Proton Spin Physics in Polarized Proton-proton Collisions at Tai Sakuma MIT
Introduction to the spin structure of the proton The naïve quark parton model - aka Static Constituent Quark Model - three stationary massive quarks each weighs approx. ⅓ of the proton mass - able to reproduce many properties of baryons; e.g., magnetic moment of proton, neutron, hyperons baryon spectrum - quarks in a s-state u no orbital angular momentum u Σ = (quarks spin carries all proton spin) d 2
Introduction to the spin structure of the proton Spin Crisis - EMC experiment at CERN in 988 polarized deep inelastic scattering (pdis) Σ = 0.4 ± 0.09 ± 0.2 Quarks spin carries only a small fraction of proton spin - Σ = 0.33 ± 0.03 ± 0.05 (recent value COMPASS, CERN, 2007) - lately less sensationally called Spin Puzzle 3
u d u Static Constituent Quark Model lack of motion of quarks lack of dynamics of quarks Σ = (contradicts with the measured value) u u d Relativistic Constituent Quark Model relativistic motion of quarks - quarks mass is tiny - proton mass is largely due to kinetic energy of quarks - Dirac equation indicates orbital motion of quarks - Σ 0.65 (still much larger than the measured value) lack of dynamics of quarks 4 Quantum Chromodynamics (QCD) dynamics are mediated by vector field, gluons axial anomaly; spin vector current is not conserved Gluons can share proton spin; ΔG 0
Introduction to the spin structure of the proton Decomposition of proton spin 2 = 2 Σ + G + L q + L g proton quark spin gluon spin orbital motion Quark spin and gluon spin contributions can be expressed in terms of polarized parton distribution functions Σ = u + ū + d + d + s + s q = (q + (x) q (x))dx 2 G = 0 g(x)dx g(x)=g + (x) g (x) 0 x : a momentum fraction Σ has been measured by pdis (Σ 0.33) How do you measure ΔG? Is it possible to measure L q + L g?
Measurement of ΔG Polarized Deep Inelastic Scattering (pdis) Polarized Semi-inclusive DIS (psidis) Polarized Proton-proton Collisions 6
Measurement of ΔG Polarized Deep Inelastic Scattering (pdis) q not as sensitive to ΔG as it is to Σ - leptons do not couple to gluons x Q 2 =-q 2 Q 2 -evolution of Δq(x, Q 2 ) potentially yields Δg(x, Q 2 ) xg 0.6 0.4 0.2 0.0-0.2-0.4-0.6 Gluon Distribution Functions of the Proton GRSV STD GS-C GRSV g = g GRSV g = 0 GRSV g = g GRSV G = -0.5 GRSV G = -0.3 GRSV G = -0.45 GRSV G = -0.6 GRSV G = -0.75 GRSV G = -0.9 GRSV G = -.05 GRSV G = 0.7 GRSV G = 0.6 GRSV G = 0.45 GRSV G = 0.3 0 3 0 2 0. x Q 2 = 4 GeV 2 global analysis of polarized parton distributions - e.g., GS, GRSV, LSS, AAC - determined Δq(x, Q 2 ) with some accuracy - constrained Δg(x, Q 2 ) little Q 2 -evolution is slow present pdis data cover a limited range of x and Q 2 almost any Δg(x, Q 2 ) fits pdis data
Measurement of ΔG Polarized Semi-inclusive Deep Inelastic Scattering (psidis) detect hadrons simultaneously with scattered leptons photon-gluon fusion process - directly sensitive to ΔG - higher-order processes HERMES at DESY SMC, COMPASS at CERN g/g 0.8 0.6 0.4 fit with G>0 fit with G<0 COMPASS, open charm, prel. 2 COMPASS, high p, Q <, prel. T 2 COMPASS, high p, Q >, prel. 2 T SMC, high p, Q > T 2 HERMES, high p, all Q, (2000) T 2 HERMES, high p, all Q, incl., prel. T 0.2-0 -0.2-0.4 8-0.6-2 0-0 x
Measurement of ΔG Polarized Proton-proton collisions gluons at the leading order challenging to determine x and Q 2 PHENIX, at RHIC, BNL 9
Measurement of ΔG Polarized Proton-proton collisions 0 Double Longitudinal Spin Asymmetries A LL - the primary quantity to measure - defined as - sensitive to Δg(x, Q 2 ); the first moment is ΔG - in the QCD factorization: A LL = i,j i,j Cross Sections σ - test QCD factorization A LL = σ σ = (σ++ + σ ) (σ + + σ + ) (σ ++ + σ )+(σ + + σ + ) dx σ = dx i,j dx 2 f i (x,q 2 ) f j (x 2,Q 2 )â LL ˆσ(cosθ ) dx 2 f i (x,q 2 )f j (x 2,Q 2 ) ˆσ(cosθ ) dx dx 2 f i (x,q 2 )f j (x 2,Q 2 ) ˆσ(cosθ ) G = 0 g(x)dx â LL, ˆσ : parton level
