# Presentation: 383286

## Cronin effect and high pt suppression from Color Glass Condensate

- Kazunori Itakura
-  (SPhT, CEA/Saclay)
- based on hep-ph/0403103
- with E.Iancu and D.Triantafyllopoulos

## Terminologies

**  ****Nuclear modification factor for p(d)A collision**
-   **Cronin effect/enhancement, Cronin peak**
-   **High pt suppression**

-           a function of  **rapidity**  and **transverse momentum** pt
-               measure deviation from “collection of A nucleons R**pA **= 1”
-         R**pA**** > 1** at middle pt ~ a few GeV, the largest point of RpA
-         R**pA <  ****1** at high pt
-              Observed in AuAu and is attributed to high energy density matter
-                                                     (which will not be created in pA collisions)
-    I will use the same terminologies for a _simpler_ quantity

## Motivation (from experiments)

- Nuclear modification
-               factor
-  **-** **Cronin peak** at =0, **suppression** at =3.2
-  **-** More **enhanced** for central at =0
-    More **suppressed** for central at =3.2
-  **-** Similar results in other experiments (PHENIX, STAR, PHOBOS)

**BRAHMS data for dAu collisions at RHIC**

## Motivation (from theory)

_**Analytic studies**__** **_
-    - Cronin effect from **classical** saturation (McL-V. model)
-          **Gelis-Jalilian-Marian03      Kharzeev-Levin-McLerran02,  Kharzeev-Kovchegov-Tuchin03**
-    - High pt suppression from **quantum** evolution (**Color**** ****Glass**** ****Condensate**)
_**Numerical studies**__  _
-   - McL.-V model
-   - Balitsky-Kovchegov equation
-           **   ****Albacete, Armesto, Kovner, **
**                 ****Salgado, Wiedemann 03**
-        from top to bottom: =0 to 10

**Some theoretical analyses based on CGC**

****** ****Need to understand physics, mechanism, and detailed picture**** **

-         **Cronin peak exists at ********=0****, but**** ****rapidly disappears after evolution****.**
**         ****For ********>1, the ratio monotonically increases as a function of pt.**** **

## Our framework (I)

**Our framework (I)**

- Ratio btw p and A wavefncs

- Nuclear modification factor

## Our framework (II)

**Our framework (II)**

**BK=Balitsky-Kovchegov, **
**JIMWLK=Jalilian-Marian,Iancu,McLerran,Weigert,Leonidov,Kovner**

- Rapidity ** large in pp/pA collision
-  **small-x component** of p or A with **large gluon density**.
- Transition to larger **
-  **nonlinear quantum** **evolution eq.**** **(BK, JIMWLK eqs).
- We work in a perturbative regime
-      Q > **QCD**
- Initial condition (=0)
-    Classical saturation
-    McL-V model
- Large rapidities
-    Saturation with quantum evolution
-    Color Glass Condensate

## Cronin effect        > 1at lower energy

## Classical Saturation

**Incoherent** multiple scattering for a large nucleus (**A >> 1**)
-                    Glauber-Mueller type rescattering
- Nucleus = collection of **uncorrelated** (randomly distributed) valence quarks     color sources for a small x gluon
**Initial condition** (=0) for the quantum evolution
- Unintegrated gluon distribution
-                   : color charge squared per unit transverse area

**McLerran-Venugopalan model**

## McLerran-Venugopalan model

-  Saturation scale
-  Bremsstrahlung at high kt
-  **Saturation and twist parts**

- Bremsstrahlung

- Saturation

## Cronin effect from MV model

- Use Bremsstrahlung for a proton
- There exists the Cronin peak.
- Its height and position
-   *R**pA* ~ 0.281 ln *A*
-   *z**max* ~ 0.435
- are essentially determined by the saturation part.
-      Higher twist terms develop a peak but far away from the real position
- At large kt, the ratio goes to 1 from above (can be checked analytically via “sum-rule”)
- The Cronin effect is due to **redistribution** of small kt gluons

**1/3**

## High pt suppression        < 1at higher energy

## Quantum evolution

_**The BK equation**_ for scattering amplitude
- Includes **nonlinear effects** due to high gluon density
****** ****Color**** ****Glass**** ****Condensate**
-          as saturated and dense gluon states
**Energy dependence** of saturation scale
**Three kinematical regimes** for p and A
-  1) CGC
-  2) BFKL                                      geometric scaling
-  3) DLA                                  (double log approximation)

## Approximate solutions in each regime
 1) CGC   

 2) BFKL                                                  anomalous dimension

                         absorptive,      scaling,       scaling violation
 3) DLA                                  (double log approximation)

-  1) _**CGC**_
-  2) _**BFKL**_                                                  **anomalous dimension**
-                          absorptive,      scaling,       scaling violation
-  3) _**DLA**_                                  (double log approximation)

- Quantum evolution

## High pt suppression (I)

- - Distinguish three kinematical regimes for proton/nucleus
- - Use the approximate solutions in each domain
- - Form the ratio as a function of
- Large difference btw saturation
- scales: *Q**s**(p,y) << Q**s**(A,y)*

## High pt suppression (II)

- One can show in the linear regime (both p and A) within the saddle point approximation that the ratio                is ....
- 1) **a ****decreasing**** function of ****rapidity**
- 2) **an ****increasing**** function of ****kt**
- 3) **a ****decreasing**** function of ****A**
- where  is the BFKL kernel in the Mellin space
-     and  is the saddle point.
-  **p****A****proton evolves faster than nucleus.**
**      ****Proton: far from saturation, fast evolution**
**      ****Nucleus: already close to saturation, slow evolution**

**General arguments**

- saturation

- DLA

## Flattening of the Cronin peak

- Compare
-     **MV(A,evolved)/DLA(p)** (black) and **MV(A,unevolved)/DLA(p)** (red).
- Suppression is due to proton’s faster evolution,
-     while the shape change, the flattening, is due to nucleus evolution

## Running coupling

## Running coupling MV model

- Running coupling
- Unintegrated gluon distribution

- Integration analytically doable

- Essentially the same results for the Cronin effect

## Solution in linear regime with absorptive boundary   Airy function
        scaling regime is narrower than the BFKL regime
Saturation scale

A dependence goes away at high energy
- Difference btw p and A becomes 
  less important 
- Reach at the universal value at yinfty

But of course it approaches to 1 at kt  infty 

-         scaling regime is narrower than the BFKL regime
- Saturation scale
- A dependence goes away at high energy
- - Difference btw p and A becomes
-   less important
- - Reach at the universal value at yinfty
- But of course it approaches to 1 at kt  infty

- Quantum evolution with running coupling

## Summary

- Developed a detailed analysis of the ratio
**-** **Cronin effect** (from MV model)
-     is due to _saturation part_ of the distribution.
-     Its height and position are computable.
**-**** **Mismatch between p’s and A’s evolutions leads to
-     **High pt suppression**  (p is faster than A), and
-     **flattening of the Cronin peak** (due to A’s evolution).
**-** Running coupling case formulated
-     Nuclear *A* dependence of saturation scale goes away.
-      the ratio approaches to universal value