Nucleon spin and parton distribution functions

Nucleon spin and parton distribution functions Jörg Pretz Physikalisches Institut, Universität Bonn on behalf of the COMPASS collaboration COMPASS Hadron 2011, Munich Jörg Pretz Nucleon Spin and pdfs 1 / 40

Motivation Motivation I: Where does the Nucleon Spin come from? 1 2 = 1 2 Σ + G +L q +L G Jörg Pretz Nucleon Spin and pdfs 2 / 40

Motivation Motivation I: Where does the Nucleon Spin come from? 1 2 = 1 2 Σ + G +L q +L G Motivation II: Parton Distribution Functions: unpolarized q(x),g(x) Jörg Pretz Nucleon Spin and pdfs 2 / 40

Motivation Motivation I: Where does the Nucleon Spin come from? 1 2 = 1 2 Σ + G +L q +L G Motivation II: Parton Distribution Functions: unpolarized q(x),g(x) helicity q(x), g(x) Jörg Pretz Nucleon Spin and pdfs 2 / 40

Motivation Motivation I: Where does the Nucleon Spin come from? 1 2 = 1 2 Σ + G +L q +L G Motivation II: Parton Distribution Functions: unpolarized q(x),g(x) helicity q(x), g(x) transversity T q(x) Transverse Momentum dependent (TMD) distributions Generalized Parton distributions (GPDs) Jörg Pretz Nucleon Spin and pdfs 2 / 40

Outline Motivation Helicity distribution of quarks and gluons mainly results from deep inelastic scattering (polarized pp E. Aschenauer) Transversity distributions & Transverse Momentum Dependent (TMD) distributions mainly asymmetries (extraction of TMDs M. Anselmino) Future measurements Jörg Pretz Nucleon Spin and pdfs 3 / 40

Helicity Distributions Jörg Pretz Nucleon Spin and pdfs 4 / 40

What do we know? helicity contribution of quarks to nucleon spin: Σ 30% But how do contributions of different flavors q(x),q = u,d,s,ū, d, s look like? gluon helicity distribution G = 1 0 g(x)dx small? But how small? How does g(x) look like? Jörg Pretz Nucleon Spin and pdfs 5 / 40

Helicity distributions How can they by measured? Find a process where one probes interaction with quark/gluon of a given polarization with respect to the parent nucleon. Can be done in two ways, using 1 double polarization in Deep Inelastic Scattering: l+ N l +hadrons+x Proton-Proton Scattering: p + p Jet/γ/hadrons + X 2 single polarization & weak interaction: p +p W ± e ± +ν Jörg Pretz Nucleon Spin and pdfs 6 / 40

Experiments Jörg Pretz Nucleon Spin and pdfs 7 / 40

Proton Asymmetry l(k)+ N(p) l (k )+X(P X ) p A 1 0.12 0.8 0.1 0.08 0.06 0.6 0.04 0.02 0-0.02 0.4 0.2 0-2 -2 x EMC SMC E143 E155 HERMES CLAS W>2.5 COMPASS -1 x 1 0 p A 1 0.8 0.6 0.4 0.2 Q 2 = (k k) 2 Q 2 > 1 GeV 2 x = Q 2 2p (k k ) good agreement, although different Q 2 at same x N N N +N A p 1 = gp 1 F p 1 = 4( u+ ū)+( d+ d)+( s+ s) 4(u+ū)+(d+ d)+(s+ s) Jörg Pretz Nucleon Spin and pdfs 8 / 40

Stamp Collection: inclusive asymmetries Jörg Pretz Nucleon Spin and pdfs 9 / 40

Result on first moments q = 1 0 q(x)dx using inclusive & semi-inclusive asymmetries, p p, neutron & hyperon decay: global analysis 1) Σ = 0.25 ± 0.05 u + ū = 0.81±0.03 d + d = 0.46±0.03 s + s = 0.11±0.06 at Q 2 = GeV 2 1 ) (DSSV) D. de Florian, R. Sassot, M. Stratmann and W. Vogelsang, Phys. Rev. D 80 (2009) 034030, [arxiv:0904.3821 [hep-ph]], (error only for measured region 0.001 < x < 1) Jörg Pretz Nucleon Spin and pdfs / 40

