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Local Bjorken NON -Scaling, the Twisted sQGP and CGC Initial State

Local Bjorken NON -Scaling, the Twisted sQGP and CGC Initial State. Azfar Adil Nuclear Theory Group Columbia University. Adil & Gyulassy, nucl-th/0505004, (Accepted in PRC) Adil & Gyulassy, In Preparation (CGC). Outline of Presentation. Local Bjorken Scaling Violations

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Local Bjorken NON -Scaling, the Twisted sQGP and CGC Initial State

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  1. Local Bjorken NON-Scaling, the Twisted sQGP and CGC Initial State Azfar Adil Nuclear Theory Group Columbia University Adil & Gyulassy, nucl-th/0505004, (Accepted in PRC) Adil & Gyulassy, In Preparation (CGC) Quark Matter 2005

  2. Outline of Presentation • Local Bjorken Scaling Violations • Rapidity “Triangle” • BGK Model • Local Scaling Violation Effects in A-A • RAA(,,b) • Rotation and Dynamical Twists • Moments and Flow • Adjustments due to CGC • Twisted Jets • Test for CGC • Conclusions Quark Matter 2005

  3. I. Nuclear Geometry and Local Bjorken Scaling Violations Quark Matter 2005

  4. The p-A “Triangle”-BGK Model • Low pT particles are produced in  space as a “triangle” • Height  A ~ A1/3 • Nucleon excitation at yi, uniform • Slope  = O(A1/3/log(s)) • RHIC  ~ 0.45, LHC ~  0.28 Figure from Brodsky, Gunion, Kuhn 1977. Quark Matter 2005

  5. And It Exists!!! • Monte Carlo event generators such as HIJING have QCD dynamics built in • The multiplicity seen in the RHIC d-A experiment has just this “triangle/trapezoid” • The shape is apparent if we look at it as a ratio Quark Matter 2005

  6. Implementation for A+B INTRINSIC LOCAL BJORKEN SCALING VIOLATION O(A1/3/log(s)) • Approximate local participant density with BGK • Can get global multiplicity • Note global multiplicity is boost invariant for A = B but not local density • Binary un-twisted Quark Matter 2005

  7. II. Local Geometry and Dynamic Effects in A-A Quark Matter 2005

  8. Our Participant Model • Distribution “inspired by” BGK model • Exponential envelope inserted to model RHIC multiplicity • Parameters set to RHIC central A-A • C ~ 1.6 • Y ~ 5 •  ~ 3 BRAHMS charged pion data (nucl-ex\0403050) Quark Matter 2005

  9. A Closer Look at Local Density • Contour Plots show particular properties of the local density • Rotation around y - axis • Zero effect for zero impact parameter • More quantitatively shown in second figure • Shift can be clearly seen • Drop due to overall exponential envelope is visible • Similar geometries studied by Hirano & Heinz (dynamical firestreak) Green - 10% , Blue - 50% , Red - 90% Quark Matter 2005

  10. III. Tomographic Probe of Geometry Quark Matter 2005

  11. How to use Tomography • Different rapidity regions effected by different initial nucleii (as seen from BGK model) • Asymmetry apparent in Participant density (rotation around y-axis) • Binary density unaffected (symmetric) • Asymmetry can be probed via jet quenching • Long range rapidity anti correlations can be recorded. • Note : CGC complicates matters, stay tuned. Quark Matter 2005

  12. || = 4 RAA = RAA(0) - RAA() || = 2 0  2 RAA vs. Azimuth and Rapidity • Nuclear Modification Factor is used to track nuclear effects • Calculated using Drees, Feng, Jia et al. •  ~ 0.25 Quark Matter 2005

  13. v2 v1 3 X v3 3 X v4 What about the Moments? • Decompose RAA into fourier moments • Moments increase in magnitude with increasing asymmetry • Higher moments increase in significance with larger b and  Quark Matter 2005

  14. IV. Effects of the CGC Quark Matter 2005

  15. Participant or Binary? • CGC does not care, only one distribution • Unintegrated distributions depend on QSAT (KLN Model) • QSAT determined using thickness function • Free parameters are normalizations of xG and dNg/dy • Set to make dNg/dy ~ 1000 at midrapidity, b =0 • Set to make Q2SAT,A/B ~ 2 GeV2 at midrapidity, b =0 • Model similar to the one used by Hirano & Nara Quark Matter 2005

  16. The Local CGC Distribution CGC Figures show <x> in fm as function of pT and  CGC affects the high pT part as well (unlike BGK), generates “fish diagrams” Quark Matter 2005

  17. RAA < 0 RAA < 0 RAA > 0 RAA > 0 Opposite Tomographic Twist Use RAA(pT,) = RAA(pT, ,0)-RAA(pT, ,) to probe higher twist for higher pT RAA changes sign both as a function of pT and  Quark Matter 2005

  18. RAA Calculations • figure at b = 9 fm • There is a finite rapidity at which the RAA flips sign, lower rapidity for higher pT • Sign flip and dip important test for CGC, not present in BGK and independent of magnitude Quark Matter 2005

  19. Conclusions • Bjorken Scaling Violation is an important effect in A-A • A well known effect (BGK) • Has observable repercussions for tomography • Including BGK effects leads to • Rotation of Participant Density • Long Range Dynamical Anti Correlations • Specific evolution of fourier moments • CGC Initial State has Non-trivial Implications • High pT matter is also “twisted” • max dependence probes material edge • Sign flip of RAA proposed as signature of CGC initial state Quark Matter 2005

  20. Acknowledgements I would like to thank the following people for their support and valuable discussions (in alphabetical order): A. Accardi, M. Djordjevic, M. Gyulassy, T. Hirano, W. Horowitz, S. Wicks Quark Matter 2005

  21. Bonus Slides Quark Matter 2005

  22. Bjorken NON Scaling at RHIC From hep-th/0410017 • Bjorken Scaling only good when parameter A1/3/log(s) =   1 • At RHIC  ~ 0.45, even at LHC will be ~ 0.28 • Something not right in theory vs. data for v2 off mid rapidity • Lets to look at whether any of this violation is from geometry Details and future of hydro at RHIC Tetsufumi Hirano Quark Matter 2005

  23. Opacity Line Integral • Opacity defined as a line integral over local participant density • (x0,y0) origination point •  = -1,0,1 • We can average over geometrical fluctuations Quark Matter 2005

  24. RAA from Another Perspective b = 6 Fm b = 6 Fm  = 2  = -2 • Try to track asymmetry in Polar Plots • Measure using Octupole Twist ‘3’ • Long range anti-correlation over rapidity • Dynamic effect due to long range anti-correlations in geometry Quark Matter 2005

  25. Octupole Twist Evolution • Evolution with rapidity and impact parameter true prediction • As one increases rapidity there is an increasing Octupole Twist • Dynamic effect of a larger transverse displacement due to rotation around y-axis • A simpler observable is RAA = RAA(0)-RAA() Quark Matter 2005

  26. The Local CGC Distribution Figures show <x> in fm as function of pT and  CGC affects the high pT part as well, generates “fish diagrams” The “tail” of the diagram signifies higher pT getting more twisted after a threshold, probe of “edge” effects Quark Matter 2005

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