1. Studies on nucleon spin at PHENIX 3 rd International Conference on New Frontiers in Physics Kolymbari, Greece August 2, 2014 Kiyoshi Tanida (Seoul National University) for the PHENIX Collaboration

2. What are we aiming at? To study proton’s spin structure The flagship question: “Where the proton spin comes from?” –Proton spin puzzle –Helicity distribution of partons in longitudinally polarized protons, especially gluons –Flavor-decomposed quark helicity distribution using Ws What’s there in transversely polarized protons? –  q ≠  q –Very hot recently –Needs more than simple collinear picture to understand 2

3. PART 1: Helicity distributions with longitudinal polarization

4. Helicity distributions Lepton deep inelastic scattering (DIS) experiments –Quasi-elastic scattering of quark and lepton at high energies where perturbation is applicable –Reaction depends on quark spin  spin structure function

5. Proton spin puzzle Quark spin carries only 20-30% of the nucleon spin  spin puzzle (crisis) What carries the rest? –Gluon spin? –Orbital angular momentum? Our Main Goal 0.2-0.3

6. What we can’t know from DIS Photon mediated  sensitive to charge 2 –u : d : s : g = 4 : 1 : 1 : 0 –Gluon is invisible! (c.f., indirect methods: Q 2 evolution, photon-gluon fusion) Can we see gluons directly?  Yes, what we need is a Polarized Proton collider 6

7. RHIC p+p accelerator complex BRAHMS & PP2PP STAR PHENIX AGS LINAC BOOSTER Pol. Proton Source Spin Rotators 20% Snake Siberian Snakes 200 MeV polarimeter Rf Dipoles RHIC pC “CNI” polarimeters PHOBOS RHIC absolute pH polarimeter Siberian Snakes AGS pC “CNI” polarimeter 5% Snake Coulomb-Nuclear Interference

8. What do we measure? ~ (parton pol.) 2 × (a LL in parton reaction) 8

9. How can we access gluons? Typical parton level diagrams （ LO ） What we actually measure are not partons, but fragmented hadrons –Come from different mix of partons –Parton information （ e.g., Bjorken x ） is obscured 9

10. Result --  0 A LL @200 GeV 10 PRD90 (2014) 012007

11. Impact on Global Analysis Including DIS and other data as well as RHIC data –Based on DSSV [PRL101 (2008) 072001, PRD 80 (2009) 034030] 11

12.  Parity Violation Asymmetry Clean flavor separation w/o fragmentation uncertainty W measurement

13. W asymmetries@500-510 GeV 13 yeye Central arm (e) – 2011-13 Muon arm – 2011,12 Consistent with theories Will be finalized soon

14. Part 2: Transverse spin physics 14

15. Transverse spin physics Transversity  q: Due to Einstein’s relativity, not the same as  q –Unexplored leading twist PDF A N ： left-right asymmetry wrt transverse polarization x F <0 x F >0 R L Left Right 15

16. Requirements for A N Helicity flip amplitude & relative phase In QCD, helicity is conserved if m q =0.  A N ~  s m q /p T ~ O(10 -3 ) in naive collinear picture

17. Reality However, large A N observed in forward particles. WHY?? We need something more  hot topic 17 PRD90 (2014) 012006

18. (ii) Collins mechanism: Transversity (quark polarization) × jet fragmentation asymmetry (i) Sivers mechanism: correlation between proton spin & parton k T SPSP p p SqSq k T, π Possible mechanisms (ex.) SPSP k T,q p p SqSq Phys Rev D41 (1990) 83; 43 (1991) 261 Nucl Phys B396 (1993) 161 18 (iii) Twist 3: quark-gluon/gluon-gluon correlation  A source for Sivers function Expectation: at large p T, A N ~ 1/p T

19. Recent results -- forward 19 No √s dependence – scaling effect? Same behavior for   &  PRD90 (2014) 012006 arXiv:1406.3541

20. Forward – p T dependence 20 Twist-3 calculation (by Kanazawa & Koike) : quite good –Though naïve 1/p T dependence not seen arXiv:1406.3541

21. Midrapidity   and  Exceeds precision of previous result by factor of 20, extends pT range [PRL 95 (2005) 202001] A N is zero within 0.1%  contrast with forward hadrons Theories must be able to explain those features at the same time. 21 PRD90 (2014) 012006

