# Presentation: 123920

## Directed Flow in Au+Au Collisions

- Markus D. Oldenburg
- Lawrence Berkeley National Laboratory
- Probing QCD with High Energy Nuclear Collisions
- Hirschegg, Austria, January 2005

## Overview

- Introduction
- Model Predictions for Directed Flow
- Measurements & Results
- Model comparisons to data
- Summary and Outlook

## Anisotropic Flow

**v****1****: “directed flow”**
**v****2****: “elliptic flow”**

-  peripheral collisions produce an asymmetric particle source in coordinate space

-  spatial
-   anisotropy
-  momentum
-     anisotropy
-  sensitive to    the EoS

-  Fourier decomposition of azimuthal particle distribution in momentum space yields coefficients of different order

## Antiflow of nucleons and 3rd flow component

- Antiflow of nucleons and 3rd flow component

- Au+Au, EkinLab= 8 *A *GeV

- L. P. Csernai, D. Röhrich, PLB 45 (1999), 454.

- J. Brachmann, S. Soff, A. Dumitru, H. Stöcker, J. A. Maruhn, W. Greiner, L. V. Bravina, D. H. Rischke,  PRC 61 (2000), 024909.

**QGP ******** v****1****(****y****) flat at mid-rapidity.**

- “Bounce off”: nucleons at forward rapidity show positive flow.
- If matter is close to softest point of EoS, at mid-rapidity the ellipsoid expands orthogonal to the longitudinal flow direction.

**<p****x****> (GeV/c)**

**y/y****cm**

- Softening of the EoS can occur due to a phase transition to the QGP or due to resonances and string like excitations.
- At mid-rapidity, antiflow cancels “bounce off”.
- Models with purely hadronic EoS don’t show this effect.

## Stopping and space-momentum correlation

- collective expansion of the system implies positive space-momentum correlation
- wiggle structure of v1(y) develops

- R. Snellings, H. Sorge, S. Voloshin, F. Wang, N. Xu, PRL 84 (2000), 2803.

- RQMD v2.4 (cascade mode)

- shape of wiggle depends on centrality, system size, and collision energy
- even pion v1(y) shows a wiggle structure or flatness at mid-rapidity

**No QGP necessary ******** v****1****(****y****) “wiggle”.**

## Directed flow (v1) at RHIC at 200 GeV

- Directed flow (v1) at RHIC at 200 GeV

- J. Adams *et al.* (STAR collaboration), PRL 92 (2004), 062301.

- charged particles

- shows no sign of a “wiggle” or opposite slope at mid-rapidity
- Predicted magnitude of a “wiggle” couldn’t be excluded.
- v1 signal at mid-rapidity is rather flat

## Charged particle v1(η) at 62.4 GeV

- Charged particle v1(η) at 62.4 GeV

- Three different methods:
**v****1****{3}**
**v****1****{EP****1****,EP****2****}**
**v****1****{ZDCSMD}**
- Sign of v1 is determined with spectator neutrons.
- v1 at mid-rapidity is not flat, nor does it show a “wiggle” structure

- STAR preliminary

- charged particles

## Centrality dependence of v1(η) at 62.4 GeV

- Centrality dependence of v1(η) at 62.4 GeV

- Different centrality bins show similar behavior.
- Methods agree very well.
- Most peripheral bin shows largest flow.

- STAR preliminary

- charged particles

## Centrality dependence of integrated v1

- integrated magnitude of v1 increases with impact parameter b
- The strong increase at forward rapidities (factor 3-4 going from central to peripheral collisions) is not seen at mid-rapidities.
- Note the different scale for mid-rapidity and forward rapidity results!

- midrapidity

- forward rapidity

- STAR preliminary

- charged particles

## Comparison of different beam energies

- Data shifted with respect to beam rapidity.
- good agreement at forward rapidities, which supports limiting fragmentation in this region

- STAR preliminary

- charged particles

-  NA49 data taken from:
-   C. Alt *et al.* (NA49 Collaboration), Phys. Rev. C 68 (2003), 034903.

**y****diff ****= y****200GeV**** – y****17.2,62.4GeV**
-          y200GeV  = 5.37
-          y62.4GeV = 4.20
-          y17.2GeV = 2.92

## v1 data and simulations at 62.4 GeV

- v1 data and simulations at 62.4 GeV

- All models reproduce the general features of v1 very well!
- At high η: Geometry the only driving force?
- 	[see Liu, Panitkin, Xu: PRC 59 (1999), 348]
- At mid-rapidity we see more signal than expected by the models.

- STAR preliminary

- charged particles

## RQMD simulations for 62.4 GeV I

**Hadron v****1** is very flat at mid-rapidity.

**Pion v****1** is very flat at mid-rapidity, too.
-    (There is a very small positive slope around η=0.)

**Proton v****1** shows a clear “wiggle” structure at mid-rapidity.
- The overall (= hadron) behavior of v1 gets more and more dominated by protons when going forward in pseudorapidity.

