# Presentation: 584510

## eA Physics @ eRHIC

- Raju Venugopalan
- Brookhaven National Laboratory

- eRHIC discussion group, Oct. 18th 2006

## eRHIC at BNL

- THE PROPOSAL
- A high energy, high intensity polarized electron/positron beam facility at BNL to colliding with the existing heavy ion and polarized proton beam would significantly enhance RHIC’s ability to probe **fundamental, universal aspects of QCD**

- Main Design

- Ring Ring Option

- Linac Ring Option

## eRHIC vs. Other DIS Facilities

**New kinematic region**
- Ee = 10 GeV (~5-12 GeV variable)
- Ep = 250 GeV (~50-250 GeV variable)
- EA= 100 GeV
**Sqrt[S****ep****] = 30-100 GeV**
**Kinematic reach of eRHIC:**
**X = 10****-4**** --> 0.7 (Q****2**** > 1 GeV****2****)**
**Q****2**** = 0 --> 10****4**** GeV****2**
- Polarization of e,p  beams (~70%) and He3 beams ~30-40% polarized
- Heavy ions of ALL species at RHIC
**Luminosity Goal:**
**L(ep) ~10****33-34**** cm****-2**** sec****-1**

**eRHIC**

- DIS

## CM vs. Luminosity

**  ****eRHIC**
- Variable beam energy
- P-U ion beams
- Light ion polarization
- Huge luminosity

- eRHIC

- ELIC-Jlab

## Cross-section:

- Kinematics:

-   g_1,...g_5 - polarized structure functions in pol. e - pol. p scattering

## DIS highlights: 

-  Bjorken scaling: the parton model.
-  Scaling violations: QCD- asymptotic freedom,
-      renormalization group; precision tests of pQCD.
-  Rapid growth of gluon density at small x,  significant
-      hard diffraction.
-  Measurement of polarized structure functions: scaling
-      violations, the “spin crisis”.
-  QCD in media: the EMC effect, shadowing, color transparency,..

## How can we probe glue with a high luminosity lepton-ion

**How can we probe glue with a high luminosity lepton-ion**
**collider ?         ****Key Measurements**

-     **Precision inclusive measurements of structure functions**
**    ****-wide sweep of nuclei from Protons to Uranium**

-  **Direct (****photon-gluon fusion****) semi-inclusive and exclusive **
**  ****probes of final states**

-  **Deeply virtual Compton scattering**

* ****observables in blue will be measured for the ***_***first time***_*** in a wide ***
***   ******kinematic domain***

***- CGC/saturation models predict ***_***significant ***_***differences***
***  ******from DGLAP type pQCD models for**** Q_s > (p_t, M)*

## Lego plots a la Bjorken and Khoze et al.

**Lego plots a la Bjorken and Khoze et al.**

**Such multi-gap events can also be studied in DIS  **

**Bj, hep-ph/9601363**

## Nobel to Friedman, Kendall, Taylor

**Nobel to Friedman, Kendall, Taylor**

## Parton model

**Parton model**

** ****Parton constituents of proton **
** ****are  “quasi-free” on interaction**
** ****time scale 1/q **

## Puzzle resolved 

- in QCD

**         ****QCD         Parton model **
**     ****Logarithmic scaling violations **

## The Hadron at high energies: I

**Parton model**

**QCD-logarithmic corrections**

## “X”-QCD--RG evolution

**“****X”-QCD--RG evolution**

**“****sea” quarks**

**Valence quarks**

## DGLAP evolution: Linear RG in Q^2

**DGLAP evolution: Linear RG in Q^2**

_**D**_okshitzer-_**G**_ribov-_**L**_ipatov-_**A**_ltarelli-_**P**_arisi

- # of gluons grows rapidly at small x...

##    Coefficient functions - C - computed to NNLO for many processes, 

-    Coefficient functions - C - computed to NNLO for many processes,
-       e.g., gg -> H              Harlander, Kilgore; Ravindran,Van Neerven,Smith; ...

-   Splitting functions -P - computed to 3-loops recently!
-                                                           Moch, Vermaseren, Vogt

- +  higher twist (power suppressed)
-    contributions...