Result on first moments q = 1 0 q(x)dx using inclusive & semi-inclusive asymmetries, p p, neutron & hyperon decay: global analysis 1) lattice QCD 2) Σ = 0.25 ± 0.05 u + ū = 0.81±0.03 0.82±0.04 d + d = 0.46±0.03 0.41±0.04 s + s = 0.11±0.06 at Q 2 = GeV 2 1 ) (DSSV) D. de Florian, R. Sassot, M. Stratmann and W. Vogelsang, Phys. Rev. D 80 (2009) 034030, [arxiv:0904.3821 [hep-ph]], (error only for measured region 0.001 < x < 1) 2 ) J. D. Bratt et al. [LHPC Collaboration], Phys. Rev. D 82 (20) 094502, [arxiv:01.3620 [hep-lat]] Jörg Pretz Nucleon Spin and pdfs / 40

Result on first moments q = 1 0 q(x)dx using inclusive & semi-inclusive asymmetries, p p, neutron & hyperon decay: global analysis 1) lattice QCD 2) Σ = 0.25 ± 0.05 u + ū = 0.81±0.03 0.82±0.04 d + d = 0.46±0.03 0.41±0.04 s + s = 0.11±0.06 at Q 2 = GeV 2 up to now only information on first moments of q+ q, because e 2 q = e 2 q 1 ) (DSSV) D. de Florian, R. Sassot, M. Stratmann and W. Vogelsang, Phys. Rev. D 80 (2009) 034030, [arxiv:0904.3821 [hep-ph]], (error only for measured region 0.001 < x < 1) 2 ) J. D. Bratt et al. [LHPC Collaboration], Phys. Rev. D 82 (20) 094502, [arxiv:01.3620 [hep-lat]] Jörg Pretz Nucleon Spin and pdfs / 40

Helicity distributions How to separate contributions from q(x) and q(x)? Principle: Measure double spin asymmetries of various hadronic final states h in l+ N l +X +hadrons N h N h N h +N h A h = q e2 q( q(x)dq(z)+ q(x)d h h q (z)) q e2 q(q(x)dq(z)+ q(x)d h h q (z)) D h q: fragmentation function Dq(z)dz h = number of hadrons of type h produces from a quark q with energy fraction in [z,z +dz] Du π+ > Dū π+ Kaon asymmetries are for example are sensitive to s ( N. Makke, Tue 16.50) Jörg Pretz Nucleon Spin and pdfs 11 / 40

Semi-Inclusive Asymmetries 0.8 A 1,p 0.6 0.4 0.2 0 π+ A 1,p K+ A 1,p -0.2-2 -1 x 0.8 π- A 1,p 1 0.8 K- A 1,p COMPASS HERMES DSSV fit 0.6 0.4 0.6 0.4 0.2 0.2 0 0-0.2-2 -1 x -2-1 x Jörg Pretz Nucleon Spin and pdfs 12 / 40

Asymmetries q in LO QCD Solve: A = B q A = (A 1,p,A π+ 1,p,AK+ 1,p,...,A 1,d,...,A K 1,d ) q = ( u, d, s, ū, d, s) B(q, D h qdz) Jörg Pretz Nucleon Spin and pdfs 13 / 40

u(x), d(x), s(x), ū(x), d(x), s(x) 0.4 x u 0.2 x d 0-0.2 0.05 x u 0-0.05 0.02 x s 0-0.02-0.04-2 assuming s = s -1 0.05 x d 0-0.05 x -2-1 COMPASS HERMES [PRD71 (2005)] DSSV x Jörg Pretz Nucleon Spin and pdfs 14 / 40

Helicity distributions from pp at RHIC Instead of measuring double spin asymmetries, one can measure single spin asymmetries and use weak interaction Done at RHIC ( p +p W ± e ± +ν at s = 500 GeV) p u + W ν p d + l A W+ L = d(x 1 )u(x 2 ) u(x 1 ) d(x 2 ) u(x 1 ) d(x 2 )+ d(x 1 )u(x 2 ) A W L = (u d) no fragmentation func.! Jörg Pretz Nucleon Spin and pdfs 15 / 40

Results STAR PHENIX Jörg Pretz Nucleon Spin and pdfs 16 / 40

Gluon Helicity Jörg Pretz Nucleon Spin and pdfs 17 / 40

How to measure G? Deep Inelastic scattering ln l +high p T hadrons+x A q& g contribution of g enhanced due to selection of high p T ln l +charmed meson+x A g clean tag of glue Polarized pp scattering p p hadrons+x A q q& q g& g g p p jet+x p p jet+jet+x p p γ +jet+x reconstruction of momentum fraction p p γ +X A q g global analysis NLO analysis of inclusive & semi-inclusive asymmetries & p p asymmetries Jörg Pretz Nucleon Spin and pdfs 18 / 40

