# Presentation: 542583

## Multi-particle production in HI Collisions at high energies

- Raju Venugopalan
- Brookhaven National Laboratory

**Hard Probes, June 9th-16th, 2006**

## Talk based on:

*Multiparticle production to NLO:* F. Gelis & RV,
-      hep-ph/0601209; hep-ph/0605246
*Plasma Instabilities:* P. Romatschke & RV,
-      PRL 96: 062302 (2006); hep-ph/0605045
*Work in preparation with *
*    *S. Jeon, F. Gelis, T. Lappi & P. Romatschke
* **Useful discussions with *
* *K. Kajantie, D. Kharzeev, L. McLerran, A. Mueller

## Outline of Talk

- How can one systematically compute multi-particle production at *early times* in HI collisions ?
-     ***- perturbative VS non-perturbative, ***
***       ******strong coupling VS weak coupling***
- I) Particle production to LO in the coupling
-        (but all orders in strong color currents)
-        ***- bulk features of multiplicity distribution***
-  II) Particle production to NLO in the coupling
-          (albeit, ditto, all orders in strong color currents)
-         ***-plasma instabilities, energy loss, thermalization...***

## HEAVY ION COLLISIONS IN THE CGC FRAMEWORK

**Color charge distribution**
**of light cone sources**

**Field of produced gluons**

## All such diagrams 

**All such diagrams **
**of Order O(1/g)**

**Nucleus-Nucleus Collisions...leading order graphs**

**Inclusive multiplicity to leading order in  **
**requires ****2 -> n Feynman graphs**** **
**- completely non-perturbative problem even for small g !**** **

**F. Gelis, RV**
**hep-ph/0601209**

## How do we systematically compute multi-particle 

_**production to leading order in g and beyond ?**_

**Problem can be formulated as a quantum field theory **
**with strong time dependent external sources**

## Keeping track of the g’s :

**Order of a generic diagram is given by **

**For vacuum diagrams with # of external legs n_E=0 ,**

-   **Arbitrary # n_J of sources all contribute **
**      ****at same order**

**=>**

**“****Tree level” LO diagrams of order**** **

**=>    ****NLO graphs of order**

## In standard field theory,

**For theory with time dependent sources,**

**Vacuum-Vacuum diagrams:**

## From unitarity, 

**From unitarity, **

**No simple counting of g’s for P_n even for n=1**
**P_n not Poissonian **
**However, simple power counting for average mult.**

## I) Leading order: O (1 / g^2) 

**Obtained by solving classical equations - result known**
** ****to all orders in (gj)^n but leading order in g!**

**Krasnitz, RV; **
**Krasnitz, Nara, RV;**
**Lappi**

## from solving Yang-Mills Equations for two nuclei

**from solving Yang-Mills Equations for two nuclei**

**Kovner,McLerran,Weigert**

**Boost invariance**
**=> 2+1 -D dynamics**

## z

**Before collision: ****Random Electric & Magnetic **
**(non-Abelian) Weizacker-Williams fields **
**in the plane of  the fast moving nucleus**

## Longitudinal E and B fields created right 

**Longitudinal E and B fields created right **
**after the collision - non-zero  **
**Chern-Simons charge**** generated**

**Kharzeev,Krasnitz,RV; Lappi, McLerran**

**After collision:**

## Gluon Multiplicity

- # dists. are infrared finite

**Krasnitz + RV, PRL 87, 192302 (2001)**

## Predictions for Au+Au multiplicity at RHIC

**Predictions for Au+Au multiplicity at RHIC**

- Krasnitz, RV

**Eskola, QM 2001**

##  Successful KLN phenomenology for multiplicities at RHIC

** ****Successful KLN phenomenology for multiplicities at RHIC**

- Kharzeev,Levin,Nardi

## Glasma = Melting CGC to QGP

- L. McLerran, T. Ludlam,
- Physics Today

## +

**+**

**Very similar to Schwinger mechanism in QED for **
**non-perturbative production of e^+ - e^- pairs**

**Analogous computation for ****chromo-electric**** background **
** ****Nayak (+ Van Nieuwenhuizen + Cooper)**

**- important for thermalization ?**

**Kharzeev, Tuchin**

## Ramifications ?

**Remarkably, ****both**** terms can be computed**
** ****by solving small fluctuations EOM with **
**retarded**** boundary conditions-**
**NLO calculations feasible in HI collisions!**

