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Initial Condition and geometry in Relativistic heavy-ion collisions 初始条件和截面几何

Initial Condition and geometry in Relativistic heavy-ion collisions 初始条件和截面几何. Initial Condition of nucleus-nucleus collisions Nuclear Geometry, Particle production, Saturation (Color-Glass Condensate) Cronin Effect. 许长补 ( 科大 /BNL). 常用量定义 I. Lab frame Fixed target expt. CMS frame

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Initial Condition and geometry in Relativistic heavy-ion collisions 初始条件和截面几何

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  1. Initial Condition and geometry in Relativistic heavy-ion collisions初始条件和截面几何 • Initial Condition of nucleus-nucleus collisions • Nuclear Geometry, Particle production, • Saturation (Color-Glass Condensate) • Cronin Effect 许长补 (科大/BNL)

  2. 常用量定义 I Lab frame Fixed target expt. CMS frame Collider expt. • Frames of reference (参照系) Would like particle distributions to be independent of reference frame. • Relativistic treatment is essential(相对论处理)Energy where, • Lorentz transforms projectile (highly Lorentz contracted) target CM moving CMS = Centre-of-Mass System v = 0 v = c or or and Clearly not Lorentz invariant. P. Jones Zhangbu Xu, USTC 2008 Lecture

  3. y z x beam direction 常用量定义 II • Longitudinal and transverse momentum (relative to the beam direction) • Rapidity (快度) • Pseudorapidity(赝快度) • Transverse mass Not Lorentz invariant. pTOT pT Invariant under boost along z. pL f Additive under Lorentz transformation. Useful relations Zhangbu Xu, USTC 2008 Lecture

  4. 粒子谱及其来源 Rapidity Transverse momentum Note: <pT> inceases with T Elab = 200 GeV/A CERN energy. Zhangbu Xu, USTC 2008 Lecture

  5. 粒子多重数和横动量谱 Multiplicity dominated by Geometry Centrality definitions: dNch/d, Impact Parameter, Participants ZDC cut dNh-/d|=0 = 280120 dNch/d|=0 = 567 138 hminus: <pT>=0.508GeV/c pp: 0.390GeV/c Zhangbu Xu, USTC 2008 Lecture

  6. Ingredients for Glauber Calculations Particle Data Book: W.-M. Yao et al., J. Phys. G 33,1 (2006) Fig 40.11 M. Miller et al, nucl-ex/0701025 • Assumptions: superposition of straight-line interactions of colliding nucleons简单直线上核子重叠 • 质子– 质子相互作用截面 • Probability density for nucleons: Wood-Saxon from e+A experiments 重核内核子密度分布 Zhangbu Xu, USTC 2008 Lecture

  7. Implementations of Glauber M. Miller et al, nucl-ex/0701025 • Optical Glauber • Smooth distribution assumed • Analytic overlap calculation from integration over nuclear shape functions, weighted with appropriate N-N cross-section • Monte Carlo Glauber • Randomly initialize nucleons sampling nuclear shape • At randomly selected impact parameter, allow nuclei to interact • Randomly sample probability of nucleons to interact from interaction cross-section • e.g. if distance d between nucleons is < √sint/p Zhangbu Xu, USTC 2008 Lecture

  8. g = 2.6 AGS SPS g = 9 RHIC g = 100 初始能量估算, I Energy density in CMS where • The Landau hydrodynamics Complete stopping of the nuclei in the centre-of-mass system (CMS). Applying this formula blindly, we find: • There are two problems with the Landau picture at high energy 1. Nuclei/nucleons have a limiting thickness (~1 fm) due to Fermi momentum. 2. It takes a proper time (t0 ~ 1 fm/c) after interacting before particles emerge. Zhangbu Xu, USTC 2008 Lecture

  9. The Bjorken hydrodynamics Partial transparency. Experimental results Measured ET distribution. The energy density is about the same in Pb+Pb as S+Au collisions at the same energy, but the volume is 4-5 times larger. Both well in excess of LQCD calcs. NA49 初始能量估算, II S+Au Pb+Pb J.D. Bjorken, Phys. Rev. D 27 (1983) 140 Consider a small volume element Energy contained in the slab is So the energy density becomes T. Alber et al, Phys. Rev. Lett. 75 (1995) 3814 calorimetry Zhangbu Xu, USTC 2008 Lecture

  10. 重核子碰撞的时空演化 p, K, N, … t p, K, N, … • Stages in the collision 1. Pre-equilibrium Hard parton scattering processes 2. Equilibration After t≤ 1 fm/c partons materialise and either hadronise or rescatter. 3. Thermal quark-gluon plasma Hydrodynamic expansion 4. Hadronization (phase transition) Quark coalescence + gluon fragmentation … or … String fragmentation 5. Hadron gas Hadrons continue to interact 6. Particle freeze-out • Chemical freeze-out 化学冻结 粒子数不再变化 • Thermal freeze-out热冻结不再有强相互作用 tf tf 6. t(eH) Hadron gas t(eQ) 5. t0 = th 6. Mixed phase Hadron gas t0 = tq 4. QGP 5. 3. 4. 2. 1. 1. Hadron formation. Parton formation and thermalisation. z A A a) Without QGP b) With QGP Zhangbu Xu, USTC 2008 Lecture