22. Summary & Outlook 22

23. Backups 23

24. The Relativistic Heavy Ion Collider accelerator complex at Brookhaven National Laboratory PHENIX STAR Brahms pp2pp 24

25. RHIC p+p accelerator complex BRAHMS & PP2PP STAR PHENIX AGS LINAC BOOSTER Pol. Proton Source Spin Rotators 20% Snake Siberian Snakes 200 MeV polarimeter Rf Dipoles RHIC pC “CNI” polarimeters PHOBOS RHIC absolute pH polarimeter Siberian Snakes AGS pC “CNI” polarimeter 5% Snake Coulomb-Nuclear Interference 25

26. PHENIX Experiment Pioneering High Energy Nuclear Interaction EXperiment 26

27. 13 Countries; 70 Institutions Abilene Christian University, Abilene, TX 79699, U.S. Baruch College, CUNY, New York City, NY 10010-5518, U.S. Collider-Accelerator Department, Brookhaven National Laboratory, Upton, NY 11973-5000, U.S. Physics Department, Brookhaven National Laboratory, Upton, NY 11973-5000, U.S. University of California - Riverside, Riverside, CA 92521, U.S. University of Colorado, Boulder, CO 80309, U.S. Columbia University, New York, NY 10027 and Nevis Laboratories, Irvington, NY 10533, U.S. Florida Institute of Technology, Melbourne, FL 32901, U.S. Florida State University, Tallahassee, FL 32306, U.S. Georgia State University, Atlanta, GA 30303, U.S. University of Illinois at Urbana-Champaign, Urbana, IL 61801, U.S. Iowa State University, Ames, IA 50011, U.S. Lawrence Livermore National Laboratory, Livermore, CA 94550, U.S. Los Alamos National Laboratory, Los Alamos, NM 87545, U.S. University of Maryland, College Park, MD 20742, U.S. Department of Physics, University of Massachusetts, Amherst, MA 01003-9337, U.S. Morgan State University, Baltimore, MD 21251, U.S. Muhlenberg College, Allentown, PA 18104-5586, U.S. University of New Mexico, Albuquerque, NM 87131, U.S. New Mexico State University, Las Cruces, NM 88003, U.S. Oak Ridge National Laboratory, Oak Ridge, TN 37831, U.S. Department of Physics and Astronomy, Ohio University, Athens, OH 45701, U.S. RIKEN BNL Research Center, Brookhaven National Laboratory, Upton, NY 11973-5000, U.S. Chemistry Department, Stony Brook University,SUNY, Stony Brook, NY 11794-3400, U.S. Department of Physics and Astronomy, Stony Brook University, SUNY, Stony Brook, NY 11794, U.S. University of Tennessee, Knoxville, TN 37996, U.S. Vanderbilt University, Nashville, TN 37235, U.S. Universidade de São Paulo, Instituto de Física, Caixa Postal 66318, São Paulo CEP05315-970, Brazil Institute of Physics, Academia Sinica, Taipei 11529, Taiwan China Institute of Atomic Energy (CIAE), Beijing, People's Republic of China Peking University, Beijing, People's Republic of China Charles University, Ovocnytrh 5, Praha 1, 116 36, Prague, Czech Republic Czech Technical University, Zikova 4, 166 36 Prague 6, Czech Republic Institute of Physics, Academy of Sciences of the Czech Republic, Na Slovance 2, 182 21 Prague 8, Czech Republic Helsinki Institute of Physics and University of Jyväskylä, P.O.Box 35, FI-40014 Jyväskylä, Finland Dapnia, CEA Saclay, F-91191, Gif-sur-Yvette, France Laboratoire Leprince-Ringuet, Ecole Polytechnique, CNRS-IN2P3, Route de Saclay, F-91128, Palaiseau, France Laboratoire de Physique Corpusculaire (LPC), Université Blaise Pascal, CNRS-IN2P3, Clermont-Fd, 63177 Aubiere Cedex, France IPN-Orsay, Universite Paris Sud, CNRS-IN2P3, BP1, F-91406, Orsay, France Debrecen University, H-4010 Debrecen, Egyetem tér 1, Hungary ELTE, Eötvös Loránd University, H - 1117 Budapest, Pázmány P. s. 1/A, Hungary KFKI Research Institute for Particle and Nuclear Physics of the Hungarian Academy of Sciences (MTA KFKI RMKI), H-1525 Budapest 114, POBox 49, Budapest, Hungary Department of Physics, Banaras Hindu University, Varanasi 221005, India Bhabha Atomic Research Centre, Bombay 400 085, India Weizmann Institute, Rehovot 76100, Israel Center for Nuclear Study, Graduate School of Science, University of Tokyo, 7-3-1 Hongo, Bunkyo, Tokyo 113-0033, Japan Hiroshima University, Kagamiyama, Higashi-Hiroshima 739-8526, Japan KEK, High Energy Accelerator Research Organization, Tsukuba, Ibaraki 305-0801, Japan Kyoto University, Kyoto 606-8502, Japan Nagasaki Institute of Applied Science, Nagasaki-shi, Nagasaki 851-0193, Japan RIKEN, The Institute of Physical and Chemical Research, Wako, Saitama 351-0198, Japan Physics Department, Rikkyo University, 3-34-1 Nishi-Ikebukuro, Toshima, Tokyo 171-8501, Japan Department of Physics, Tokyo Institute of Technology, Oh-okayama, Meguro, Tokyo 152-8551, Japan Institute of Physics, University of Tsukuba, Tsukuba, Ibaraki 305, Japan Chonbuk National University, Jeonju, Korea Ewha Womans University, Seoul 120-750, Korea Hanyang University, Seoul 133-792, Korea KAERI, Cyclotron Application Laboratory, Seoul, South Korea Korea University, Seoul, 136-701, Korea Myongji University, Yongin, Kyonggido 449-728, Korea Department of Physocs and Astronomy, Seoul National University, Seoul, South Korea Yonsei University, IPAP, Seoul 120-749, Korea IHEP Protvino, State Research Center of Russian Federation, Institute for High Energy Physics, Protvino, 142281, Russia INR_RAS, Institute for Nuclear Research of the Russian Academy of Sciences, prospekt 60-letiya Oktyabrya 7a, Moscow 117312, Russia Joint Institute for Nuclear Research, 141980 Dubna, Moscow Region, Russia Russian Research Center "Kurchatov Institute", Moscow, Russia PNPI, Petersburg Nuclear Physics Institute, Gatchina, Leningrad region, 188300, Russia Saint Petersburg State Polytechnic University, St. Petersburg, Russia Skobeltsyn Institute of Nuclear Physics, Lomonosov Moscow State University, Vorob'evy Gory, Moscow 119992, Russia Department of Physics, Lund University, Box 118, SE-221 00 Lund, Sweden Feb 2011