**Gelis & RV**

**Ramifications ?**

## In QCD, for example, 

**2**

**Relation to energy**
**loss ? **
**Gyulassy-Wang, **
**BDMPS-****Z****-SW, DGLV, AMY**
**Would include **
**both**** radiative and **
**collisional contributions **
**at ****early**** times**

## Pair production: solve Dirac equation in background field of 

- Pair production: solve Dirac equation in background field of
- two nuclei...

**Gelis,Kajantie,Lappi PRL 2005**

**Ratio of quarks to glue **
**roughly consistent **
**with a chemically equilibrated QGP**

## Relation to instabilities - violations of boost invariance ?

**Boost invariance is **_**never**_** realized:**
**a) Nuclei always have a finite width at finite energies**
**b) Small x quantum fluctuations cause violations of **
**    ****boost invariance that are of order unity over **
**     **

**FIRST TRY****: Perform ****3+1-D**** numerical simulations **
**of Yang-Mills equations for Glasma exploding **
**into the vacuum- ****SIMILAR TO PART OF NLO COMPUTATION**

**Romatsche + RV**

## Weibel instability even for very small 

**violations of boost invariance (3+1 -D YM dynamics)**

**Romatschke, RV**
**PRL 96 (2006) 062302**

- For an expanding system,

## ~ 2 * prediction from HTL kinetic theory

**~ 2 * prediction from HTL kinetic theory**

**Growth rate proportional to plasmon mass...**

## Instability saturates at late times-possible 

**Instability saturates at late times-possible **
**non-Abelian saturation of modes ?**

## Distribution of unstable modes also similar 

**Distribution of unstable modes also similar **
**to kinetic theory**

**Arnold, Lenaghan, Moore, Yaffe**
**Romatschke, Strickland, Rebhan**

## Very rapid growth in max. frequency when modes of 

**Very rapid growth in max. frequency when modes of **
**transverse magnetic field become large - ****“bending” effect ?**** **

## Statuatory Note: Effects at same order_x0001_ not included in this 

**Growth in longitudinal pressure...**

**Decrease in transverse pressure...**

**Right trends observed but too little too late... **
**also confirmed in HTL study -**** ****Romatschke-Rebhan**

_**Statuatory Note**_**: *****Effects at same order******_x0001_****** not included in this ***
***                             ******exploratory study***

## Violations of boost invariance => exploding sphalerons!

**( Kharzeev, Krasnitz, RV ;  Shuryak ;  Arnold, Moore)**

**(Very) preliminary results for very small & very large **
**Violations of boost invariance**

**(Lappi, RV)**

**- possible relevance for metastable P and CP odd states**

**(Kharzeev, Pisarski, Tytgat)**

## Summary and Outlook

**to *****systematically***** compute particle production**
**in AA collisions to ****NLO **
**Pieces of this algorithm exist: **
**     ****Pair production computation of Gelis, Lappi and **
**        ****Kajantie very similar **
**     ****Likewise, the 3+1-D computation of Romatschke **
**        ****and RV + 3+1-D computations of Lappi**

**Summary and Outlook**

##  Result should include

**     ****All LO and NLO small x evolution effects**
**     ****NLO contributions to particle production**
**      **

** ****Very relevant for studies of ****energy loss, thermalization, **
**     ****topological charge,**** at early times**
**   ****Relation to kinetic theory formulation at late times **
**      ****in progress  ****(Gelis, Jeon, RV, in preparation)**** **
**      **

## EXTRA  BACKUP SLIDES

## Dispersion

**Dispersion**
**relation:**

**Just as for a **
**Debye screening **
**mass**

## Compute components of the Energy-Momentum Tensor

## Construct model of initial conditions with fluctuations:

**i)**

**This construction explicitly satisfies Gauss’ Law**