AGS&RHIC Users’ Meeting, BNL, June 20 th 2007 o Introduction Nucleon spin structure The importance of low-x o Physics with the NCC and FVTX The origin of proton spin: gluon spin  measurement of ΔG = ∫ ΔG(x)dx (FVTX and NCC) Explore the nature of transverse spin asymmetries in QCD  measurement of quark transversity distributions (NCC)  measurement of the Sivers distribution (FVTX) Spin structure of the quark sea  precision measurement + flavor separation of Δq(x), Δq(x) in W-production (muon trigger in combination with FVTX and NCC) o Conclusions Spin Physics with the NCC and FVTX M. Grosse Perdekamp UIUC and RBRC

Physics Motivation: Spin2 July 9 th Scientific Achievements The hydrogen atom is the fundamental bound state of the electromagnetic force. We have learned to understand its wave function in terms of its electron and proton constituents and found: Quantum mechanics Relativistic Quantum Field Theory Precise ab initio calculations for increasingly complex systems governed by the electromagnetic force. From History, an Analogy: The Hydrogen Atom as Laboratory for the Electromagnetic Force

Physics Motivation: Spin3 July 9 th Scientific Questions The nucleon is the fundamental bound state of the strong nuclear force. What is the nucleon wave function in terms of quarks and gluons? What is the origin of the nucleon mass? What is the origin of the nucleon spin? How does the nucleon wave function change in cold nuclear matter? Can QCD be used to make ab initio calculations of the nulceon wave function? The Nucleon as Laboratory for the Strong Interaction

Physics Motivation: Spin4 July 9 th Physics Goals determine first moment of the spin dependent gluon distribution ∫ 0 1 ΔG(x)dx over a large range in x. measure nuclear effects on the gluon distribution in nucleons in nuclei in particular at low x. Flavor separation of q and anti-quark spin distributions in W-production Measurement of trans- versity quark distributions. Establish magnitude of the gluon Sivers effect. Nucleon Structure in PHENIX: The Origin of Nucleon Spin + Nuclear Effects Sivers Effect

Physics Motivation: Spin5 July 9 th Experimental Approach to Quark and Gluon Structure of the Nucleon Hard Scattering! (I)Go to high energy limit where perturbative QCD calculations ab intio are possible (II) Measure & analysis (spin-dependent) cross sections and extract information on quark and gluon degrees of freedom! Measure: Cross sections/structure functions at high energy Extract: Quark- and Gluon Distribution Functions using ab initio QCD analysis! Important quality criteria: QCD calculation in- dependent of arbitrarily choosen factorization and renormalization scales!

Physics Motivation: Spin6 July 9 th NLO-pQCD calculation –Private communication with W.Vogelsang –CTEQ6M PDF. –direct photon + fragmentation photon –Set Renormalization scale and factorization scale p T /2,p T,2p T NLO perturbative QCD shows good agreement with the experimental cross sections. Stability against choice of scales! Perturbative QCD vs RHIC data Direct Photon Cross Section (similar results for neutral pions and charged hadrons)

Physics Motivation: Spin July 9 th AGS LINAC BOOSTER Polarized Source Spin Rotators Partial Snake Siberian Snakes 200 MeV Polarimeter AGS Polarimeter Rf Dipole RHIC pC Polarimeters Absolute Polarimeter (H jet) P HENIX P HOBOS B RAHMS & PP2PP S TAR Siberian Snakes Helical Partial Snake Strong Snake Spin Flipper 2005 Complete! RHIC Spin RHIC Spin: Probing Proton Spin Structure Through High Energy  a Novel Experimental Method ! Polarized p-p Collisions  a Novel Experimental Method ! RHIC – pp – luminosity projections total recorded in PHENIX ∫Ldt ~ 1.7 fb -1 Future improvement com- pared to present data set luminosity: ∫Ldt ~ x 100 figure of merit: P 4 ∫Ldt ~ x 300 ∫Ldt ≈ 15 pb (present data set) ∫Ldt ≈ 85 pb – 2012, √s=200 GeV ∫Ldt ≈ 300 pb – 2012, √s=500 GeV ∫Ldt ≈ 1300 pb – 2016, √s=500 GeV  Upgrades will be available for most of RHIC spin integrated luminosity! 15pb pb -1

Physics Motivation: Spin8 July 9 th Polarized p-p as a Precision Tool for the Study of Nucleon Structure (A) Improved theoretical tools: e.g. resummation, NLO perturbative QCD (B) Build on experimental results from DIS + unpolarized p-p (C) Consistency: PDFs from DIS + QCD vs cross sections at RHIC (D) Multiple channels which provide access to spin dependent PDFs with independent experimental and theoretical uncertainties. e.g. ΔG  inclusive hadrons  inclusive photons  jet + photon  open heavy flavor Critical: large PHENIX DAQ bandwidth (~ 8kHz) for highest possible rates in multiple channels (including at low p T !)