  11. A Pictorial View of Micro-Bangs at RHIC Huge Stretch Transverse Expansion High Temperature (?!) Nuclei pass thru each other < 1 fm/c Thin Pancakes Lorentz g=100 The Last Epoch: Final Freezeout-- Large Volume Zhangbu Xu, USTC 2008 Lecture

  12. Energy density • dN/dh~=650 <Et> = 0.5 GeV • Thermalization time: <1fm (flow) • E >5 GeV/fm3 • Phase boundary: 1 GeV/fm3 • Normal nuclear density0.16GeV/fm3 PHENIX whitepaper Zhangbu Xu, USTC 2008 Lecture

  13. Dense Gluons at small x What happens when gluons are packed densely They overlap with each other and combine with each other Effective gluons with higher momentum become weakly coupled But don’t be fooled, the over all interaction is still strong Zhangbu Xu, USTC 2008 Lecture

  14. Model Predictions I: ColorGlassCondensate(色玻璃凝结体) • Qs2 ~ s(xGA(x, Qs2))/(RA2) • dNch/d/(RA2)  Qs2/ s • dNch/d/Npart  1/ s Gluon Saturation Saturation model: J. Schaffner-Bielich, et al. nucl-th/0108048 D. Kharzeev, et al. hep-ph/0111315 Relevant Scale:Qs2dNch/d/(RA2) Zhangbu Xu, USTC 2008 Lecture

  15. Dipole picture Cross section is only related to the size Of the dipole Stasto, Golec-Biernat, Kwiecinski (2001) Zhangbu Xu, USTC 2008 Lecture

  16. Models prior to RHIC PRL 85, 3100 (2000) PRL 88, 22302 (2002) PRL 91, 052303 (2003) arXiv:nucl-ex/0405027 Particle Density near Mid-Rapidity Zhangbu Xu, USTC 2008 Lecture

  17. Gluon Saturation: Multiplicity D. Kharzeev, et al., nucl-th/0108006 Multiplicity Comparison: centrality and pseudorapidity dependence Model assumes: gluons from initial state directly converted to hadrons Zhangbu Xu, USTC 2008 Lecture

  18. Where do the projectile nucleons go? Rapidity Loss 25  1 (25  5) TeV is stopped for particle production72 GeV/N!!! D. Ouerdane, M. Murray Zhangbu Xu, USTC 2008 Lecture

  19. Particle Production Along the Beam Axis M. Murray, P. Steinberg Strong rapidity dependenceMultiplicity & flow correlated • Measured  =2.260.02 Zhangbu Xu, USTC 2008 Lecture

  20. Initial state? partonic energy loss gluon saturation Is suppression an initial or final state effect? Final state? How to discriminate? Turn off final state d+Au collisions Zhangbu Xu, USTC 2008 Lecture

  21. Inclusive Hadron RdAu Evidence from d+Au measurements for final-state suppression of high pT hadrons in Au+Au collisions at RHIC Zhangbu Xu, USTC 2008 Lecture

  22. s Cronin Data Cronin effect larger for protons compared to pions Zhangbu Xu, USTC 2008 Lecture

  23. Accardi hep-ph/0212148 Kharzeev hep-ph/0307037 Extrapolation & Predictions at RHIC Straub PRL 68(1992)452 Decrease vs Beam Energy RHIC: Px=1 1<RM<2, 2.5<PM<4.5 Zhangbu Xu, USTC 2008 Lecture

  24. y=0 As y grows Kharzeev, Kovchegov, and Tuchin, Phys. Rev. D 68 , 094013 (2003) Possible evidence of gluon saturation at forward rapidity See also J. Jalilian-Marian, Nucl. Phys. A739, 319 (2004) STAR collaboration, PRL [nucl-ex/0602011] • Observe significant rapidity dependence similar to expectations from a “toy model” of RpA within the Color Glass Condensate framework. Zhangbu Xu, USTC 2008 Lecture

  25. Initial state? gluon saturation Kharzeev hep-ph/0307037 Mono-jet from scattering over dense gluons • Gluon Saturation:Production and correlation in d+Au forward rapidity PRL 97 (2006) 152302 Zhangbu Xu, USTC 2008 Lecture

  26. Summary • Geometry is very important in Relativistic heavy ion collisions => most of it relies on Glauber model • New QCD Frontier: Color Glass Condensate Zhangbu Xu, USTC 2008 Lecture

  27. 作业题 • 金-金对撞的碰撞截面是多少? • 1cm2 • 3x10-22cm2 • 6x10-24cm2 • 4x10-26cm2 • 0 • 估计(演算)Bjorken 能量密度~4.6 GeV/fm3 at RHIC • 什么是色玻璃凝结(CGC)？它的存在依赖于粒子是否加速吗？ Zhangbu Xu, USTC 2008 Lecture

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