Measurement of ΔG Polarized Proton-proton collisions determination of parton-level kinematics in DIS, it can be always determined x = Q2 2Mν in pp, not unless two outgoing partons are measured 2 3 4 x = ˆp T s (e +y 3 + e +y 4 ) x 2 = ˆp T s (e y 3 + e y 4 ) dijets, γ - jet
RHIC as a polarized proton-proton collider The world s first and only polarized proton-proton collider s = 23 ~ 500 GeV PHOBOS 2 RHIC BRAHMS 0 2 Run s [GeV] Ldt[pb ] a Polarization b Run-2 200 0.47 4% Run-3 200 2.5 34% Run-4 200 3.2 46% Run-5 200 2.7 46% PHENIX 8 Yellow 6 Siberian Snakes 4 Blue Run-6 200 44.9 58% 62 0.325 50% OPPIS AGS Booster Partial Snake AtR Run-8 200 9.2 44% Run-9 500 52.6 40% 200 53.5 56% LINAC 200m AGS a Delivered luminosity at b Average polarization 2 Brookhaven National Laboratory (BNL), Long Island, NY
Detector =- =0 BEMC = a full-azimuth calorimeter Blue BBC Yellow a full-azimuth tracking device TPC West East 3 Tai Sakuma
Jets at Jets are sprays of particles which are moving approximately in the same direction from the collision point. 4
Jets at Parameters of Recent Jet Analysis JP 7 JP 40 billion polarized proton-proton JP 6 JP 0 JP 8 JP 2 collisions at 200 GeV, RHIC Run-6 Jet Patch Trigger - E T > 8.3 GeV in a jet patch JP JP 5 JP 0 JP 9 JP 3 z - minimum bias condition Jet Patches JP 4 Jet Definition - Charged tracks in TPC 2009 Tai Sakuma - Energy deposits in BEMC towers - Mid-point cone (R=0.7) Dijet Definition - Two-leading p T jets 5 a dijet event
Jets at two quantities to measure - Jet Spin Asymmetries A LL to extract Δg(x, Q 2 ) - Jet Cross Sections test theory used to extract Δg(x, Q 2 ) from A LL pdf, pqcd, jet definitions, hadronization and underlying events 6 two final states to observe - Dijets - the best channel at RHIC started at Run-6 - Inclusive jets - best alternative at measured for Run-3/4/5/6/9
Jets at Parton Level Jets at three levels " " MC Theory (pqcd) Data () MC Hadron Level # # $# " $ $ " " $ " # K s 0 $ " " $ # $ $ " Detector Level Data and theory are corrected to hadron level using Monte Carlo (MC) simulation
Jets at Data-MC comparison of inclusive jets Correction factors are determined with MC samples which well reproduce data..0 26.9 < pt < 39.63 GeV 39.63 < pt < 59.96 GeV 39.63 < pt < 59.96 GeV 0 5 0 4 0 3 0 2 0 (Data - MC) / MC 0 - Run-6 Data MC 20 40 60 80 p T [GeV] Preliminary Preliminary Jet Profile (r) 0.8 0.6 0.4 0.2.0 0.8 0.6 0.4 0.2.44 < pt < 7.3 GeV 0.2 0.4 0.6 0.8 r/r from Jet Axis Preliminary 7.3 < pt < 26.9 GeV Data MC 0.2 0.4 0.6 0.8 MC: Pythia 6.4 + Geant 3 26.9 < pt < 39.63 GeV 2.3 < pt < 26.9 GeV 7.3 < pt < 2.3 GeV Preliminary.44 < pt < 7.3 GeV Data MC 8 20 30 40 50 60 pt [GeV] 0.8 <η<0.8 0.2 0.4 0.6 0.8 Neutral Energy Ratio R T
Jets at Data-MC comparison of dijets max(p T ) > 0.0 GeV min(p T ) > 7.0 GeV 0.8 <η<0.8 η 3 η 4 <.0 ϕ > 2.0 Data are well described by MC 0 5 0 4 MC: Pythia 6.4 + Geant 3 Preliminary Dijet Yield 0 4 0 3 0 2 0 24 < M < 36 GeV 36 < M < 53.6 GeV 53.6 < M < 84.5 GeV Data MC 84.5 < M < 68.5 GeV Preliminary 0 4 0 3 0 2 0 Dijet Yield 0 3 0 2 0 Run-6 Data MC (Data - MC) / MC 0-0 - 30 50 70 90 0 M jj [GeV] -0.5 0.0 0.5-0.5 0.0 0.5-0.5 0.0 0.5-0.5 0.0 0.5 24 < M < 36 GeV 36 < M < 53.6 GeV 53.6 < M < 84.5 GeV 84.5 < M < 68.5 GeV 9 (Data - MC) / MC 0 - Preliminary 50 00 M jj [GeV] Dijet Yield (Data - MC) / MC 0 4 0 3 0 2 0 0 - Data MC Preliminary 0.5.0.5 0.5.0.5 0.5.0.5 0.5.0.5 0 4 0 3 0 2 0 0 -