Physics Motivation: Spin9 July 9 th ¨ standard ∆G from DIS ∆G =0 max ∆G from DIS min ∆G possible Run 5 A LL (   ): First constraints for ∆G(x) Mutiple Channels vs DAQ Bandwidth: Photon Trigger ~ 1500 Hz Photon Trigger L=6x10 31 cm -2 s -1  Photon trigger rate for a threshold at 2.1 GeV is ~ 1.5kHz  Even at small p T A LL is statistics limited: Δ stat A ~ 2x10 -3, Δ sys A < 5x10 -4  Continue data taking with low threshold!

Physics Motivation: Spin10 July 9 th ¨ Future A LL (c,b) Projections with VTX Mutiple Channels vs DAQ Bandwidth: Electron Trigger ~1500 Hz Electron Trigger systematic limit L=6x10 31 cm -2 s -1  electron rate for a threshold at 0.9 GeV is ~ 1.5kHz  need ∫Ldt=320pb -1 before systematics limited at low p T !  Continue data taking with low threshold!

Physics Motivation: Spin11 July 9 th ¨ Mutiple Channels and DAQ Bandwidth Large bandwidth and trigger capabilities are critical to fully benefit from measurements in multiple channels, e.g. ΔG(x) ! PHENIX DAQ and trigger are ideal.  In addition to testing experimental and theoretical uncertainties in independent physics channels this approach leads in PHENIX also to the best statistical precision for results on spin dependent nucleon distribution functions. Final results on spin dependent observables, e.g. ∫ΔG(x) dx will come from inclusive Next-to-Leading-Order perturbative QCD analysis of the asymmetries from all experimental channels.

Low x is important

Physics Motivation: Spin13 July 9 th Nucleon Structure: 40 Years of Experiment  Deep Inelastic Lepton-Nucleon Scattering!  2000  2010  1995  2007 ongoing q(x) -- G(x) -- ∆q(x) – DVCS -- δq(x) -- Sivers -- ∆G(x) -- ∆q(x) -- ∆s(x) SLAC DIS, polarized-DIS CERN DIS, polarized-DIS FNAL DIS, pp DESY collider-DIS, polarized-DIS JLAB DIS, polarized-DIS RHIC polarized-pp Polarized p-p scattering is a new experimental technique for the precision study of spin dependent nucleon structure and Has to compete in a well established and advanced field.  An important “history lesson” is the central role low-x data have played

Physics Motivation: Spin14 July 9 th The Importance of Low x, Example ΔΣ Quark Spin Contribution to the Proton Spin. Measurements at SLAC: 0.10 < x SLAC <0.7 vs CERN: 0.01 < x CERN < < x SLAC < 0.7 A 1 (x) x-Bjorken EMC, Phys.Lett.B206:364,1988: 1319 citations in SPIRES EMC, Nucl.Phys.B328:1,1989, 1138 citations in SPIRES 0.01 < x CERN < 0.5 E130, Phys.Rev.Lett.51:1135,1983: 412 citations. Evaluation of ΔG=∫ 0 1 G(x)dx requires large x coverage in particular towards low x QPM expectation !

ΔG = ∫ 0 1 ΔG(x)dx

Physics Motivation: Spin16 July 9 th RHIC: Measurement of ΔG = ∫ 0 1 ΔG(x)dx ?

Physics Motivation: Spin17 July 9 th NLO QCD Analysis of DIS A 1 + A LL (π 0 ) M. Hirai, S. Kumano, N. Saito, hep-ph/ (Asymmetry Analysis Collaboration) DIS A 1 + A LL (π 0 ) ACC03 x

Physics Motivation: Spin18 July 9 th PHENIX π 0 A LL vs GSA-LO and GSC-NLO A LL p T [GeV] GSA-LO GSC-NLO PHENIX-2005-PPG063 GSA-LO: ΔG = ∫ΔG(x)dx = 1.7 GSC-NLO: ΔG = ∫ΔG(x)dx = 1.0 Large uncertainties resulting from the functional form used for ΔG(x) in the QCD analysis! GSA-LO and GSC-NLO courtesy Marco Stratmann and Werner Vogelsang

Physics Motivation: Spin19 July 9 th ΔG(x) A, B and C from Gehrmann Stirling present x-range Much of the first moment ΔG = ∫ΔG(x)dx might emerge from low x! Some theoretical guidance: ΔG(x) ≤ x G(x) but G(X) diverges faster than x -1 ! NEED TO EXTEND MEASUREMENTS TO LOW x !!

