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

December 15, One of the Key Questions Polarized gluons and its distribution… What was known before today’s premier facilities existed?What was known before today’s premier facilities existed? What will we know using today’s premier facilities?What will we know using today’s premier facilities? What needs to be done to address the remaining questions in future?What needs to be done to address the remaining questions in future? Summary/Conclusion/Message : Need precise data at low xNeed precise data at low x Require high CM and Q 2Require high CM and Q 2 As wide a range in Q 2 as possibleAs wide a range in Q 2 as possible

December 15, Summary/Conclusion PRD (112002) 1998 Spin 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!

December 15, RHIC >> gg high energy BRAHMS & PP2PP STAR PHENIX AGS LINAC BOOSTER Spin Rotators (longitudinal polarization) Solenoid Partial Siberian Snake Siberian Snakes 200 MeV Polarimeter AGS Internal Polarimeter Rf Dipole RHIC pC Polarimeters Absolute Polarimeter (H  jet) AGS pC Polarimeters Strong AGS Snake Helical Partial Siberian Snake PHOBOS Spin Rotators (longitudinal polarization) Spin flipper Siberian Snakes Installed and commissioned during FY04 run Commissioned during FY05 run Installed and commissioned during FY05 run Run6: ~60-65% beam polarizations ~2 x /cm 2 /sec

December 15, RHIC Spin: inclusive  0 and jet Spin2006

December 15,  G Prospects: Left: A LL (  0 ) prospects by 2009 (65 pb-1 luminosity intregrated by PHENX using  0 double spin asymmetriesLeft: A LL (  0 ) prospects by 2009 (65 pb-1 luminosity intregrated by PHENX using  0 double spin asymmetries Right: A LL (jets) prospects by 2012 by STAR with 500 GeV in Center of Mass dataRight: A LL (jets) prospects by 2012 by STAR with 500 GeV in Center of Mass data (From Research Plan for Spin Physics at RHIC, February 2005)

December 15, Now in the x space… how does this look? Spin plan: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  G(x) very significantly, but with limited significantly, but with limited x reach. x reach. Low x behavior will remain unconstrained

December 15, One “recent” attempt of global analysis.... Asymmetry analysis collaboration (AAC)Asymmetry analysis collaboration (AAC) –Hirai, Kumano, Saito Pre-print: hep-ph/ Pre-print: hep-ph/ Recent: hep-ph/ Recent: hep-ph/ hep-ph/ : clearly says….

December 15, W. Vogelsang This should not be surprising…. RHIC now DIS now pQCD works For sure pQCD“questionable” RHIC in future

December 15, eRHIC vs. Other DIS Facilities New kinematic regionNew kinematic region E e = 10 GeV (~5-12 GeV variable)E e = 10 GeV (~5-12 GeV variable) E p = 250 GeV (~ GeV variable)E p = 250 GeV (~ GeV variable) E A = 100 GeVE A = 100 GeV Sqrt[S ep ] = GeVSqrt[S ep ] = GeV Kinematic reach of eRHIC:Kinematic reach of eRHIC: –X = > 0.7 (Q 2 > 1 GeV 2 ) –Q 2 = 0 --> 10 4 GeV 2 Polarization of e,p and light ion beams at least ~ 70% or betterPolarization of e,p and light ion beams at least ~ 70% or better Heavy ions of ALL species at RHICHeavy ions of ALL species at RHIC –High gluonic densities Luminosity Goal:Luminosity Goal: –L(ep) ~10 33 cm -2 sec -1 eRHIC DIS

December 15, Low x Proton Spin Structure eRHIC 250 x 10 GeV Luminosity = ~85 inv. pb/day Fixed target experiments 1989 – 1999 Data 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

December 15, An Exercise:  G from fits to eRHIC g 1 (x,Q 2 ) Constrain better the shape and the first moment  G determined from the Scaling violations of g1 SMC Published 1998: First Moment of  G(x) 1.0 +/- 1.0 (stat) +/- 0.4 (exp.syst) +/- 1.5 (low x) ~ one week eRHIC reduces statistical & low-x errors by ~ low x (~10 -4 to )--> strong coupling, functional form at low -x, renorm. & fact. scales

December 15, Summary Importance of low x, high Q 2 and wide Q 2 range demonstrated for polarized gluons, but there are other important measurements which also suffer due to lack of low x dataImportance of low x, high Q 2 and wide Q 2 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 structureUnderstanding the nucleon spin depends crucially on exploring the low x spin structure A high luminosity polarized electron proton collider is required.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…..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…..

December 15, Spin & Low x Surprises….. Stern & Gehrlach (1921) Space quantization associated with directionStern & Gehrlach (1921) Space quantization associated with direction Goudschmidt & Ulhenbeck (1926): Atomic fine structure & electron spin magnetic momentGoudschmidt & Ulhenbeck (1926): Atomic fine structure & electron spin magnetic moment Stern (1933) Proton anomalous magnetic moment 2.79  NStern (1933) Proton anomalous magnetic moment 2.79  N Kusch(1947) Electron anomalous magnetic moment  0Kusch(1947) Electron anomalous magnetic moment  0 Prescott & Yale-SLAC Collaboration (1978) EW interference in polarized e-d DIS, parity non-conservationPrescott & Yale-SLAC Collaboration (1978) EW interference in polarized e-d DIS, parity non-conservation European Muon Collaboration (1989) Spin Crisis/PuzzleEuropean Muon Collaboration (1989) Spin Crisis/Puzzle (Finite size of the proton)Elastic e-p scattering at SLAC (1950s)  Q2 ~ 1 GeV2 (Finite size of the proton) (Parton structure of the proton)Inelastic e-p scattering at SLAC (1960s)  Q2 > 1 GeV2 (Parton structure of the proton) (Un-polarized EMC effect, nuclear shadowing?)Inelastic mu-p scattering off p/d/N at CERN (1980s)  Q2 > 1 GeV2 (Un-polarized EMC effect, nuclear shadowing?) Unexpected rise of F2 at low x, diffraction in e-p, Saturation/CGC (??)Inelastic e-p scattering at HERA/DESY (1990s)  Q2 > 1 GeV2 Unexpected rise of F2 at low x, diffraction in e-p, Saturation/CGC (??)

December 15, The spin crisis & its aftermath European Muon Collaboration’s discovery in 1988/89European Muon Collaboration’s discovery in 1988/89 –Quarks (+ anti-quarks) do not carry the expected fraction of nucleon spin! –CERN, SLAC and DESY experiments continued in 1990s… Nature’s message: Look again, look elsewhere….Nature’s message: Look again, look elsewhere…. Quark Model QCD + Orbital motion ? Spin 2006 Ellis’s beer