Inclusive Jet Cross Section 0 5 0 4 Inclusive Jet Cross Section pp @ 200 GeV Cone Radius = 0.7-0.8 < < 0.8 pp 200 GeV, RHIC Run-6 update from the previous measurements based on Run-3/4 data [PRL 97 (2006) 25200] with smaller acceptance and cone size d 2 / 2dp T d [pb/gev] 0 3 0 2 0 d 2 2dp T d Run-6 Systematic Uncertainty Preliminary Ldt = 5.39 pb well described by theory which is used to extract 0. Theory NLO pqcd + CTEQ6M polarized parton distributions from inclusive jet A LL provide reference for heavy-ion collisions Had. and UE. Corrections 5 20 25 30 35 40 45 50 55 p T [GeV] 20 d 2 σ 2πdp T dη = Ldt 2π p T η C N jets N jets : Detector-level jet yields C: Correction factors 2π p T η: Phase space volume Ldt: Luminosity (Data - Theory) / Theory -.0-0.5 0.0 0.5.0 Run-6 Data-theory Comparison of Inclusive Jet Cross Section pp @ 200 GeV Cone Radius = 0.7-0.8 < < 0.8 5 20 25 30 35 40 45 50 55 p T [GeV] Systematic Uncertainty Theoretical Uncertainty Ldt = 5.39 pb Preliminary
Dijet Cross Section Dijet Cross Section 05 pp @ 200 GeV Cone Radius = 0.7 max(pt) > 0 GeV, min(pt) > 7 GeV -0.8 < < 0.8, <.0 04 pp 200 GeV, RHIC Run-6 the first measurement at RHIC well described by theory which can be used to extract d3/dmd3d4 [pb/gev] > 2.0 Preliminary 03 Ldt = 5.39pb d 3 02 dmd3d4 Run-6 0 Systematic Uncertainty polarized parton distributions from dijet ALL Theory NLO pqcd + CTEQ6M Had. and UE. Corrections 30 40 50 60 70 80 90 Mjj [GeV] 2 Detector-level dijet yields Correction factors Phase space volume Luminosity.0 Theoretical Uncertainty Ldt = 5.39 pb -.0 Njets : C: Mjj η 3 η4 : Ldt: Systematic Uncertainty (Data - Theory) / Theory -0.5 0.0 0.5 d3 σ = Njets dmjj dη3 dη4 Ldt Mjj η3 η4 C Preliminary Data-theory Comparison of Dijet Cross Section pp @ 200 GeV Cone Radius = 0.7 max(pt) > 0 GeV, min(pt) > 7 GeV -0.8 < < 0.8, <.0, > 2.0 30 40 50 60 Mjj [GeV] Run-6 Theory: CTEQ6M NLO pqcd Had. UE. Corrections 70 80 90
Inclusive Jet Double Longitudinal Spin Asymmetry A LL pp 200 GeV, RHIC Run-6 second update - Run-5 data [PRL 00 (2008) 232003] ALL 0. 0.08 0.06 2006 Preliminary GRSV-std GRSV g=g GRSV g=0 GRSV g=-g GS-C - Run-3/4 data [PRL 97 (2006) 25200] 0.04 inconsistent with large ΔG probed 0.02 < x < 0.3 Gluon Distribution Functions of the Proton 0.02 0-0.02 Online polarization 0 5 20 25 30 35 p (GeV/c) T 0.6 0.4 DSSV GRSV STD GS-C GRSV g = g GRSV g = 0 GRSV g = g probed by RHIC A LL provided significant constraint on Δg(x, Q 2 ) in a global analysis of polarized pdf, DSSV 0.2 [PRL 0 (2008) 07200] xg 0.0 confirmed the relevance of a probing wider -0.2 range of x -0.4-0.6 GRSV G = -0.5 GRSV G = -0.3 GRSV G = -0.45 GRSV G = -0.6 GRSV G = -0.75 GRSV G = -0.9 GRSV G = -.05 GRSV G = 0.7 GRSV G = 0.6 GRSV G = 0.45 GRSV G = 0.3 Q 2 = 4 GeV 2 stimulated the discussion of the measurements of the orbital motions of partons 0 3 0 2 0. x
Dijet Double Longitudinal Spin Asymmetry A LL the first measurement of dijet A LL consistent with DSSV prediction as a function of invariant mass M jj 0.08 0.06 0.04 Dijet A LL pp @ 200 GeV Cone Radius = 0.7 max(p T ) > 0 GeV min(p T ) > 7 GeV -0.8 < < 0.8, <.0 > 2.0 Data Run-6 Sys. Uncertainty Preliminary - relevant for the first measurement - not optimal for the purpose A LL 0.02 0.00 will be extended to wider acceptance with η dependence -0.02 GRSV STD DSSV GRSV g = 0 GRSV g = g Ldt = 5.39pb 30 40 50 60 70 80 M jj [GeV] 23
Summary The spin puzzle remains unsolved polarized DIS showed quarks spin carry only ~30% of the proton s spin RHIC-Spin suggested a possibility of small gluon s spin contribution RHIC-Spin will extend the kinematical coverage of the measurement The possibility of measuring orbital motions is being explored 2 = 2 Σ + G + L q + L g 24