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Small x issues in nucleon spin structure (focus: polarized gluon distribution). Abhay Deshpande Stony Brook University RIKEN BNL Research Center December 15, 16, 2006 Washington DC. One of the Key Questions. Polarized gluons and its distribution…

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small x issues in nucleon spin structure focus polarized gluon distribution

Small x issues in nucleon spin structure(focus: polarized gluon distribution)

Abhay Deshpande

Stony Brook University

RIKEN BNL Research Center

December 15, 16, 2006

Washington DC

one of the key questions
One of the Key Questions

Polarized gluons and its distribution…

  • What was known before today’s premier facilities existed?
  • What will we know using today’s premier facilities?
  • What needs to be done to address the remaining questions in future?
  • Summary/Conclusion/Message:
  • Need precise data at low x
  • Require high CM and Q2
  • As wide a range in Q2 as possible


summary conclusion prd 112002 1998 spin muon collaboration s na47 experiment at cern
Summary/Conclusion PRD (112002) 1998Spin Muon Collaboration’s NA47 Experiment at CERN

From COMPASS, PHENIX and STAR…. But…..

Similar message from E143 PRD (112003) 1998… same issue of PRD, and any other

theory or experimental effort that was concluding at the time!


rhic gg collider @ high energy
RHIC >> gg collider @ high energy

RHIC pC Polarimeters

Absolute Polarimeter (H jet)



Siberian Snakes

Siberian Snakes



Spin Rotators

(longitudinal polarization)

Spin flipper

Spin Rotators

(longitudinal polarization)

Solenoid Partial Siberian Snake



Helical Partial Siberian Snake


200 MeV Polarimeter

AGS Internal Polarimeter

Rf Dipole

AGS pC Polarimeters

Strong AGS Snake


~60-65% beam polarizations

~2 x 1031/cm2/sec

Installed and commissioned during FY04 run

Commissioned during FY05 run

Installed and commissioned during FY05 run


rhic spin inclusive p 0 and jet
RHIC Spin: inclusive p0 and jet



d g prospects 2009 2012
DG Prospects: 2009-2012
  • Left: ALL (p0) prospects by 2009 (65 pb-1 luminosity intregrated by PHENX using p0 double spin asymmetries
  • Right: ALL (jets) prospects by 2012 by STAR with 500 GeV in Center of Mass data

(From Research Plan for Spin Physics at RHIC, February 2005)


now in the x space how does this look
Now in the x space… how does this look?
  • Spin plan:
    • 65 pb-1 at √s=200GeV & 70% pol
    • 309 pb-1 at √s=500GeV & 70% pol

RHIC Spin Plan 2005, Feb. 11

Note the limited x range!

RHIC will constrain DG(x) very

significantly, but with limited

x reach.

Low x behavior will remain



one recent attempt of global analysis
One “recent” attempt of global analysis....
  • Asymmetry analysis collaboration (AAC)
    • Hirai, Kumano, Saito
  • Pre-print: hep-ph/0603213
  • Recent:hep-ph/0607063

hep-ph/0607063: clearly says….



This should not be surprising….



pQCD works

For sure



DIS now

W. Vogelsang

RHIC in future


erhic vs other dis facilities
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[Sep] = 30-100 GeV
  • Kinematic reach of eRHIC:
    • X = 10-4 --> 0.7 (Q2 > 1 GeV2)
    • Q2 = 0 --> 104 GeV2
  • Polarization of e,p and light ion beams at least ~ 70% or better
  • Heavy ions of ALL species at RHIC
    • High gluonic densities
  • Luminosity Goal:
    • L(ep) ~1033cm-2 sec-1




low x proton spin structure
Low x Proton Spin Structure

Fixed target experiments

1989 – 1999 Data

eRHIC 250 x 10 GeV

Luminosity = ~85 inv. pb/day

10 days of eRHIC run

Assume: 70% Machine Eff.

70% Detector Eff.

Studies included statistical error & detector smearing to confirm

that asymmetries are measurable. No present or future approved

experiment will be able to make this measurement


an exercise d g from fits to erhic g 1 x q 2
An Exercise: DG from fits to eRHIC g1(x,Q2)

Constrain better the shape and the first moment

DG determined from the Scaling violations of g1

SMC Published 1998: First Moment of DG(x)

1.0 +/- 1.0 (stat) +/- 0.4 (exp.syst) +/- 1.5 (low x)

-- one week eRHIC reduces statistical & low-x errors by ~3-5

-- low x (~10-4 to 10-2)--> strong coupling, functional form at low -x,

renorm. & fact. scales


  • Importance of low x, high Q2 and wide Q2 range demonstrated for polarized gluons, but there are other important measurements which also suffer due to lack of low x data
  • Understanding the nucleon spin depends crucially on exploring the low x spin structure
  • A high luminosity polarized electron proton collider is required.
  • Historically, low x and spin have been variables of high return in terms of major discoveries that fundamentally changed our understanding of nature. Both together in an EIC certainly show high promise…..


spin low x surprises
Stern & Gehrlach (1921) Space quantization associated with direction

Goudschmidt & Ulhenbeck (1926): Atomic fine structure & electron spin magnetic moment

Stern (1933) Proton anomalous magnetic moment 2.79 mN

Kusch(1947) Electron anomalous magnetic moment 1.00119m0

Prescott & Yale-SLAC Collaboration (1978) EW interference in polarized e-d DIS, parity non-conservation

European Muon Collaboration (1989) Spin Crisis/Puzzle

Elastic e-p scattering at SLAC (1950s)  Q2 ~ 1 GeV2 (Finite size of the proton)

Inelastic e-p scattering at SLAC (1960s)  Q2 > 1 GeV2 (Parton structure of the proton)

Inelastic mu-p scattering off p/d/N at CERN (1980s)Q2 > 1 GeV2 (Un-polarized EMC effect, nuclear shadowing?)

Inelastic e-p scattering at HERA/DESY (1990s) Q2 > 1 GeV2 Unexpected rise of F2 at low x, diffraction in e-p, Saturation/CGC (??)

Spin & Low x Surprises…..