A Review of  G measurements: Present & Future Abhay Deshpande RIKEN BNL Research Center Snowmass 2001 Working Group: Fixed Target Experiments Riken BNL Research Center

July 3, Snowmass 2001, Delta G2 Overview Fixed target polarized DIS experiments  Their need to evaluate first moments of spin structure functions Methods used to get the first moments: Old & New  New: pQCD analysis at NLO  Allows to access  G  Lessons…-- features and faults  Other “direct methods” in DIS –Photon Gluon Fusion-to access  G: Lessons-- Features and faults Polarized Gluon Measurements at Colliders  RHIC spin program present and near future  Future polarized electron proton colliders: EIC/eRHIC, Polarized HERA….THERA and their ability to get Delta G.

July 3, Snowmass 2001, Delta G3 Polarized DIS To date fixed target experiments only Both: Probe and the Target need to be polarized Electron beams up to 50 GeV/c on fixed (solid and gaseous) targets were predominantly used at SLAC (EXXX series) and DESY (HERMES) Muon beams GeV/c on fixed (solid) targets were used at CERN(EMC,SMC) Compared to un-polarized DIS, the kinematic range is small

July 3, Snowmass 2001, Delta G4 How far does “polarized DIS” have to go!

July 3, Snowmass 2001, Delta G5 Need to evaluate the first moments and the methods… old/new Measure A 1 (x,Q2) Use parameterizations of F 2 and R to get g 1 (x,Q2) To move data to a fixed Q 0 -- OLD Method: assume A 1 independent of Q -- New Method: use pQCD analysis at NLO which treat the Q2 evolution using DGLAP equations -- Assign appropriate uncertainties Extrapolate to unmeasured high and low x regions -- Assign appropriate uncertainties…! Evaluate first moments of spin structure functions

July 3, Snowmass 2001, Delta G6 A bit of theory… g1(x,Q2) and its evolution GLAP Evolution Pij s are Polarized splitting functions known to NLO

July 3, Snowmass 2001, Delta G7 The Method Chose a starting scale Q2 = 1 GeV2 Parameterize the polarized parton distributions with functional form: Each PD is normalized such that: become the first moment of the parton distributions First moments of singlet and gluon distributions are free parameters while the first moment of the nonsinglet is either fixed by Bjorken sum rule or in some ambitious analyses left free too. minimization is performed for g1 measurements from experiments and evolved value of g1 using the parton distribution functions and the DGLAP evolution equations at the measured x,Q2 of the data point. SMC PR D (112002)

July 3, Snowmass 2001, Delta G8 Results & Uncertainties… Fit to world data 133 data points (CERN,SLAC,DESY) 10 free parameters Chi2 = using only statistical errors Experimental systematic errors handled separately Uncertainties of theoretical origin also handled separately SMC PRD 1999 (112002)

July 3, Snowmass 2001, Delta G9 PDFs and Systematic Uncertainties Experimental Sources -- Systematic uncertainties on A1 -- Uncertainties of F2 and R parameterizations Theoretical Sources -- Functional form of initial pdf  Change that redo fits  Start at a different initial scale and repeat fits -- Factorization and renormalization scales  Change by a factor of 2 up/down repeat fits -- Value of  S / Other smaller effects due to quark mass thresholds, a_8…

July 3, Snowmass 2001, Delta G10 Lack of low x data… consequences Q2 = 10 GeV2 Regge/QCD SMC Results

July 3, Snowmass 2001, Delta G11 Neutron structure function… E154/SLAC Consequence: Unertainties in low x for Bjorken sum rule… Acceptable? No… measure low x!

July 3, Snowmass 2001, Delta G12 Observation: Features and Faults Method reliable… (refer to unpolarized NLO analysis of F2), uncertainties estimates rather straightforward.. Although tedious. Largest uncertainties come from the unmeasured low x region. pQCD analysis needs large Q2 arms which are absent in available data Need a collider experiment e-N with sufficiently large CM energy to cross the low x barrier at the same time have large enough values of Q2 so that pQCD methods can be reliably be used to get at a the values of Delta G.

July 3, Snowmass 2001, Delta G13 Other methods to get at  G: Photon-Gluon Fusion HERMES Collaboration, PRL 84 (2000) Signal Background

July 3, Snowmass 2001, Delta G14 High pT Hadron:PGF HERMES Results No estimate of theoretical Uncertainty

July 3, Snowmass 2001, Delta G15 Experimental & Theoretical Difficulties at low Scales Fraction of VDM and its uncertainty?Scale dependence significant? A high energy polarized collider will overcome these! W. Vogelsang, SPIN2000 HERMES Collaboration

July 3, Snowmass 2001, Delta G16 RHIC: Polarized Proton Collider BRAHMS & PP2PP (p) STAR (p) PHENIX (p) AGS LINAC BOOSTER Pol. Proton Source 500  A, 300  s Spin Rotators Partial Siberian Snake Siberian Snakes 200 MeV Polarimeter AGS Internal Polarimeter Rf Dipoles RHIC pC Polarimeters Absolute Polarimeter (H jet) 2  Pol. Protons / Bunch  = 20  mm mrad

July 3, Snowmass 2001, Delta G17 RHIC Spin Physics Program Production Heavy Flavors Direct Photon Jet Photon STAR + PHENIX Jet W Production STAR +PHENIX STAR +PHENIX+PHOBOS BRAHMS

