# Presentation: 318133

## Do Gluons Carry Proton Spin? – toward resolving the “Spin Crisis”

- Alexander Bazilevsky
- Physics Department, BNL
- Brookhaven Lecture
- January 21, 2009

## Outline

- Why Spin
- Role of the Spin
- Proton Spin Structure and Spin Crisis
- Why Gluons
- Role of Gluons
- Probing Gluon Spin Contribution
- What’s next

## Spin

- Fundamental Concept in Physics

- Appears in all levels: from galaxies to elementary particles

## Spin

- Spin is a fundamental quantum mechanical property of elementary particles (like mass, charge)
- Carries the same mathematical meaning as angular momentum (rotational motion in classical mechanics)
- Spin in quantum mechanics is quantized in units of Planck’s constant h, and can be either integer (0, 1, 2 etc) or half-integer (1/2, 3/2 etc);
**Proton**, **neutron** and **electron **are spin-1/2 particles
- Spin plays central role in theory of strong interaction, Quantum Chromodynamics (**QCD**)

## Spin and particle internal structure

- Associated with particle spin is magnetic moment
- (like rotating electrically charged body)

- e – electric charge
- m – mass
- S - spin

- From quantum  theory (Dirac equation):
- g~2 for elementary (point-like)  1⁄2-spin particle
- _Confirmed __in the experiment for __**electrons**__ __and__ __**muons**_

- Compositeness of proton and neutron!

- Triumph of quantum theory!

**S**

**N**

## Nucleon Spin 

- Quark Model: proton and neutron are made of three quarks
- p = (uud)
- n = (ddu)

|  | Charge | Spin |
| --- | --- | --- |
| p | +e | 1/2 |
| n | 0 | 1/2 |

- Another triumph?
- So, quarks carry nucleon spin ?!

|  | Charge | Spin |
| --- | --- | --- |
| u | +2/3e | 1/2 |
| d | -1/3e | 1/2 |

- 

- Compute proton (neutron) magnetic moment in terms of quark magnetic moments

- Nucleons   protons and neutrons

## ... Proton Spin Crisis

**... Proton Spin Crisis**

- EMC (CERN) experiment:
- Deep Inelastic Scattering (DIS) of high energy polarized muons on polarized protons

- Quark (and anti-quark) contribution to proton spin is small:
**=****12 ±****9(stat)**** ±14(****syst****) ****%**

- What carries the proton spin ?!

- Nucl. Phys. B328, 1-35 (1989) – one of the most cited papers!  >1200 citations

## Proton Spin Structure

- Partons   (anti)quarks and gluons

## Probing Proton Structure

- r

- γ*(Q2)

- e

- e’

- ~1.5 fm

- Proton

- Virtuality (4-momentum transfer2) **Q****2** gives the distance scale **r** at which the proton is probed.

- r ≈ hc/Q = 0.2fm/Q[GeV]

- HERA ep collider:  rmin≈ 1/1000 proton diameter

- Ee=27.5 GeV, Ep=920 GeV

## Parton Distribution Functions (PDF)or parton densities

*f*(*x*) - Parton Distribution Function (PDF):
- probability for a parton to carry fraction *x* of the proton momentum

*P*

- Proton

- Higher probe *Q*2 – better resolution
- Start resolving more virtual (short life) stuff, sea quarks and gluons with lower x
- So, different *Q*2 probes see proton structure differently:  *f*(*x*)  *f*(*x*,*Q*2)
- Once *f*(*x*,*Q*2) is known at some Q02 scale, it can be calculated for any other Q2

## Polarized PDF

*q(x,Q**2**)  =*

- D*q**(x,Q**2**)=*

- helicity (longitudinal spin) distribution

- unpolarised distribution

- Quarks

- Quark
- spin

- Proton
- spin

*q* = *u*,*d*,*s* ...

## Polarized PDF from DISAsymmetry Analysis Collaboration M. Hirai, S. Kumano and N. Saito, PRD69, 054021 (2004)

**Polarized PDF from DIS**Asymmetry Analysis Collaboration M. Hirai, S. Kumano and N. Saito, PRD69, 054021 (2004)

- Valence distributions well determined
- Sea Distribution poorly constrained
- Gluon very poorly constrained: can be either positive, 0, negative!

