International School on: Quark-Gluon Plasma and Heavy Ion Collisions: Past, Present, Future Villa Gualino, Turino, Italy Soft Probes Christoph Blume University of Heidelberg.
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International School on: Quark-Gluon Plasma and Heavy Ion Collisions: Past, Present, Future Villa Gualino, Turino, Italy Soft Probes Christoph Blume University of Heidelberg What are Soft Probes ? Particles below a certain pt threshold (e.g. 2 GeV/c) Processes with small momentum transfer ⇒ pQCD not applicable Use effective theories, transport models, statistical models Characterize global (bulk) properties of heavy ion reactions Sensitive to the late stage of the reaction Probe hadronization features Christoph Blume Villa Gualino, Turino, 7-12 March 2011 Space-Time Diagram Freeze-Out Hadronization QGP formation Hard scatterings Incoming nuclei Christoph Blume Villa Gualino, Turino, 7-12 March 2011 Observables Temperature Strangeness Resonances Femtoscopy Correlations Flow Jets + Heavy Flavor Photons Christoph Blume Villa Gualino, Turino, 7-12 March 2011 Global Event Characteristics How much of the incoming beam energy is transformed into particle production and collective effects? ⇒ Stopping (transfer of baryon number) How many particles are produced in a collision and what energy densities can be achieved? ⇒ Charged particle multiplicities How can one define the centrality of a reaction? ⇒ Zero degree energy, multiplicities, ... Christoph Blume Villa Gualino, Turino, 7-12 March 2011 Femtoscopy What is the size of the particle emitting fireball? What are its dynamic properties? ⇒ Evidence for transverse expansion What is the lifetime of the fireball? ⇒ Freeze-out time ⇒ Emission duration Christoph Blume Villa Gualino, Turino, 7-12 March 2011 Stopping Baryon-Number Distributions Lower energies: yP yT y y y0 Christoph Blume Higher energies: yP yT y y’p y’T y y0 Villa Gualino, Turino, 7-12 March 2011 How to Measure Baryon-Number Distributions Net-proton distributions: Protons - Antiprotons - = Other contributions (neutrons, hyperons) usually ignored (difficult to measure) Christoph Blume Villa Gualino, Turino, 7-12 March 2011 Energy Dependence of Net-Protons BRAHMS: PRL93, 102301 (2004) Christoph Blume Villa Gualino, Turino, 7-12 March 2011 Energy Dependence of y RHIC (sNN = 200 GeV): E = 25.7 ± 2.1 TeV E/Nucleon = 72.0 ± 6.0 GeV Rapidity shift: Christoph Blume Energy loss: Villa Gualino, Turino, 7-12 March 2011 Inelastic Energy per NN Collision Central data Energy of single net-baryon: Christoph Blume Total inelastic energy per NN collision: Villa Gualino, Turino, 7-12 March 2011 Inelasticity of Heavy Ion Collisions Central data p+p Inelasticity: Christoph Blume ⇒ ≈ 70% of available energy is transformed into particle production and expansion of fireball (p+p ≈ 50%) Villa Gualino, Turino, 7-12 March 2011 Net-protons: 3 valence Quarks (uud ) dn/dy (a.u.) Rapidity Distributions of Baryons Central Pb+Pb, 158A GeV Net s: 2 valence (ud ) + 1 produced Quark (s ) Net s: 1 valence (d ) + 2 produced Quarks (ss ) Omegas: 3 produced Quarks (sss ) y Christoph Blume Villa Gualino, Turino, 7-12 March 2011 Multiplicities Charged Particle Multiplicities Very simple observable “Just” need to count tracks 1st ALICE paper a week after beginning of heavy ion data taking But can already kill a lot of models ... Christoph Blume Villa Gualino, Turino, 7-12 March 