of partonic constituents of the incoming nuclei and the rescattering of the produced partons and hadrons. Transverse phase space is ideal to study the initial conditions after the collision. Motivation:=>Estimation of the Bjorken energy density of the produced fireball thru the estimation of ET on an event by event basis to verify if a condition for deconfinement does exist. => Study of particle production mechanism =>Study of Quark-Hadron phase transitions thru fluctuation observables like ET and the ratio of it’s components. The hadronic transverse energy (EThad) is measured thru the TPC reconstructed tracks (PID and momentum information). The electromagnetic transverse energy (ETem) is measured thru the calorimeter tower hits after correcting for the hadronic contaminations. ICHIC-Goa School

  36. ET Distributions @ 62.4 GeV Au+Au Collisions Minimum-bias distribution of electromgnetic transverse energy Minimum-bias distribution of hadronic transverse energy ICHIC-Goa School

  37. STAR Preliminary Minimum-bias distribution of total transverse energy Transverse energy distribution for different centrality classes. 62.4 GeV Au+Au Collisions 62.4 GeV Au+Au Collisions Raghunath Sahoo ICHIC-Goa School

  38. STAR Preliminary The excitation function of dET/dy per participant pair from AGS to RHIC. Raghunath Sahoo • The EKRT model (based on final state Gluon saturation) underestimates the final transverse energy. ICHIC-Goa School

  39. 4. Source size, R from HBT measurements ICHIC-Goa School

  40. p1 r1 x1  source (x)‏ “b” x2 r2 p2 “a” “L” Robert Hanbury Brown and Richard Twiss HBT Intensity Interferometry Intensity interferometry has an intimate relation with Michelson amplitude interferometry Amplitude interferometry measured from detectors 1 and 2 : | A1 + A2 |2 = | A1|2 + | A2|2 + ( A1* A2 + A1 A2*) The later term in the parenthesis is the called the “fringe visibility” . Averaged over, <V2> = 2 < | A1|2| A2|2> + <A1*2A22> + <A12A2*2> The first term r.h.s above is just twice the correlation of the intensities landing in the two detectors. <V2>  2<I1I2> Debasish Das Ph.D. thesis Interference is a phenomenon associated with the superposition of two or more waves. The two-particle correlations arise from the interference of particle wave-functions and depend on whether the particles are bosons or fermions The goal of intensity interferometry is to extract the space-time information of the heavy-ion collision source from the momentum spectra which are the only measureable quantities making use of quantum statistical correlations between the pairs of identical particles. ICHIC-Goa School

  41. Courtesy of S. Bass p1 r1 x1  source (x)‏ “b” x2 r2 p2 “a” “L” The correlation function is defined as the ratio of the probability for the coincidence of p1 and p2 relative to the probability of observing p1 and p2 separately : F.T. of pion source Measurable! Probing source geometry through interferometry Correlation function constructed experimentally, C2 (q) = A (q) / B (q) (normalized to unity at large q), A (q)  is the pair distribution in momentum difference q = p2 - p1 for pairs of particles from the same event. B (q)  is the corresponding distribution for pairs of particles from different events. ICHIC-Goa School

  42. p1 r1 x1  source (x)‏ “b” x2 r2 p2 “a” “L” Au+Au R ~ 6 fm p+p R ~ 1 fm d+Au R ~ 2 fm Source geometry C2(Qinv) Qinv (GeV/c) ICHIC-Goa School

  43. if a pion is emitted, it is more likely to emit another pion with very similar momentumwhich makes the HBTeffect experimentally measuring this enhanced probability: quite challenging Measuring the Source geometry ICHIC-Goa School

  44. Rside p1 Rlong q Rlong – along beam direction p2 Rout– along “line of sight” Rout Rside –  “line of sight” Detailed source geometry Debasish Das Ph.D. thesis ICHIC-Goa School

  45. Beam energy dependence of pion HBT STAR Debasish Das Ph.D. thesis Pion rapidity density is proportional to the freezeout volume => Constant Freezeout Volume (freezeout at a constant density). ICHIC-Goa School

  46. Now finally to Bjorken Energy Density ICHIC-Goa School

  47. Compiled by Raghunath Sahoo Bjorken Energy Density: Excitation function t = 1 Bjorken Energy density increases logarithmically with center of mass energy. ICHIC-Goa School

  48. Rough Estimation for AuAu 10GeV Bjorken Energy Density – for different centralities Bjorken Energy density is unique for given centrality and beam energy and can be used as an estimator for different physics topics. ICHIC-Goa School

  49. SUMMARY • What did we try to learn today: • Measurement of charged particle multiplicity and rapidity distributions • Measurement of pT spectra and extraction of effective temperature • Radial flow and estimation of thermal temperature • Source sizes from HBT parameters • Estimation of energy density • Work in progress: Use of f for making an EoS plot • Work in progress: EoS plot from experimental estimations and comparison with lattice END OF LECTURE-1 ICHIC-Goa School

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