How to measure G? hadrons N q hadrons γ N g q q γ hadrons Leading order photon gluon fusion Jörg Pretz Nucleon Spin and pdfs 18 / 40

How to measure G? N g c 0 - D K π + γ D + D 0 π + soft K π + π + soft ) 2 N/ (MeV/c 1200 00 800 600 0 COMPASS 2007 DKπ (D* tagged) Preliminary 0 N(D ) = 4600 c 400 200 photon gluon fusion 0-600 -400-200 0 200 400 600 M 0 2 (MeV/c ) D Kπ M - N D 0 N D 0 g N g D 0+N D 0 Jörg Pretz Nucleon Spin and pdfs 18 / 40

Results on G from DIS (high p T and open charm) COMPASS, open charm, prel. 02-07 g/g 1 0.8 0.6 2 2 COMPASS, high p, Q >1 (GeV/c), prel. 02-06 T 2 2 COMPASS, high p, Q <1 (GeV/c), prel., 02-04 T 2 HERMES, single high p hadrons, all Q, arxiv:02.3921 T 2 2 SMC, high p, Q >1 (GeV/c) T G = 2.5 0.4 0.6 0.2 0 0.2-0.2-0.4-0.6-2 2 GRSV at µ 2 =3 GeV -1 x g Data show small values of g/g at gluon momentum fraction x g 0.1 Jörg Pretz Nucleon Spin and pdfs 18 / 40

Results on G from DIS (high p T and open charm) COMPASS, open charm, prel. 02-07 g/g 1 0.8 0.6 2 2 COMPASS, high p, Q >1 (GeV/c), prel. 02-06 T 2 2 COMPASS, high p, Q <1 (GeV/c), prel., 02-04 T 2 HERMES, single high p hadrons, all Q, arxiv:02.3921 T 2 2 SMC, high p, Q >1 (GeV/c) T G = 2.5 0.4 0.6 0.2 0 0.2-0.2-0.4 NLO -0.6-2 2 GRSV at µ 2 =3 GeV -1 x g Data show small values of g/g at gluon momentum fraction x g 0.1 Result of open charm NLO analysis Jörg Pretz Nucleon Spin and pdfs 18 / 40

Results on G from DIS (high p T and open charm) G/G 0.8 0.6 0.4 0.2 2 2 Q = 13 (GeV/c) COMPASS open charm COMPASS (set 1) COMPASS (set 2) DSSV LSS (set 1) LSS (set 2) 0-0.2-0.4 COMPASS preliminary -2 x Compared with NLO global analyses COMPASS: inclusive asymmetries & open charm LSS: E. Leader, A. V. Sidorov and D. B. Stamenov, arxiv:12.5033 [hep-ph], inclusice & semi-inclusive asymmetries DSSV: inclusice, semi-inclusive asymmetries & pp data Jörg Pretz Nucleon Spin and pdfs 18 / 40-1

Results from RHIC Two examples from RHIC PHENIX: π 0 production cross section STAR: jet cross section Jörg Pretz Nucleon Spin and pdfs 18 / 40

(more polarized pp E. Aschenauer) Jörg Pretz Nucleon Spin and pdfs 18 / 40 Results from RHIC Two examples from RHIC PHENIX: π 0 asymmetry STAR: jet asymmetry

Results from global fit on all helicity pfds about 500 data points fitted, inclusive & semi-inclusive asymmetries, RHIC pp data analysis does not (yet) include direct measurements from DIS, because NLO calculation are not available, (except for open charm) M. Stratmann, DIS 2011 D. de Florian, R. Sassot, M. Stratmann and W. Vogelsang, Phys. Rev. D 80 (2009) 034030, [arxiv:0904.3821 [hep-ph]] Jörg Pretz Nucleon Spin and pdfs 19 / 40

Results from global fit on all helicity pfds driven by inclusive data driven by pp data driven by semi-inclusive data about 500 data points fitted, inclusive & semi-inclusive asymmetries, RHIC pp data analysis does not (yet) include direct measurements from DIS, because NLO calculation are not available, (except for open charm) M. Stratmann, DIS 2011 D. de Florian, R. Sassot, M. Stratmann and W. Vogelsang, Phys. Rev. D 80 (2009) 034030, [arxiv:0904.3821 [hep-ph]] Jörg Pretz Nucleon Spin and pdfs 19 / 40

Error on g truncated first moments: 0.2 0.05 g(x)dx = 0.005+0.129 0.164 1 0.001 g(x)dx = 0.013+0.702 0.314 Jörg Pretz Nucleon Spin and pdfs 20 / 40