Physics Motivation: Spin20 July 9 th Increase integrated luminosity by factor 8 (2008) Extend measurements to low x  Di-hadron Production extends (2008) measurements to x  0.01 NLO treatment available: Marco Stratmann -- INPC 2007 (EMC forward calorimeters available in STAR and PHENIX!) Forward detector upgrades for direct (2011  ) photons and heavy flavor + highest luminosity reach x  Next Steps for ΔG(x) in PHENIX

Physics Motivation: Spin21 July 9 th Direct Photons (NCC) + Heavy Flavor (VTX+FVTX) NCC direct photons

Transverse Spin

Physics Motivation: Spin23 July 9 th Sivers in SIDIS vs Drell Yan Important test at RHIC of the fundamental QCD prediction of the non-universality of the Sivers effect! requires very high luminosity (~ 250pb -1 )

Physics Motivation: Spin24 July 9 th DY vs SIDIS, what do we learn? The Sivers effect arises from soft gluon interactions in the final state (SIDIS) or initial state (Drell Yan). Need to modify naïve concepts of factorization which reduce hard scattering to partonic processes and neglect soft gluon interactions in the initial or final state: hard scattering matrix elements are modified with gauge link integrals that account for initial and final state soft gluon exchange. A modified concept of universality has been obtained which shows how the presence of initial or final state interactions can impact transverse momentum dependent distribution; eg. the Sivers function changes sign between SIDS and Drell Yan! There may be exciting applications elsewhere, eg. other transverse momentum dependent effects or the understanding nuclear effects in hard scattering.

Physics Motivation: Spin25 July 9 th Simple QED example: DIS: attractive Drell-Yan: repulsive Same in QCD: As a result: Non-universality of Sivers Asymmetries: Unique Prediction of Gauge Theory ! from Werner Voglesang

Physics Motivation: Spin26 July 9 th Drell Yan at RHIC Large x  forward rapidity (Les Bland) Heavy flavor background (Ming Liu) ϒ-states J/Ψ Drell Yan Ψ’Ψ’ charm bottom  4 GeV < Q < 10 GeV b-background: use FVTX

Physics Motivation: Spin27 July 9 th x Sivers Amplitude 0 Experiment SIDIS vs Drell Yan: Sivers| DIS = − Sivers| DY *** Test QCD Prediction of Non-Universality *** HERMES Sivers Results Markus Diefenthaler DIS Workshop Műnchen, April RHIC II Drell Yan Projections Feng Yuan Werner Vogelsang

Δq(x), Δq(x)

Physics Motivation: Spin29 July 9 th Semi-Inclusive DIS: e+p  e+ h +X Quark & Anti-Quark Helicity Distributions u quarks large positive polarization d quark have negative polarization sea quarks (u, d, s,s) compatible with 0 in the measured x-range 0.02 < x < 0.6. [HERMES, PRL92(2004), PRD71(2005)] x Future: Precision DIS at JLAB-12 and at a possible electron – ion collider! xΔu(x) xΔd(x) xΔu(x) xΔd(x) xΔs(x) How well do we know hadron fragmentation functions ?  new analysis of e+e- data, Hirai, Kumano, Nagai, Sudo hep-ph/ , INPC 2007 Possible Improvements  include e-p, p-p and e+e- in fragmentation function analysis  done! De Florian, Sassot, Stratmann hep-ph/  “add data” from b-factories e+e-  hadrons

Physics Motivation: Spin30 July 9 th Belle MC <1% of data sample  work in progress Possible Impact on the Knowledge of Hadron FFs from Analysis of b-Factory Data FF Compilation of data available for the char- ged hadron FF Belle MC: Charged h +/-, pions, kaons, protons precision at high z!  h+,-  pions  kaons  protons Input for precision measurements of quark helicity distributions in SIDIS, with JLab-12 and a possible future electron- polarized proton collider.

Physics Motivation: Spin31 July 9 th Another Alternative: W-production at RHIC SIDIS: large x-coverage uncertainties from knowing fragmentation functions Ws in polarized p-p: limited x-coverage high Q 2  theoretically clean no FF-info needed Background: Absorber (S/B 3:1), isolation using FVTX/NCC additional factor 3-5 Hermes – 243 pb -1 PHENIX – 800 pb -1

Physics Motivation: Spin32 July 9 th Present vs with upgrades Inclusive hadrons + photons heavy flavor, photons, photon-jet  increase x-range  parton kinematics not possible without upgrades, A N for inclusive hadronen A T in Interference-Fragmentation A T Collins FF in jets A N for back-to-back hadronen A N,T jets, Ds, DY Physics Goals determine first moment of the spin dependent gluon distribution, ∫ 0 1 ΔG(x)dx. flavor seperation of quark and anti-quark spin distri- butions measurement of trans- versity quark distributions. Measurement of the Sivers distributions Nucleon Spin Structure: Physics Impact of VTX, FVTX, NCC and Muon Trigger Upgrades Sivers Effect

Physics Motivation: Spin33 July 9 th Summary RHIC and it’s experiments are the world’s first facility capable of colliding high energy polarized protons with high polarization and luminosity. The planned detector upgrades significantly strengthen PHENIX’ capabilities to study nucleon structure: (1) Measurement of the gluon spin contribution ∫ΔG(x)dx  large x-range  event-by-event kinematics  heavy flavor + photon jet are new channels with independent experimental and theoretical uncertainties (2) First measurements with spin dependent W-production! (3) Transverse spin: Collins fragmentation and Gluon Sivers in multiple channels. Test fundamental prediciton on non-universality of the Sivers function in Drell Yan!