Nucleon Polarized Parton Distribution Functions G K Mallot

Nucleon Polarized Parton Distribution Functions G. K. Mallot CERN/PH PANIC 08, 9 -14 November 2008, Eilat, Israel

Quarks, Gluons & the Nucleon • Baryons make up all of the visible matter. – How are they made up from quarks and gluons? • In QCD many cross-sections factorize in – calculable hard part and – universal soft part (PDFs) • Experimental findings: – Quarks & gluons share longitudinal momentum 50/50 – Quark spins carry only about 30% of the nucleon spin Panic, 10 November 2008 G. K. Mallot 2

Spin Structure: a Global Endeavour • polarized DIS (long. double spin asymmetries): – fixed-target (FT) lepton–nucleon scattering EMC – lepton-nucleon collider (HERA unpol. , future EIC) • polarized semi-inclusive DIS EMC • polarized pp collisions (RHIC) Panic, 10 November 2008 G. K. Mallot 3

DIS Panic, 10 November 2008 G. K. Mallot 4

World Data on xg 1 (x, Q 2) p d Panic, 10 November 2008 G. K. Mallot 5

CLAS Proton data from V. Burkhard, ar. Xiv: 0711. 1703 v 2 • very precise CLAS data (EG 1) • mostly resonance region • low Q 2, W • used to determine higher twist terms (Leader et al. , PRD 75, 074027, 2007) Panic, 10 November 2008 G. K. Mallot 6

QCD Analysis of data NLO DGLAP: • choose renormalization scheme (MS, AB, jet, …) and Q 02 • optionally fix non-singlet moments from hyperon decays • choose PDF parametrizations for non-singlet and singlet quark and for gluon • fit to g 1 or A 1 data • functional form of PDFs may bias error bands (and more) • NNLO, higher twist, … Panic, 10 November 2008 G. K. Mallot 7

QCD analysis of pol. DIS data • extra problems in polarized case: – no positivity constraint for PDFs – no momentum sum rule • non-singlet distributions well determined • singlet quark distribution rather well determined • however, anti-quark and strange distributions still have large uncertainties • gluon distribution has still large uncertainties, information only from scaling violations Panic, 10 November 2008 G. K. Mallot 8

DIS: Unpolarized vs Polarized F 2 (x, Q 2) proton g 1 (x, Q 2) Q 2 (Ge. V 2) Panic, 10 November 2008 G. K. Mallot Q 2 (Ge. V 2) 9

QCD analyses • • many groups performing World Data fits AAC 06, LSS 06, BB 02, GRSV 01, …; exp: COMPASS 06, … most recent DSSV 08, AAC 08 → later most complete DSSV 08 AAC 06 Singlet gluon note: errors of AAC account for simultaneous deviation of all parameters Panic, 10 November 2008 G. K. Mallot

COMPASS deuteron g 1 • about 6 times more precise at low x than SMC • find +ve and –ve ΔG solutions Q 2 = 3 Ge. V 2 Panic, 10 November 2008 G. K. Mallot 11

LSS 06 / COMPASS 06 • Compass and LSS 06 find two solutions with small ∆G > 0 and ∆G < 0 • LSS 06 includes HT and CLAS data • How to tell sign of ∆G? Panic, 10 November 2008 G. K. Mallot ∆G > 0 ∆G < 0 12

Polarized e + N at EIC Range of a Future EIC at BNL Panic, 10 November 2008 G. K. Mallot 13

(SI)DIS Panic, 10 November 2008 G. K. Mallot 14

Flavour-tag: Semi-inclusive DIS Factorization! 1 0 Panic, 10 November 2008 d h dz = G. K. Mallot 15

Semi-inclusive asymmetries • E. g. : Asymmetries with an additional positive hadron Ah+ (deuteron) Panic, 10 November 2008 G. K. Mallot 16

Flavour separated PDF xΔu xΔd Asymmetries can in LO be related to q by where xΔu xΔd xΔs Panic, 10 November 2008 G. K. Mallot 17

Strange quark sea semi-inclusive data incl. kaon ΔQ = Δq+Δq ΔS = 0. 037± 0. 019 ± 0. 027 range 0. 02 < x < 0. 6 Q 2 = 2. 5 Ge. V 2 • ΔS < 0 expected from incl. data • • Panic, 10 November 2008 G. K. Mallot Q 2= 2. 5 Ge. V 2 18

PDF from SIDIS (LO) EMC and DSS FF • Δuv + Δdv, Δu -bar+Δd-bar insensitive to FF • Δu+Δd-bar consistent with 0 • Δs and errors 2 -3 times larger with EMC with DSS FF Panic, 10 November 2008 G. K. Mallot 19