Summary Helicity distributions G = 1 0 g(x)dx 0± 1 2 certainly small compared to large values G 2 3 proposed to explain Σ 25%, not small compared to the total spin of the proton of 1 2! x-dependence of g(x) not very well determined only limited x-range (0.05 < x < 0.3) is covered Σ = 0.25±0.05 u and d rather well known open questions: ū = d, s = s? Jörg Pretz Nucleon Spin and pdfs 21 / 40

Transverse Momentum Dependent Distributions Jörg Pretz Nucleon Spin and pdfs 22 / 40

Transverse Momentum Dependent Distributions nucleon quark unpol. long. trans. unpol. f 1(q) f1t( 0 q) q N k T unpolarized Sivers long. g 1( q, g) g 1T helicity trans. h 1 h 1L h 1( T q),h 1T Boer-Mulders 8 distributions at leading twist, many more at higher leading twist, k T transversity Jörg Pretz Nucleon Spin and pdfs 23 / 40

Transverse Momentum Dependent Distributions nucleon quark unpol. long. trans. unpol. f 1(q) f1t( 0 q) q N k T unpolarized Sivers long. g 1( q, g) g 1T helicity trans. h 1 h 1L h 1( T q),h 1T k T Boer-Mulders 8 distributions at leading twist, many more at higher leading twist, transversity Concentrate on the two most prominent ones: Transversity (Collins) & Sivers Jörg Pretz Nucleon Spin and pdfs 23 / 40

Collins & Sivers asymmetries in semi-incl. DIS N 1+A Coll sin(φ h Φ S π)+a Siv. sin(φ h +Φ S )+... A Coll. = e 2 q T q 0 T Dh q e 2 q q 0 T Dh q, A Siv. = e 2 q T 0 qdh q e 2 q 0 T Dh q Jörg Pretz Nucleon Spin and pdfs 24 / 40

Collins & Sivers asymmetries in semi-incl. DIS p A Coll 0.1 0 preliminary COMPASS 2007 proton data COMPASS HERMES PLB 693 (20) Transversity 0.1 0.2 positive π negative π 2 1 x 2 1 x p A Siv 0.1 preliminary 0.1 COMPASS 2007 proton data COMPASS HERMES (PRL 3 (2009)) Sivers 0 0 0.1 0.1 0.2 positive π 0.2 negative π k T 2 1 x 2 1 x Jörg Pretz Nucleon Spin and pdfs 25 / 40

Collins & Sivers asymmetries in semi-incl. DIS for kaons p A Coll 0.1 0 COMPASS HERMES PLB 693 (20) 2 rescaled by (1-<y>)/(1-<y>+<y> ) 1 preliminary COMPASS 2007 proton data Transversity 0.1 0.2 positive K negative K 2 1 x 2 1 x p A Siv 0.1 preliminary 0.1 COMPASS 2007 proton data COMPASS HERMES (PRL 3 (2009)) Sivers 0 0 0.1 0.1 0.2 positive K 0.2 negative K k T 2 1 x 2 1 x Jörg Pretz Nucleon Spin and pdfs 26 / 40

Collins & Sivers asymmetries from JLab Hall A neutron Collins and Sivers moments obtained from 3 He target 16.0363v1 [nucl-ex] Jörg Pretz Nucleon Spin and pdfs 27 / 40

A N from p p π 0 +X A N T q 0 T Dh q + T 0 qdq h +... }{{}}{{} Collins Sivers Jörg Pretz Nucleon Spin and pdfs 28 / 40

Summary Transversity & Sivers Measured asymmetries on different targets for different hadrons in the final state allow for a global analysis to extract various pdfs Wait for next presentation by M. Anselmino Jörg Pretz Nucleon Spin and pdfs 29 / 40

Future Experiments Jörg Pretz Nucleon Spin and pdfs 30 / 40

Future programs Continuation of measurements COMPASS, RHIC, JLab polarized Drell-Yan process give access to TMDs (particular interesting Sivers function: f1t (DY) = f 1T (SIDIS)) COMPASS, RHIC, FAIR, J-PARC, NICA Deep Virtual Compton Scattering to measure correlated space-momentum distributions in the nucleon, i.e. Generalized Parton Distributions (GPDs) COMPASS, JLab Polarized electron nucleon collider talks related to these subjects: ( E.-M. Kabuß, Tue. 16.30, H. Moutarde, Tue. 15.30, B. Musch, Tue. 14.30) Jörg Pretz Nucleon Spin and pdfs 31 / 40