-  STRUCTURE OF HIGHER ORDER CONTRIBUTIONS IN DIS

## increasing

- But... the phase space density decreases
- -the proton becomes more dilute

**Resolving the hadron **
**-DGLAP evolution**

## RG evolution...

## Gluon density saturates at f=

- - Large x

- - Small x

**Resolving the hadron**
**-BFKL evolution**

## Proton

**Proton**

-  **Proton is a dense many body system at high energies**

**QCD Bremsstrahlung**

## Mechanism for  parton saturation: 

**Competition  between  “attractive”  bremsstrahlung**
**and “repulsive”  recombination  effects.**

- Maximal phase space density =>

##    Higher  twists (power suppressed-in         )   

- beyond the OPE- at small x.

-    Higher  twists (power suppressed-in         )
-        are important when:

-    Leading twist “shadowing’’ of these contributions can
-        extend up to                               at small x.

## F_L is a positive definite quantity- more sensitive to higher twists than F_2 ?

**F_L is a positive definite quantity- more sensitive to ****higher twists**** than F_2 ?**
**- clarify comparision with leading twist NLO pQCD at low x and moderate**

## Golec-Biernat & Wusthoff’s model

**where **

**&**

**Parameters:**

## Geometrical scaling at HERA

- Scaling seen for all x < 0.01 and

- (Golec-Biernat,Kwiecinski,Stasto)

## Comparison with Data

**Comparison with Data**

**FS  model** **with/without saturation** and **IIM** **CGC model  ** hp-ph/0411337.

**Fit F****2 ****and predict**
**x****IP****F****2****D(3**)

- F2

- F2

- FS(nosat)

- x

- CGC

- FS(sat)

## Comparison with Data

**Exclusive J/Psi production: Kowalski-Teaney**

## Diffractive Vector Meson Production: 

**R_{A1,A2} = 1 =>  Pomeron flux is A -independent**
**                    ****= f(A1,A2) - universal form**

**Diffractive Vector Meson Production:**

**Very sensitive to small x glue!**

**Brodsky,Gunion,Mueller,**
**Frankfurt,Strikman**

## III: Hard diffractive processes

- “Pomeron”
-  exchange

- 30 % of eRHIC eA events may be hard diffractive events-
- Study sizes and distributions of Rapidity Gaps

## Viewing the hadron in the transverse plane 

**at high energies...**

- Y_0 ---> Y+Y_0

**Gluon radiation**

**Gluon radiation & recombination**

##  Overlapping gluon clouds... at large impact 

**    ****parameters, interplay between perturbative **
**    ****(hard Pomeron) and non-perturbative (soft **
**    ****Pomeron) physics...**
** ****By studying the “t” dependence of diffractive **
**     ****final states , can we learn **
**     ****more about the transition regime ?**

**S-matrix:**

##  Shadowing and diffraction:

**  ****Is shadowing a non-perturbative leading twist phenomenon, or is **
**   ****generated by  weak coupling, high parton density effects?**
**What is the relation of shadowing to diffraction? AGK rules relating**
**   ****the two are valid at low parton densities-how do these generalize**
**   ****to large parton densities?**

**Armesto,Capella,Kaidalov, Salgado**

## structure functions 

**Cartoon of ratio of nuclear **
**structure functions**

**Uncertainity in ratio of Ca to nucleon **_**gluon**_** distributions**
**-Hirai,Kumano,Nagai, hep-ph/0404093**

**Armesto**

## Ratio of Gluon densities in Lead to Proton at 

- x

- in x range

**Factor 3 uncertainity in glue => Factor 9 uncertainity in **
**Semi-hard HI-parton cross-sections at LHC!**

## ?

**eA at eRHIC****      ****same parton density as ep at LHC energies!**

## Reasonable 

**Reasonable **
**agreement with**
**forward spectra**

**Hayashigaki et al.**

## Virtual photon coherence length: 

**Virtual photon coherence length:**

** ****x_Bj << 0.01  : Photon coherence length exceeds nuclear size**
** ****0.01 < x_Bj < 0.1:  Intermediate length scale between R_p **
**   **
**                                ****& R_A**
** ****x_Bj >> 0.1: Photon localized to longitudinal size smaller than**
**                         ****nucleon size**

## Slide 37

## II: Extracting gluon distributions in pA relative to eA

- Direct photons

- Open charm

- Drell-Yan

**As many channels...but more convolutions, kinematic **
**constraints-limit precision and range.**

## Drell-Yan

- But very difficult to see scaling violations

- Impressive reach...