## From inclusive polarized DIS ... 

- Only information about input and scattered lepton (*e*, ) is recorded
*x* and *Q*2 reconstructed from kinematics
- Does not distinguish quark and antiquark
- Scattering ~charge2
- Do not have direct access to gluon
- Probe it through scaling violation (Q2 dependence of quark PDFs) -                     with very poor precision currently

**Utilizes virtual photon to probe nucleon spin structure**

*e’* (’)

*e* ()

- *

- Change in q vs Q2 is defined by the probability that quark and gluon radiate quark

*g*

*g*

## ... To polarized pp collider

**Utilizes strongly interacting probes**

- Probes gluon directly
- Higher energies  clean pQCD interpretation
- 100 GeV protons on fixed target: s=14 GeV
- 100 GeV + 100 GeV protons at a collider: s=200 GeV
- Elegant way to explore quark and anti-quark polarizations through W production

**Polarized Gluon Distribution Measurements (****G****): **
- Use a variety of probes
- Access to different gluon momentum fraction x
- Different probes – different systematics
- Use different beam energies
- Access to different gluon momentum fraction x

*g*

## RHIC as polarized proton collider

**AGS**

**LINAC**

**BOOSTER**

- Pol. Proton Source
- 500 mA, 300 ms

**Spin Rotators**

- Partial Siberian Snake

**Siberian Snakes**

- 200 MeV Polarimeter

- AGS Internal Polarimeter

- Rf Dipoles

**RHIC pC Polarimeters**

**Absolute Polarimeter **
**             (H jet)**

- 2  1011 Pol. Protons / Bunch
- e = 20 p mm mrad

## RHIC Progress

| Parameter | Unit | 2002 | 2003 | 2004 | 2005 | 2006 |
| --- | --- | --- | --- | --- | --- | --- |
| No. of Bunches | -- | 55 | 55 | 56 | 106 | 111 |
|  Bunch Intensity | 1011 | 0.7 | 0.7 | 0.7 | 0.9 | 1.3 |
| Store Energy | GeV | 100 | 100 | 100 | 100  | 100  |
| * | m | 3 | 1 | 1 | 1  | 1  |
| Peak Luminosity | 1030cm-2s-1 | 2 | 6 | 6 | 10 | 35 |
| Average Luminosity | 1030cm-2s-1 | 1 | 4 | 4 | 6  | 20 |
| Collision points | -- | 4 | 4 | 4 | 3 | 2 |
| Time in store | % | 30 | 41 | 38 | 56 | 46 |
| Average Polarization, store | % | 15 | 35 | 46 | 50 | 60 |

## PHENIX and STAR

**STAR:**
**Large acceptance with azimuthal symmetry**
**Good tracking and PID**
**Central and forward calorimetry**

**PHENIX:**
**High rate capability**
**High granularity**
**Good mass resolution and PID**
**Limited acceptance**

## Observables 

- High Energy Proton scattering can be seen as a scattering of constituent partons: *gg*, *qg*, *qq*

- f

- f

- 

- p

- p

- xb

- xa

## RHIC Spin Measurements

- g

- q

- p

- p

- Jet

- Other exp.

- _Check theory (__pQCD__) __works_

- This exp.

- Theory

## Particle Yield in pp

**Particle ****Yield**** ****in *****pp***

- ||<0.35

**PHENIX: ****pp****0 ****X**
**PRD 76, 051106 (R)**

**STAR: ****ppjet**** X**
**PRL 97, 252001**

- Good agreement between theory (pQCD) calculations and data  confirmation that pQCD can be used to extract spin dependent pdf’s from RHIC data.
- Same comparison fails at lower energies

## Probing G in pol. pp collisions 

- ++ - particle production from beam with the same helicity
- + - particle production from beam with the opposite helicity

- For inclusive Jet or hadron production:

## Measuring ALL

- (N) Yield
- (R) Relative Luminosity
-       (collision rate)
- (P) Polarization

- Bunch spin configuration (+ or  helicity) alternates every 106 ns
- Data for all bunch spin configurations are collected at the same time
-  Possibility for false asymmetries is greatly reduced