## Summary I

- Directed flow v1 of charged particles at 62.4 GeV was measured.
- The mid-rapidity region does not show a flat signal of v1. A finite and non-zero slope is detected.
- The centrality dependence of v1(η) shows a smooth decrease in the signal going from peripheral to central collisions.
- At mid-rapidity there’s no significant centrality dependence of v1 observed, while at forward rapidities directed flow increases 3-fold going from central to peripheral collisions.
- At forward rapidities our signal at 62.4 GeV agrees with (shifted) measurements at 17.2 and 200 GeV.

## Summary II

- Model predictions for the pseudorapidity dependence of v1 agree very well with our data, especially at forward rapidities.
- The very good agreement between different models indicates a purely geometric origin of the v1 signal.
- RQMD simulations show a sizeable wiggle in protons v1(η), only.
- Measurements of identified particle v1 at mid-rapidity will further constrain model predictions.
- High statistics measurement of v1 at 200 GeV to come.

## Directed flow v1 vs. transverse momentum pt

- Directed flow v1 vs. transverse momentum pt

- magnitude of v1 increases with pt and then saturates
- Note the different scale for mid-rapidity and forward rapidity results!

- STAR preliminary

- pt-dependence of v1 still awaits explanation by models!

- Backup

## Antiflow of nucleons 

- “Bounce off”: nucleons at forward rapidity show positive flow.
- If matter is close to softest point of EoS, at mid-rapidity the ellipsoid expands orthogonal to the longitudinal flow direction.
- Softening of the EoS can occur due to a phase transition to the QGP or due to resonances and string like excitations.
- At mid-rapidity, antiflow cancels “bounce off”.

- J. Brachmann, S. Soff, A. Dumitru, H. Stöcker, J. A. Maruhn, W. Greiner, L. V. Bravina, D. H. Rischke,  PRC 61 (2000), 024909.

**QGP ******** v****1****(****y****) flat at mid-rapidity.**

- Baryon density

- Au+Au, EkinLab= 8 *A *GeV

## 3rd flow component

- L. P. Csernai, D. Röhrich, PLB 45 (1999), 454.

- At lower energies straight line behavior of v1(y) was observed.
- QGP forms rather flat disk at mid-rapidity
- expansion takes place in the direction of largest pressure gradient. i.e. in the beam direction
- In peripheral collisions the disk is tilted and directed flow opposite to the “standard” direction develops.
- Models with purely hadronic EoS don’t show this effect.

- protons

**QGP ******** v****1****(****y****) flat at mid-rapidity.**

## Stopping and space-momentum correlation

- collective expansion of the system implies positive space-momentum correlation
- wiggle structure of v1(y) develops
- shape of wiggle depends on:
- centrality
- system size
- collision energy

- R. Snellings, H. Sorge, S. Voloshin, F. Wang, N. Xu, PRL 84 (2000), 2803.

## Stopping and space-momentum correlation II

- nucleons show strong positive space-momentum correlation
- pions show a positive space-_*rapidity*_ correlation (without a wiggle)
- positive space-momentum correlation makes pion v1(y) follow s1(y) and mid-rapidity
- at forward rapidities shadowing is the main source of pion v1
- depending on the strength of these two effects, even pion v1(y) shows a wiggle structure or flatness at mid-rapidity

**No QGP necessary ******** v****1****(****y****) “wiggle”.**

- √s = 200 GeV

- R. Snellings, H. Sorge, S. Voloshin, F. Wang, N. Xu, PRL 84 (2000), 2803.

## Stopping and shadowing in UrQMD

- space-momentum correlation can be addressed by rapidity dependence of v1
- (weak) negative slope of v1(y) for protons at mid-rapidity
- at forward rapidities proton v1 shows “bounce off” effect
- pions show an overall negative slope of v1(y) (shadowing at forward rapidities)

- M. Bleicher and H. Stöcker, PLB 526 (2002), 309.

**UrQMD 1.2**

**No QGP necessary ******** proton v****1****(****y****) “wiggle”.**

## RQMD simulations for 62.4 GeV II- slope of v1 at midrapidity -

- The overall (= **hadron**) slope of v1 at mid-rapidity is very small.
- It is dominated by **pions**.
**Protons** show a much larger and negative slope at mid-rapidity.

## RQMD energy scan

- √sNN = 5 GeV

- √sNN =62.4 GeV

- √sNN = 30 GeV

- √sNN = 10 GeV

## RQMD energy scan II

- √s = 5 GeV

- √s = 62.4 GeV

- √s = 30 GeV

- √s = 10 GeV