2011 Charged Particle Multiplicity Densities at Mid-Rapidity central A+A ALICE: PRL105, 252301 (2010) Christoph Blume Villa Gualino, Turino, 7-12 March 2011 Model Comparisons Extrapolation QCD based MC models Initial gluon density saturation ALICE: PRL105, 252301 (2010) Christoph Blume Villa Gualino, Turino, 7-12 March 2011 Energy Density in Heavy Ion Collisions (Bjørken) Before the collision: Nucleus A Nucleus B After the collision: Nucleus B’ PRD27, 140 (1983) Nucleus A’ Region of maximal energy deposition Connection between spatial coordinate z and measured rapidity y for a given produced particle: Assuming a constant formation time: Christoph Blume Villa Gualino, Turino, 7-12 March 2011 Energy Density in Heavy Ion Collisions (Bjørken) (II) Volume in region of maximal energy density: Particle density at formation time τ0: Energy density at formation time τ0: ⇒ Christoph Blume Villa Gualino, Turino, 7-12 March 2011 Energy Density in Heavy Ion Collisions (Bjørken) (III) Estimates of experimentally achieved energy densities: SPS (sNN = 17.3 GeV): RHIC (sNN = 200 GeV): LHC (sNN = 2.76 TeV): 0 3 GeV/fm3 0 6 GeV/fm3 0 ≥ 18 GeV/fm3 Compare to critical energy density for QGP formation (lattice QCD): 0 0,7 GeV/fm3 Christoph Blume Villa Gualino, Turino, 7-12 March 2011 Measurement of Event Centrality (Example ALICE) Spectator Fireball Participants Spectator Rapidity V0 Christoph Blume Zero Degree Calorimeter Villa Gualino, Turino, 7-12 March 2011 Centrality Selection Christoph Blume Villa Gualino, Turino, 7-12 March 2011 Centrality Dependence of Charged Multiplicities ALICE: PRL106, 032301 (2011) Christoph Blume Villa Gualino, Turino, 7-12 March 2011 Model Comparisons ALICE: PRL106, 032301 (2011) Christoph Blume Villa Gualino, Turino, 7-12 March 2011 Femtoscopy Narrabri Interferometer, Australia Robert Hanbury Brown + Richard Q. Twiss Christoph Blume Villa Gualino, Turino, 7-12 March 2011 Narrabri Interferometer, Australia Christoph Blume Villa Gualino, Turino, 7-12 March 2011 HBT Correlation Function 2-Photon correlation function: Distance d between detectors ⇒ Enhancement due to Bose-Einstein statistics of photons Christoph Blume Villa Gualino, Turino, 7-12 March 2011 Goldhaber-Goldhaber-Lee-Pais (GGLP-)Effect (1959) Christoph Blume Villa Gualino, Turino, 7-12 March 2011 Bose-Einstein Correlations in Heavy Ion Physics Width of correlation function is inversely proportional to the size of the particle emitting source ⇒ Measurement of fireball size in heavy ion reactions Information on source dynamics ⇒ Transverse expansion ⇒ Lifetime ⇒ Emission duration Literature: U.A. Wiedemann and U. Heinz, Phys.Rept. 319, (1999) M.A. Lisa and S. Pratt, arXiv:0811.1352 Christoph Blume Villa Gualino, Turino, 7-12 March 2011 Quantum Correlations (Bose Einstein) Source Q : Single particle wave function: Amplitude Phase Propagation x → x’ Coherent source: f (x) have fixed relation to each other for all x Chaotic source: f (x) are randomly distributed Christoph Blume Villa Gualino, Turino, 7-12 March 2011 Quantum Correlations (Bose Einstein) (II) Total source Q : sum over all emission points x : Probability to observe one particle: = 0 for chaotic source Density of emission points: Christoph Blume Villa Gualino, Turino, 7-12 March 2011 Quantum Correlations (Bose Einstein) (III) Source Q : Pair wave function: Christoph Blume Villa Gualino, Turino, 7-12 March 2011 Quantum Correlations (Bose Einstein) (IV) Probability to observe a pair with k1 and k2 emitted from source Q : Christoph Blume Villa Gualino, Turino, 7-12 March 2011 Quantum Correlations (Bose Einstein) (V) Relative momentum q = k1 – k2 Effective emission distribution: Fourier transformed distribution Correlation function: Christoph Blume Villa Gualino, Turino, 7-12 March 2011 General 2-Particle Correlations Identical bosons: ⇒ enhancement for small q Gaussian static source: ⇒ q Identical fermions: ⇒ depletion for small q Christoph Blume Villa Gualino, Turino, 7-12 March 2011 Interactions Coulomb interaction: All charged particles (e.g. π- π-) Usually corrected for or taken into account in fit in the case of Bose-Einstein correlations (⇒ Gamow-factor) Strong interaction: Can be neglected for pions, but affects heavier particles (e.g. kaons) Main influence in the case of baryon-baryon correlations (e.g. pp) Christoph Blume Villa Gualino, Turino, 7-12 March 2011 Dynamical Sources Particle sources expand Differently in longitudinal and transverse direction ⇒ 3-dimensional radius parameters Yano-Koonin-Podgoretskii (YKP) Bertsch-Pratt (BP) Interpretation of radius parameter as source size meaningless ⇒ Lengths of homogeneity Radius parameter depend on transverse momentum (kt) of the pairs Flow introduces space momentum correlations Also: resonance decays, jets, ... Christoph Blume Villa Gualino, Turino, 7-12 March 2011 Bertsch-Pratt Parametrisation 3-dimensional parametrization: Long: defined by beam-axis Mixed term vanishes at mid-rapidity Christoph Blume Villa Gualino, Turino, 7-12 March 2011 Bertsch-Pratt Parametrisation high mass or mT low mass or mT M.A. Lisa and S. Pratt, arXiv:0811.1352 Christoph Blume Villa Gualino, Turino, 7-12 March 2011 Radius Parameters for an Expanding Source Rlong: Proportional to thermal ,,Freeze-Out”-time f (Y. Sinyukov). Tf: freeze-out temperature mT: transverse mass of the pair Rside: Sensitive to transverse expansions-velocity T (U. Heinz, B. Tomasik, U. Wiedemann) RGeo: Geometrical, static radius Rout: Sensitive to emission duration Christoph Blume Villa Gualino, Turino, 7-12 March 2011 Entries How to Measure Two-Particle Correlations m real pairs S Entries qinv = n uncorrelated pairs from event mixing B qinv Christoph Blume Villa Gualino, Turino, 7-12 March 2011 Correlation Functions (Example) NA49: central Pb+Pb @ 158A GeV, PRC77, 064908 (2008) Christoph Blume Villa Gualino, Turino, 7-12 March 2011 kt-Dependence of Radius Parameters Central Pb+Pb @ 158A GeV Christoph Blume Villa Gualino, Turino, 7-12 March 2011 Longitudinal Expansion from Bose-Einstein Correlations > 15% 10 - 15% 5 - 10% NA45: Pb+Pb @ 158A GeV, NPA714, 124 (2003) Christoph Blume Villa Gualino, Turino, 7-12 March 2011 < 5% Transverse Expansion from Bose-Einstein Correlations > 15% 10 - 15% 5 - 10% NA45: Pb+Pb @ 158A GeV, NPA714, 124 (2003) Christoph Blume Villa Gualino, Turino, 7-12 March 2011 < 5% Combination of Bose-Einstein Correlations and Spectra Bose-Einstein Corr.: Spectra: EPJ C2, 661 (1998) Christoph Blume Villa Gualino, Turino, 7-12 March 2011 Energy Dependence of Radius Parameter kt = 0.2 GeV PRC77, 064908 (2008) Christoph Blume Villa Gualino, Turino, 7-12 March 2011 dNch/dη (Energy) Dependence of Radius Parameter ALICE: PLB696, 328 (2011) Christoph Blume Villa Gualino, Turino, 7-12 March 2011 dNch/dη (Energy) Dependence of Freeze-Out Time ALICE: PLB696, 328 (2011) Christoph