# Presentation: 195817

##  Factorization, the Glasma & the Ridge

**Raju Venugopalan**
**Brookhaven National Laboratory**

**RBRC VISCOUS HYDRO WORKSHOP, APRIL 28TH, 2008**

## Talk based on:

-  ***High energy factorization in nucleus- nucleus collisions****,* **F. Gelis, T. Lappi & R. Venugopalan**, **arXiv:0804.2630**
-  ***Glasma flux tubes and the near side ridge phenomenon at RHIC***, **A. Dumitru, F. Gelis, L. McLerran and R. Venugopalan**,
**    ****arXiv:0804.3858**

## Talk Outline

** ****Introduction - the Glasma**
** ****Theory framework for multi-particle  production in the Glasma**
** ****Ridgeology**
**Two particle correlations in the Glasma**
**    ****- the Glasma flux tube picture**

##  Glasma 

**Glasma (\Glahs-maa\):**** **
***Noun:**** ***non-equilibrium matter **
**between Color ****Glass**** Condensate (CGC)**
**& Quark Gluon Plas****ma**** (QGP)**

**Ludlam, McLerran, Physics Today (2003****)**

## Why is the Glasma relevant ?

* **Intrinsic interest:*

***The Glasma is key to quantitative understanding ***
***of  matter produced in HI collisions***

- Glasma fields are among strongest
- Electric & Magnetic fields in nature.
- What are their properties ?

## Before the Little Bang

- Nuclear wavefunction at high energies

**Bremsstrahlung**

**Recombination**

**+**

**= Saturation:**

****** ********S****Y**

## Hadron wave-fns: universal features

** ****T. Ullrich -based on**
**Kowalski, Lappi, RV ; PRL 100, 022303 (2008)**

**C****G****C**** Effective Theory**
**= classic fields + strong **
**stochastic sources**

******S**(QS2) << 1

## How is Glasma formed in a Little Bang ?

** ****Problem: Compute particle production in field **
**    ****theories with *****strong time dependent***** sources**

## In QCD, solve Yang-Mills Eqns. for two nuclei

## Numerical Simulations of classical Glasma fields

**LO Glasma fields are boost invariant**

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

## Multiplicity to NLO 

**(=O(1) in g and all orders in (g********)****n ****)**

**+**

**Gluon pair production**

**One loop contribution**
** ****to classical field **

**Initial value problem with retarded boundary conditions**
**- can be solved on a lattice in real time**

**Gelis, RV (2006)**

**(*****a la***** Gelis,Kajantie,Lappi for Fermion pair production)**

## RG evolution for a single nucleus: JIMWLK equation

- (keeping leading log
-  divergence)

## RG evolution for 2 nuclei

**Log divergent contributions**
**crossing nucleus 1 or 2:**

**Contributions across both **
**nuclei are finite-no log **
**divergences**
**=> factorization**

## NLO and QCD Factorization

**Gelis,Lappi,RV (2008)**

**What small fluctuations go into wave fn.**
** ****and what go into particle production ?**

**Small x (JIMWLK)**
**evolution of nucleus A**
** ****-- sum (********S****Y)****n ****terms**

**Small x (JIMWLK)**
**evolution of nucleus B**
**---sum (********S****Y)****n ****terms**

## From Glasma to Plasma

** ****NLO factorization formula:**

-  **With spectrum, can compute T******** - and match to **
**     ****hydro/kinetic theory**

## Two particle correlations in the Glasma 

**Can it explain the near side ridge ?**

## Ridgeology*

- * Rudy Hwa

- Near side peak+ ridge **(from talk by J. Putschke,STAR collaboration)**

- Jet spectra

- Ridge spectra

**p****t,assoc,cut**

**p****t,assoc,cut**

- inclusive

- inclusive

- STAR preliminary

- STAR preliminary

## Evolution of mini-jet with centrality

-  Binary scaling reference followed until sharp transition at ρ ~ 2.5
-  ~30% of the hadrons in central Au+Au participate in the same-side correlation