28. The PHENIX Detector Philosophy –high resolution & high-rate at the cost of acceptance –trigger for rare events Central Arms –|  | < 0.35,  ~  –Momentum, Energy, PID Muon Arms –1.2 < |  | < 2.4 –Momentum (MuTr) Muon piston calorimeter –3.1 < |  | < 3.9 28

29. Forward Calorimetry: MPC Muon Piston Calorimeter (3.1 < |h| < 3.9) : lower x  10 -3 29 Cluster (   dominant) A LL Decay photon π 0 Direct photon PTPT Fraction of clusters

30. How to extract  g(x)? (1)  0 s come from quarks and gluons of various x  Deconvolution necessary Are we sure that we understand contribution of partons? YES! –NLO-pQCD calculation reproduces  well    @200 GeV,  ~0 PRD76:051106,2007 30

31. How to extract  g(x)? (2) Practical analysis –Assume functional form: e.g.,  g(x)=Cg(x)x  (1-x)  –Search optimum parameters using data, including DIS. Ex ： GRSV （ M. Gluck et al., PRD 63 (2001) 094005. ） – Assume  G, other parameters are determined from DIS. – Several versions for various  G （ GRSV-std, max, min,... ） Several other analyses –For the same integral,  G,  g(x) could be very different –Our measurement mostly constrains  G [0.02,0.3] 31

32. Global Fit including Run9  0 A LL By S.Taneja et al (DIS2011) ala DSSV with slightly different uncertainty evaluation approach DSSV DSSV + PHENIX Run9  0 A LL No node … Uncertainties decreased A node at x~0.1 ? 32

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