Blume Villa Gualino, Turino, 7-12 March 2011 Other Two-Boson Correlations: Kaons long out side K+ K- NA49: PLB557, 157 (2003) Christoph Blume Villa Gualino, Turino, 7-12 March 2011 Two Fermion Correlations: Proton – Proton Fermi-Dirac statistics Coulomb interaction Strong interaction (2He res.) Christoph Blume ⇒ anti-correlation for small q ⇒ anti-correlation for small q ⇒ enhancement Villa Gualino, Turino, 7-12 March 2011 More Exotic Correlations ... STAR: PRC74, 064906 (2006) Christoph Blume NA49: CERN-PH-EP-DRAFT-NA49-2011-001 Villa Gualino, Turino, 7-12 March 2011 Different Particle Correlations Compared STAR: Au+Au, √sNN = 200 GeV M.A. Lisa and S. Pratt, arXiv:0811.1352 Christoph Blume Villa Gualino, Turino, 7-12 March 2011 Soft Probes I Heavy ion collisions are very effective in translating beam energy into particle production, collective effects ⇒ 70% of incoming energy (stopping) Very high energy densities can be achieved ≥ 18 GeV/fm3 @ LHC (Bjorken estimate) Size of the fireball @ LHC from Bose-Einstein correlations: V ≈ 300 fm3 Freeze-Out times τ ≥ 10 fm/c Christoph Blume Villa Gualino, Turino, 7-12 March 2011 Observables Temperature Strangeness Resonances Femtoscopy Correlations Flow Jets + Heavy Flavor Photons Christoph Blume Villa Gualino, Turino, 7-12 March 2011 Energy Dependence of Net-Protons Christoph Blume Villa Gualino, Turino, 7-12 March 2011 Kinematics (I) Center-of-mass energy in nucleon-nucleon system: ECM sNN E1 E 2 2 w ith: sNN P1 P2 2 p1 p 2 2 ,P 4 - momentum One particle in rest (fixed target): 1/ 2 E CM m12 m22 2E1 E 2 1 1 2 cos m12 m22 2E1,lab m2 1/ 2 Christoph Blume Villa Gualino, Turino, 7-12 March 2011 Kinematics (II): Transverse Direction Beam axis = z-axis Transverse spectra are Lorentz-invariant! Transverse momentum: pt p x2 p y2 Transverse mass: mt pt2 m02 , m0 rest mass xT: xT pt ptmax 2pt sN N Christoph Blume Villa Gualino, Turino, 7-12 March 2011 m 0 s N N Kinematics (III): Longitudinal Direction Feynman-x: x F pz* pz*,max 2pz* Properties: sN N m 0 s N N Orthogonal to px, py Not Lorentz-invariant Rapidity: 1 E pz y 2 E pz Properties: E pz ln mt p tanh1 z E Not orthogonal to px, py Not Lorentz-invariant, but shape of distributions does not change Christoph Blume Villa Gualino, Turino, 7-12 March 2011 Kinematics (IV): Longitudinal Direction Pseudorapidity: 1 p pz ln tan 2 p pz 2 Properties: Similar to rapidity, but shape of distributions depends on Lorentz-system Requires only measurement of polar angle θ (no mass) Important relations: E mt cosh y p pt cosh p z mt sinh y p z pt sinh Christoph Blume dpz mt cosh y E dy Villa Gualino, Turino, 7-12 March 2011 Rapidity Feynman-x 2p z* xF sN N 2mt sinh y * sN N Christoph Blume Villa Gualino, Turino, 7-12 March 2011 Comparison: Feynman-x and Rapidity _ pp → p (p) + X @ 158 GeV Christoph Blume Villa Gualino, Turino, 7-12 March 2011 Comparison: Feynman-x and Rapidity pp → π+ (π-) + X @ 158 GeV Christoph Blume Villa Gualino, Turino, 7-12 March 2011 Rapidity Pseudorapidity Rapidity Pions Pseudorapidity y/ m 02 dN dN 1 2 d dp t mt cosh 2 y dy dp t Christoph Blume Villa Gualino, Turino, 7-12 March 2011 Kinematics (V): Invariant Cross Section Lorentz-invariant values: dp x dpy Differential cross section: d d E since: dpx dpy dpz dpx dpy dy 3 dpz E 3 dy dpz E d 3 df dy pt dpt 1 1 d 2 2 pt dy dpt azimuthal sym. d 2 dy dpt2 1 Christoph Blume Villa Gualino, Turino, 7-12 March 2011 systems