- M. Daugherty Session IX

## Update: the ridge comes into its own

- PHOBOS: the ridge extends to very high rapidity

- PHENIX: sees a ridge

## For particles to have been emitted from the same 

**For particles to have been emitted from the same **
**Event Horizon****, causality dictates that **

**If **Y **is as large as (especially) suggested by**
**PHOBOS, correlations were formed very early**
**- in the Glasma...**

## An example of a small fluctuation spectrum...

## After a HI collision, classical fields form a 

**After a HI collision, classical fields form a **
**Glasma flux tube**** with longitudinal chromo E & B fields**

**Typical size of flux tube **
**in transverse direction is **
**1 / Q****S**

## 2 particle correlations in the Glasma (I)

- +

- =

**Leading (classical) contribution**

**Note:** *Interestingly, computing leading logs at NLO, both *
*diagrams can be expressed as the first diagram with *
*sources evolved a la JIMWLK Hamiltonian*

**Gelis, Lappi, RV**

## 2 particle correlations in the Glasma (II)

**Leading color “topologies”:**

**“****single diffractive”**

**“****interference” graph**

## 2 particle correlations in the Glasma (III)

**Suppressed color “topologies”:**

**“****single diffractive”**
**(emission from different **
**quark lines in amp. and **
**complex conjugate amp.)**

**“****double diffractive”**

## 2 particle spectrum

**Simple “Geometrical” result:**

** ******** ****4 (more accurate result requires numerical **
**soln. of YM eqns. - in progress.**

**with K_N ******** 0.3 **

## 2 particle spectrum...

**Not the whole story... particle emission from the Glasma **
**tubes is isotropic in the azimuth**
**Particles correlated by transverse flow (or at high p****T**** by **
**opacity effects) - are highly localized **
**transversely, experience same transverse boost**

## 2 particle spectrum...

**Centrality dependence of V****r**** from blast wave fits**
**Centrality dependence of Q****S**** a la Kharzeev-Nardi**

## Ridge from flowing Glasma tubes

**K****N**** ~ 0.1**

**Angular dist. **
**appears to require larger boosts,**
**or absorption by medium **
**a la Shuryak**

## Conclusions

**I.  *****Ab initio***** (NLO) calculations of the initial Glasma**
**    ****in HI collisions are becoming available**
**III. Deep connections between QCD factorization **
**     ****and turbulent thermalization **
**IV. Possible explanation of interesting 2 particle **
**     ****correlations - the near side Ridge @ RHIC**

## Extra Slides

## Some possible ridge explanations

- New approaches used in to attempt to disentangle
-  System size dependence
-  Identified particle correlation
-  Di-hadron correlation with respect to reaction plane
-  3-particle correlation

- QCD bremsstrahlung radiation boosted
- by transverse flow
- S.A.Voloshin, Phys.Lett.B. 632(2007)490
- E.Shuryak, hep-ph:0706.3531

- Broadening of quenched jets in turbulent color fields
- A.Majumder et.al
- Phys. Rev. Lett.99(2004)042301

- Recombination between thermal and shower partons  at intermediate pT
- R.C. Hwa & C.B. Chiu
- Phys. Rev. C 72 (2005) 034903

- In medium radiation and longitudinal flow push
- N.Armesto et.al Phys.Rev.Lett.
- 93(2007) 242301

- Momentum Kick Model
- C.Y. Wong  hep-ph:0712.3282

## Sharp turn-on of the ridge

- At low pT (untriggered), extension in  turns on abruptly
- Scaling between energies points to transverse particle density
- Are there signs of this in other analyses? Not clear (need to beat down v2 effect)

- =2.7

- =2.7

## Multi-particle Correlations

**Small flow in “jet”-like events**

- T: 3<pT<4 GeV
- A: 1<pT<2 GeV