July 3, Snowmass 2001, Delta G18 New Experiments for Measurements Polarized ppPolarized DIS RHIC/BNLHERA/DESY, and CERN/SPS Production Heavy Flavors Direct Photon Jet Photon STAR PHENIX pQCD at low x Photo production of charm and high hadron pairs Polarized HERA & EIC HERMES COMPASS Jet Single and Di-Jets DIS &Photoproduction EIC: Electron Ion Collider 3-10 GeV e  GeV polarized protons

July 3, Snowmass 2001, Delta G19 from Prompt Photon Production Double Spin Asymmetry Gluon Compton (85% of )Annihilation (15% of )

July 3, Snowmass 2001, Delta G20 Prompt Photon Production Direct access to both in PHENIX and STAR Jet for x-gluon reconstruction Observables: Double spin asymmetries

July 3, Snowmass 2001, Delta G21 Kinematic range RHIC vs. Others  G from Heavy Flavors prompt photon

July 3, Snowmass 2001, Delta G22 for leading Pions: Year 2 Use high in order to tag Jet Model Calculation using PYTHIA and polarized PDFs from Gehrmann, Sterling 10% of design Luminosity Pion Asymmetries Gluon A Gluon B Gluon C

July 3, Snowmass 2001, Delta G23 The Electron Ion Collider (EIC) w.r.t. Other Experimental Facilities New kinematic region to be explored EIC = eRHIC + EPIC Kinematic Reach for DIS: High Luminosity! EVERY THING I SAY ABOUT EIC FROM NOW IN TERMS OF ITS PHYSICS CAPABILITIES HOLDS ALSO FOR POLARIZED HERA COLLIDER

July 3, Snowmass 2001, Delta G24 The EIC w.r.t. Other Experimental Facilities Large luminosity and high CM Energy makes EIC unique! Variable CM energy enhances its versatility!

July 3, Snowmass 2001, Delta G25 If the EIC is built at RHIC  “eRHIC” I. Ben-Zvi et al./S. Peggs et al. Use the existing infrastructure and resources of the RHIC at BNL RHIC: Polarized proton beams  50 GeV  250 GeV  ?  325 GeV Exists an unused Experimental Hall: The one at 12 o’clock position of the present RHIC reserved for “future major detector” Add a electron LINAC beam energy variable: 3 GeV  12 GeV RHIC at BNL Ring-Linac Design Blue ring Yellow ring Electron Linac

July 3, Snowmass 2001, Delta G26 Spin Structure Function g 1 at low x A. Deshpande et al. ~5-7 days of data A Unique Measurement! No present/future approved experiment will measure this. 3 years of data

July 3, Snowmass 2001, Delta G27 pQCD analysis of g1 structure function at NLO gives the first moment of the polarized gluon distribution. Present value and uncertainty is: (at Q2 = 1 GeV2) 1.0 (stat) (exp.sys.) (theory/low-x) Major source of uncertainty from low x unmeasured region: Theory completely unconstrained in this region. If EIC data is obtained and the analysis is repeated, the theoretical uncertainties improve by factors of 3-5; the statistical uncertainty improves by even bigger factors Complimentary determination of  G to that from RHIC Spin First Moment of the  G(x). A. Deshpande et al.

July 3, Snowmass 2001, Delta G28 Result of Di-Jet analysis at NLO G. Radel et al./A.Deshpande et al. Easy to differentiate between different scenarios of  G: Improves  G by factor of ~3 Combined analysis: Di-Jet + pQCD analysis of g1:  G constrained by these two together further improves the uncertainties by additonal factor of ~3 Effectively factors of 10 improvement in  G can be expected! Statistical accuracy shown for EIC for 2 luminosities Detector smearing effects studied NLO analysis for Di-Jet Included

July 3, Snowmass 2001, Delta G29 Polarized Parton Distribution of the Photon Photoproduction studies with single and di-jet and one and 2 high pT opposite charged hadrons. At high enough energies the photon can resolve itself into its parton content With polarized protons asymmetries related to the spin structure of the photon can be extracted! A UNIQUE measurement! Asymmetries sensitive to the gluon structure as well! Resolved PhotonDirect Photon

July 3, Snowmass 2001, Delta G30 Spin structure of polarized photon! M. Stratmann & W. Vogelsang Statistical uncertainty with 1 inv.fb. ~2wks running for EIC Single and double jet asymmetries ZEUS Acceptance cuts Will resolve the photon spin structure easily! Direct Photon Resolved Photon

July 3, Snowmass 2001, Delta G31 Summary of  G Measurements Polarized gluon density remains to be measured. Ample evidence for it being non-zero & positive. Attempts to measure them have been serious but have had limited success due to various things: a) Beam facilities of the past + Detectors b) Kinematics covered by data make the interpretation difficult. Future dedicated experiments at colliders will do better:  High energy colliders … better detector designs … will cover larger kinematic regions which have little theoretical issues Starting with RHIC Spin leading to possible EIC at BNL or Polarized HERA at DESY the prospects of accessing  G and chances of uncovering other surprises remain very good!

July 3, Snowmass 2001, Delta G32 References for Material Related to Polarized e-p colliders EIC, Polarized HERA, THERA Will soon become… Everything you ever wanted to know about future polarized & Unpolarized lepton-hadron colliders but were afraid to ask….