Dependence of Δs on FF • Compass data 0. 004 < x < 0. 3 from kaon A 1 a • • first moment Δs =-0. 01± 0. 01 (= Δs ) • 0. 004 < x < 0. 3, Q 2 = 3 Ge. V 2 and DSS 2007 FF Panic, 10 November 2008 G. K. Mallot 20

pp at RHIC Panic, 10 November 2008 G. K. Mallot 21

Inclusive π0 Cross-section • Excellent agreement of NLL with data Panic, 10 November 2008 G. K. Mallot 22

from: K. Nakano, Spin 2008 √s=200 and 64. 2 Ge. V 64. 3 Ge. V 200 Ge. V • big improvement with Run 6 • π0 data incompatible with large ΔG • rather strong NLL effect in 64. 2 Ge. V Panic, 10 November 2008 G. K. Mallot 23

Sensitivity to xg √s = 200 Ge. V from: K. Nakano, Spin 2008 • no xg info on eventby-event basis • √s = 200 Ge. V: 0. 02 < xg < 0. 3 • √s = 62. 4 Ge. V: 0. 06 < xg < 0. 4 – slightly higher xg, better statistics Panic, 10 November 2008 G. K. Mallot 24

pp → jet + X PRL 100, 232003 (2008) • 2005 inclusive data: 2 pb− 1, ~50% pol. • 2006 di-jet data in progress: Panic, 10 November 2008 G. K. Mallot 25

DSSV 08: De Florian, Sassot, Stratmann, Vogelsang; PRL 101 (2008) 072001 Global Analysis DIS Panic, 10 November 2008 SIDIS G. K. Mallot pp 26

Global Analysis of (SI)DIS and pp • Data: EMC, SLAC-Exxx, SMC, HERMES, COMPASS, Hall-A, CLAS, PHENIX, STAR • NLO/NLL, MS, Q 20=1 Ge. V 2, εSU(2, 3) fitted • Fragmentation functions from new DSS fit (PRD 75 (2007) 114010 ; D 76 074033) Panic, 10 November 2008 G. K. Mallot 27

DSSV 08 PDFs Panic, 10 November 2008 G. K. Mallot 28

DSSV 08 & AAC 08 gluon PDFs • DSSV 08 AAC 08 RHIC x Panic, 10 November 2008 M. Hirai, S. Kumano ar. Xiv: 0808. 0413 v 1 G. K. Mallot 29

Comparison of gluon PDFs Panic, 10 November 2008 G. K. Mallot 30

Δs • Δs positive at large x (Hermes SIDIS) • Compass kaon asymm. not yet included • first moment < 0 from DIS • node in strangeness distribution x Panic, 10 November 2008 G. K. Mallot 31

PDF first moments (DSSV 08) EMC (1988): Panic, 10 November 2008 G. K. Mallot 32

Δg/g from FT hadrons Panic, 10 November 2008 G. K. Mallot 33

Hadron production in DIS via PGF Principle: Gluon polarization enters via photongluon fusion (PGF) q • measure q Panic, 10 November 2008 • calculate , and background by Monte Carlo G. K. Mallot 34

Analysed channels analysed data sets: – high-p. T hadron pairs (no ID, pions/kaons) • Q 2 > 1 Ge. V 2 • Q 2 < 1 Ge. V 2 or unmeasured LEPTO PYTHIA – high-p. T single hadron • small Q 2 or unmeasured PYTHIA – single charmed meson • quasi-real photons AROMA, RAPGAP All analyses in LO till now Panic, 10 November 2008 (plus parton showers) G. K. Mallot 35

Δg/g from FT hadrons all Q 2 g Photon Gluon Fusion ~ 30% q Leading Order Q 2 < 1 Ge. V 2 q QCD Compton + qg, gg q, g Resolved g ~50% use also inclusive ALL Panic, 10 November 2008 G. K. Mallot 36

Δg/g from open charm • cleanest process – no or little physics background (LO, QCDC) • observe asymmetry in D meson production – – statistics limited only one D meson via D→πK (BR ~ 4%) combinatorial background large drastically reduced when looking to D* decay in coincidence with slow pion Panic, 10 November 2008 G. K. Mallot 37

Δg/g from FT hadrons (LO) (2000) high-p. T single low-p. T (2004) Panic, 10 November 2008 data points at different scales ~ 1 – 10 Ge. V 2 charm G. K. Mallot 38

Summary • • All results point to small Δg/g The strange sea is strange First global analysis of DIS, SIDIS and pp Very precise data for hadron production in FT – These data must be included in the gobal analyses – However, the full NLO description needs to be worked out first (in progress) Details during this session and in the plenary talks by D. Hasch and W. Vogelsang on Wednesday morning Panic, 10 November 2008 G. K. Mallot 39