# Presentation: 881550

## Gluon Polarization in the Nucleon

- Werner Vogelsang
- RBRC & BNL Nuclear Theory
**PANIC 05,  10/24/2005**

## Outline:

****** ****The parton distribution ********g(x,Q****2****) **

****** ********g and the proton spin**

****** ****Conclusions**

****** ********g and the axial anomaly**

****** ****Expectations for ********g**

****** ****Phenomenology of ********g in pol. high-energy scatt.**

## The parton distribution g(x,Q2) 

## To understand the spin structure of 

**To understand the spin structure of **
** ****hadrons in terms of quarks and gluons**

## Slide 5

## Slide 6

## Gluon distributions:

**This is the quantity that appears in pol. high-energy scattering !**

## Properties of parton distributions:

**• **** ****all these operators need renormalization**
**    ********  ****scale dependence / “evolution”**** of parton distributions**

## Slide 9

## Glück, Reya, Stratmann, WV  ‘96 / ‘00

**Glück, Reya, Stratmann, WV  ‘96 / ‘00**

## Evolution of first moment:

## g(x,Q2) and the proton spin 

## where

**where**

**Jaffe, Manohar; Ratcliffe; **
**Ji; Teryaev; Jaffe, Bashinskii;**
**Ji, Hoodbhoy, Lu; ...**

## LO evolution:   Ratcliffe; Ji, Tang, Hoodbhoy; Hägler, Schäfer 

## g and the axial anomaly

## How does the QCD axial anomaly enter 

** ****nucleon spin structure ?**

## singlet :

## Proposal by  Altarelli, Ross; Altarelli, Stirling; Efremov, Teryaev; ...

**• **** ****idea is that axial charge can be small if  ********G is large**

## How large ?

**• **** ****early estimates (late ‘80s) :**

## •  “perturbative-anomaly” scenario controversial in the

**     ****literature**

**Jaffe, Manohar**

**• ****  ****is huge gluon spin contribution better than small quark one ...?**

**• ****  ****in any case,  has given boost to attempts to measure ********G**

## Expectations for g

## Ideally ...

**Lattice;**
**low-energy**
**models:**
**confinement, ...**

**Nucleon Structure seen**
**by hard probes & **
**asymptotic**
**freedom**

## •  constituent quark model estimates :

**Jaffe; Barone, Calarco, Drago**

****** ****ambient gluon fields**

## Slide 24

## •  G on the lattice ?

**Non-local operator, except for A****+**** = 0 gauge ...**

**Attempt by**** Mandula ‘90 :**

## Phenomenology of g in polarized

**           ****high-energy scattering**

## Slide 27

## •   g  can be probed in other reactions in polarized

**    ****high-energy scattering :**

## •  important to have adequate (and proven) theoretical

**    ****framework :**

****** ****higher-order (NLO) corrections**

****** ****comparison to data for unpolarized cross sections**

**• **** ****need variety of probes **

****** ****often sizable, reduce scale dependence**

**• **** ****eventually, will need a “CTEQ-style”  global analysis**

## RHIC offers best possibilities to probe g :

**RHIC offers best possibilities to probe ********g :**

## •  Calculations are already successful in unpolarized pp at RHIC:

- •**  ****Calculations are already successful in unpolarized pp at ****RHIC****:**

## Slide 32

## •  it’s a stretch to conclude anything about the integral G ...

**Ellis, Karliner**

- • ** ****it’s a stretch to conclude anything about the integral ********G ...**

- •**  ****Theory good enough ?**** **

## Conclusions & Outlook:

- •  gluon polarization promises to be an important piece for
-    our understanding

- • carried by tremendous efforts in experiments :
-    **RHIC, HERMES,  COMPASS  --  eRHIC ? **

- • complementarity of lepton-nucleon scattering and pp !

- • improvements in models, lattice ?

## N. Saito

**N. Saito**

## “AB scheme”

**“****AB scheme”**