- RHIC

## ALL: jets

**A****LL****: jets**

- Run2003&2004: PRL 97, 252001
- Run2005: PRL 100, 232003

**STAR Preliminary Run2006 (****s=200 GeV****)**

- Large and modest gluon polarization scenarios are not consistent with data

**GRSV Models:**
- “G = G”:    G(Q2=1GeV2)= 1.9
- “G = -G”:   G(Q2=1GeV2)= –1.8
- “G = 0”:     G(Q2=1GeV2)=0.1
- “G = std”:   G(Q2=1GeV2)=0.4

## ALL: 0

- Run3,4,5: PRL 93, 202002; PRD 73, 091102;
-                    PRD 76, 051106 (R)

**PHENIX ****Run2006 ****(****s=200 ****GeV****)**
** arXiv:0810.0694**

- Statistical precision of RHIC ALL data started to dominate in G constraint

- Uncertainty from DIS data

## From ALL(pT) to g(xgluon) 

- 2(G)

- Generate g(x) curves for different
- Calculate ALL(pT) for each G
- Compare ALL data to curves (produce 2 vs G):

- From pQCD:
- pT = 212 GeV/c  
- xgluon = 0.02  0.3

## G: Global Fit

- PRL 101, 072001(2008)
- First truly global analysis of polarized DIS, SIDIS and RHIC results

- Daniel de Florian
- Rodolfo Sassot
- Marco Stratmann
- Werner Vogelsang

- Uncertainty estimation:
- 2=1          (optimistic)
- 2/2=2%  (conservative)
- ... Truth is in between

- 2/2=2%

## G: From DIS to RHIC

- Considerable improvement in G determination
- (a lot of work still needed for correct error estimation)

- DIS+RHIC: DSSV-2008
- RHIC data constrains G at 0.02<x<0.3

- DIS: AAC-2004

## So, the Proton Spin

## G at RHIC: what’s next

- Improve exp. uncertainties and move to higher pT (higher *x*)

- Different s (colliding beam energy)
- Different *x*
- Important cross check: measurements for the same *x* at different Q2

*pp*  ** + *jet* and *pp*  *jet* + *jet** *
- Map g vs *x*

## Improve exp. uncertainties

- Need more FOM=P4 L (stat. uncertainty ~ 1/FOM)

- A factor of 3-4 reduction in stat. errors expected in next s=200 GeV RHIC Run (2009 or 2010)

- xg(x)

## pp  jet + jet

***pp***** **** jet + jet**

- Parton kinematics (*x*gluon) is well constrained
- Sensitivity not only to the integral G but also to the shape g(*x*)
- Better sensitivity to G compared to inclusive jet measurements *pp*jet+X
- Higher *x* asymmetries are not diluted by low *x* asymmetries as in inclusive measurements
- More exclusive triggering (smaller background)

- 31.5  40.5

- 30.5  4-0.5

- 31.5  4-0.5

- 30.5  40.5
- 3-0.5  4-0.5

- MJet-Jet

- ALL

## pp   +X

- Golden channel:
- Theoretically clean
- Small contamination (~15% from qq-bar annihilation
- Linear in G  sign of G
- Rare probe (needs a lot of luminosity)

- Expectations

## Flavor decomposition

- Measured through longitudinal single spin asymmetry AL in W production at s=500 GeV

**First data expected ****in ****a few weeks!**

- Fixes (anti)quark flavor and its spin direction

## eRHIC

- Electron – Proton (and Ion) Collider

- Precise imaging gluon and sea quarks in the proton
- Get access to parton orbital momentum

- Electron energy range from 3 to 20 GeV
- Peak luminosity of 2.6  1033 cm-2s-
- High electron beam polarization (~80%)

## Summary

**So, Do Gluons Carry Proton Spin? – **
**Current ****d****ata ****indicate on small or zero contribution**
- Higher precision and extended *x* range measurements of G are necessary (RHIC, eRHIC etc.)
- World wide quest in determining the parton orbital angular momentum contribution (JLab, eRHIC etc.)

- Proton
- Spin

- Gluon
- Contribution:
- ~0?

- Parton Orbital
- Momentum:
- ???

- (Anti)quark
- Contribution:
- 0.10–0.15

## The Story of Spin		Sin-Itiro Tomonaga

- It is a mysterious beast, and yet its practical effect prevail the whole of science. The existence of spin, and statistics associated with it, is the most subtle and ingenious design of Nature – without it the whole universe would collapse.