Future polarized Electron Nucleon Collider Experiment JLab HERMES ENC COMPASS EIC (12 GeV) @FAIR/GSI @BNL/JLab s/gev 2 23 50 180 300 000 x bj,min = 1 ys 5 2 2 2 6 3 4 3 4 for y = 0.9 and Q 2 > 1GeV 2 L/(1/cm 2 /s) 38 32 32 33 32 33 34 (P T P B f) 2 0.026 0.16 0.41 0.026 0.24 Huge gain in effective luminosity (P T P B f) 2 L for polarization measurements, plus gain due to better reconstruction of hadronic final state compared to fixed (solid state) target experiments better reconstruction of gluon momentum fraction x measurement of g(x) Talk on EIC J. Lee, Thu. 14.55 Jörg Pretz Nucleon Spin and pdfs 32 / 40

Summary & Outlook Jörg Pretz Nucleon Spin and pdfs 33 / 40

Summary New results on helicity distributions q, g, transversity and TMDs Jörg Pretz Nucleon Spin and pdfs 34 / 40

Summary New results on helicity distributions q, g, transversity and TMDs Full Flavor decomposition u, d, s, ū, d, s Jörg Pretz Nucleon Spin and pdfs 34 / 40

Summary New results on helicity distributions q, g, transversity and TMDs Full Flavor decomposition u, d, s, ū, d, s Σ = 0.25±0.05, G 0± 1 2 Jörg Pretz Nucleon Spin and pdfs 34 / 40

Summary New results on helicity distributions q, g, transversity and TMDs Full Flavor decomposition u, d, s, ū, d, s Σ = 0.25±0.05, G 0± 1 2 Nucleon Spin Puzzle still not solved Jörg Pretz Nucleon Spin and pdfs 34 / 40

Summary New results on helicity distributions q, g, transversity and TMDs Full Flavor decomposition u, d, s, ū, d, s Σ = 0.25±0.05, G 0± 1 2 Nucleon Spin Puzzle still not solved New physics program at COMPASS(CERN), JLab, RHIC(BNL) to investigate Generalized Parton Distributions (GPDs) and Transverse Momentum Distributions (TMDs) Jörg Pretz Nucleon Spin and pdfs 34 / 40

Spare Jörg Pretz Nucleon Spin and pdfs 35 / 40

u(x)dx d(x)dx s(x)dx 0.54 0.52 0.5 0.48 0.46 0.44 0.42-0.2-0.22-0.24-0.26-0.28-0.3-0.32 0-0.02-0.04-0.06-0.08-0.1 R SF = 2 3 4 5 6 7 R SF D K + s (z)dz D K + u (z)dz u(x)dx d(x)dx ( u(x)- d(x))dx 0.04 0.02 0-0.02-0.04 0.02 0-0.02-0.04-0.06-0.08-0.1 0.1 0.08 0.06 0.04 0.02 0-0.02 2 3 4 5 6 7 R SF Jörg Pretz Nucleon Spin and pdfs 36 / 40

ū(x) and d(x) x( u - d) 0.1 0.05 0 COMPASS DSSV Bourrely-Soffer-Buccella Kumano-Miyama Wakamatsu x(d - u) -0.05-0.1-2 0.3 0.004 ū(x) d(x)dx = 0.06±0.04±0.02-1 1 x Jörg Pretz Nucleon Spin and pdfs 37 / 40

s(x) and s(x) from COMPASS Data x s, x s 0.04 0.02 0-0.02-0.04 x s x s 0.1 x( s - s) 0.05 0-0.05-0.1-2 -1 x Jörg Pretz Nucleon Spin and pdfs 38 / 40

Cross Section vs. p T ) -2 (pb (GeV/c) T dσ dp T π p 2 1 3 2 1 NLO pqcd curves by W. Vogelsang (2011) (DSS FF, CTEQ6M5) µ=p /2 µ=pt T µ=2p T preliminary η c.m.s. [-0.,2.38] -1-2 COMPASS 2004 + µ d µ h X ( s = 17.4 GeV) 2 2 Q < 0.1 (GeV/c), p > 15 GeV/c + h normalization uncertainty % stat. error syst. error σ σ 0.2 0-0.2 1 1.5 2 2.5 3 3.5 p (GeV/c) T Jörg Pretz Nucleon Spin and pdfs 39 / 40

Unpolarized PDFs xf(x) 2 1.8 1.6 1.4 1.2 1 0.8 0.6 0.4 0.2 0-4 u, d s -3 g/ -2 d V -1 uv x 1 Jörg Pretz Nucleon Spin and pdfs 40 / 40