Local Bjorken NONScaling the Twisted s QGP and
Local Bjorken NON-Scaling, the Twisted s. QGP and CGC Initial State Azfar Adil Nuclear Theory Group Columbia University Adil & Gyulassy, nucl-th/0505004, (Accepted in PRC) Adil & Gyulassy, In Preparation (CGC) 10/29/2020 Quark Matter 2005 1
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 10/29/2020 Quark Matter 2005 2
I. Nuclear Geometry and Local Bjorken Scaling Violations 10/29/2020 Quark Matter 2005 3
The p-A “Triangle”-BGK Model • Low p. T particles are produced in space as a “triangle” – Height A ~ A 1/3 • Nucleon excitation at yi, uniform • Slope = O(A 1/3/log(s)) • RHIC ~ 0. 45, LHC ~ 0. 28 Figure from Brodsky, Gunion, Kuhn 1977. 10/29/2020 Quark Matter 2005 4
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 10/29/2020 Quark Matter 2005 5
Implementation for A+B INTRINSIC LOCAL BJORKEN SCALING VIOLATION O(A 1/3/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 10/29/2020 Quark Matter 2005 6
II. Local Geometry and Dynamic Effects in A-A 10/29/2020 Quark Matter 2005 7
Our Participant Model • Distribution “inspired by” BGK model • Exponential envelope inserted to model RHIC multiplicity • Parameters set to RHIC central A-A BRAHMS charged pion data (nucl-ex 403050) – C ~ 1. 6 – Y~5 – ~ 3 10/29/2020 Quark Matter 2005 8
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 Green - 10% , Blue - 50% , Red - 90% • 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) 10/29/2020 Quark Matter 2005 9
III. Tomographic Probe of Geometry 10/29/2020 Quark Matter 2005 10
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. 10/29/2020 Quark Matter 2005 11
RAA vs. Azimuth and Rapidity | | = 4 RAA = RAA(0) - RAA( ) • Nuclear Modification Factor is used to track nuclear effects | | = 2 • Calculated using Drees, Feng, Jia et al. – ~ 0. 25 0 10/29/2020 2 Quark Matter 2005 12
What about the Moments? v 2 • Decompose RAA into fourier moments • Moments increase in magnitude with increasing asymmetry • Higher moments increase in significance with larger b and 10/29/2020 Quark Matter 2005 v 1 3 X v 3 3 X v 4 13
IV. Effects of the CGC 10/29/2020 Quark Matter 2005 14
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 x. G and d. Ng/dy – Set to make d. Ng/dy ~ 1000 at midrapidity, b =0 – Set to make Q 2 SAT, A/B ~ 2 Ge. V 2 at midrapidity, b =0 – Model similar to the one used by Hirano & Nara 10/29/2020 Quark Matter 2005 15
The Local CGC Distribution CGC • Figures show <x> in fm as function of p. T and • CGC affects the high p. T part as well (unlike BGK), generates “fish diagrams” 10/29/2020 Quark Matter 2005 16
Opposite Tomographic Twist RAA < 0 RAA > 0 • Use RAA(p. T, ) = RAA(p. T, , 0)-RAA(p. T, , ) to probe higher twist for higher p. T • RAA changes sign both as a function of p. T and 10/29/2020 Quark Matter 2005 17
RAA Calculations • figure at b = 9 fm • There is a finite rapidity at which the RAA flips sign, lower rapidity for higher p. T • Sign flip and dip important test for CGC, not present in BGK and independent of magnitude 10/29/2020 Quark Matter 2005 18
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 p. T matter is also “twisted” – max dependence probes material edge – Sign flip of RAA proposed as signature of CGC initial state 10/29/2020 Quark Matter 2005 19
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 10/29/2020 Quark Matter 2005 20
Bonus Slides 10/29/2020 Quark Matter 2005 21
Bjorken NON Scaling at RHIC From hep-th/0410017 • Bjorken Scaling only good when parameter A 1/3/log(s) = 1 • At RHIC ~ 0. 45, even at LHC will be ~ 0. 28 • Something not right in theory vs. data for v 2 off mid rapidity • Lets to look at whether Details and future of hydro at RHIC any of this violation is Tetsufumi Hirano from geometry 10/29/2020 Quark Matter 2005 22
Opacity Line Integral • Opacity defined as a line integral over local participant density – (x 0, y 0) origination point – = -1, 0, 1 • We can average over geometrical fluctuations 10/29/2020 Quark Matter 2005 23
RAA from Another Perspective b = 6 Fm = -2 • • b = 6 Fm =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 10/29/2020 Quark Matter 2005 24
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 yaxis • A simpler observable is RAA = RAA(0)-RAA( ) 10/29/2020 Quark Matter 2005 25
The Local CGC Distribution • Figures show <x> in fm as function of p. T and • CGC affects the high p. T part as well, generates “fish diagrams” • The “tail” of the diagram signifies higher p. T getting more twisted after a threshold, probe of “edge” effects 10/29/2020 Quark Matter 2005 26
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