# Presentation: 190575

## Ridges and v2 without hydrodynamics

- Rudolph C. Hwa
- University of Oregon

- Int’nal Symposium on Multiparticle Dynamics
- Berkeley, August 2007

## Prevailing paradigm on azimuthal asymmetry in heavy-ion collisions at low pT is hydrodynamical flow.

- Calling v2 “elliptic flow” is a distinctive mark of that paradigm.

- Are there any alternatives?
- Why bother?

- What if hydrodynamics is found invalid at early times?

## Results on single-particle distributions from hydro 

- Results on single-particle distributions from hydro

- Kolb & Heinz, QGP3

- 0=0.6 fm/c (RHIC 130, 200), 0=0.8 fm/c (SPS 17)

- RHIC 130 GeV

## “Elliptic flow” -- v2

- Agree with data for pT<1.5GeV/c possible only if 0~0.6 fm/c

## Conventional wisdom

- Azimuthal anisotropy can be understood in terms of hydrodynamical flow for pT<1.5 GeV/c

- It requires fast thermalization.  0=0.6 fm/c

## Conventional wisdom         BNL-PR

-    strongly interacting QGP     	perfect liquid

- What is the direct _experimental _evidence that either verifies or falsifies the conclusion on perfect liquid?

- Not expected nor understood in QCD.

- What if 0=1-1.5 fm/c?          	If so, then the hydro results would disagree with data.			How much of sQGP and perfect liquid can still be retained?

- Instability?

## Alternative approach

-   must be sensitive to the initial configuration  (hard)
-   must be able to describe the bulk behavior   (soft)

- For pT<1.5 GeV/c (the region that hydro claims success)
- we consider semi-hard scattering:

- Semi-hard parton qT ~ 2-3 GeV/c  (0.1 fm/c) can have significant effect on thermal partons for pT<1.5 GeV/c.

## Ridgeology

## Jet structure

- Putschke, QM06

- R

- J

- ridge  R _J_et     J

## In a high pT jet, a hard- scattered parton near the surface loses energy to the medium.

- Power-law behavior is a sign of _J_et production

##  puzzle

-   distribution of associated particles shows what seems like jet structure.

- Blyth (STAR) SQM 06

## The  puzzle is solved by recognizing that the  trigger and its associated particles are all produced by the thermal partons in the ridge.

- The  puzzle is solved by recognizing that the  trigger and its associated particles are all produced by the thermal partons in the ridge.

## Jet

- Putschke, QM06

## It is a Jet-less jet.

- Ridges of low pT hadrons are there, with or without triggers, so long as there are semi-hard partons near the surface to generate enhanced thermal partons.

- _Summary of ridgeology_

-   Ridges are the recombination products of enhanced thermal 		partons stimulated by semi-hard scattering near the surface.
-   At low pT there can be ridges without Jets (peaks).

## Azimuthal Asymmetry

- Now to

- Relevant physics must be sensitive to the 	initial configuration.

- Phantom jets are produced at early times, if hard enough,  but should be soft enough so that there are many of 		them produced in each collision.

- (That is not true at large forward .)

## Initial configuration

- Each scattering sends semi-hard partons in random directions.

- If the phantom jets are soft enough, there are many of them, all restricted to || < .

- Recoil partons thermalize the bulk medium.

- Thermalization of partons takes time, but the average direction of each ridge is determined at initial time.

## Bulk

- partons

## v2

## Slide 21

## Slide 22

## Use T=45 MeV

- Use T=45 MeV

- T=0.29 GeV

- Get T”=2.12 GeV

## Slide 24

## Slide 25

## Centrality dependence

- (b)=cos-1 b/2R

- at pT=0.5 GeV/c Max[v2]=pT/T’’=0.075

## STAR:  Au-Au at 130 GeV

- PRC 66, 034904 (2002)

## sin2(b)  f() = sin(2cos-1)

- Normalized impact parameter

- =b/2R

- sin2(b)  f() = sin(2cos-1)

- f() is universal, so it should be the same for Cu-Cu and at other √s.

- STAR data on v2 for Au-Au at 130GeV, normalized to 1 at max: =1/√2

## Nouicer (PHOBOS) QM06 

- Nouicer (PHOBOS) QM06

## Proton 

## Transverse kinetic energy  EK

- pT for pion	    mT-mp for proton

- A property that is independent of the hadron species h.  T’’ is a property of the partons that recombine.

## KET Scaling 

**PHENIX preliminary**** **

**KE****T**** Scaling **

**Mesons**

**Baryons**

- R.Lacey, ETD-HIC 07

## Forward rapidity

- =0

- >0

- Mid-rapidity region

-  Semi-hard scattering involve small x partons
-  more phantom jets
-  many ridges

-  larger x partons, thus lower multiplicity
-  fewer phantom jets
-  ridge effect reduced

## Slide 34

## Conclusion

-    Azimuthal anisotropy is mainly a ridge effect. No fast thermalization or hydrodynamical flow are needed.
-    Hydrodynamics may still be applicable after some time, but it is not needed for v2, for which the relevant physics at <1 fm/c is crucial --- semi-hard scattering at qT<3.
-    For pT<1.5 GeV/c, the analysis is simple, and the result can be expressed in analytic form that agrees with data.
-    For pT>1.5 GeV/c, shower partons must be considered. Jet dominance (>3GeV/c) will saturate v2.
**   ****No part of the study suggests that the medium behaves like a perfect fluid.**

## EXTRA   SLIDES

## In peripheral collisions there are some complications.   It is harder to produce protons in the bulk because of lower density of soft partons. (remember pp collisions) Thermal parton distributions in Fuud are not factorizable. T in B(pT) is lower.

- Thus phantom jets are relatively more effective in enhancing the thermal partons for p production at large b.

- So B(pT)/R(pT) for proton is smaller than for pion

- Hence, v2(pT,b) continues to increase for (b) smaller than /4.

## How universal is			? 

- Ridge phenomenology is rudimentary, and at low pT there is no unreliable framework to do theoretical calculation.

- Enhanced thermal partons in the ridge:  T’/T=1+?

- Since the bulk T encapsules the dependences on: energy, system size, thermalization,

## v2 at all  and various s

- PHOBOS  PRL 94, 122303 (2005)

- v2 at all  and various s

- ’ ~ ln x for some <mT>

## v2  R/B decreases with increasing ’ as a function of F(x), 	thus exhibiting a scaling behavior. 

- Recombination of thermal partons in comoving frame at .

- Exponential

- Ridge due to semi-hard parton at ’>  of bulk.        R/B decreases with increasing x as a function of F(x).

- v2  R/B decreases with increasing ’ as a function of F(x), 	thus exhibiting a scaling behavior.