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Measurement of polarized distribution functions at HERMES Alessandra Fantoni (on behalf of the HERMES Collaboration) The spin puzzle & the HERMES experiment Polarised quarks distributions Transversity 13 th International QCD Conference Montpellier 03-07 July 2006

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HERa MEasurement of Spin (DESY) HERa MEasurement of Spin (DESY) 180 Researchers from 30 Institutions of 12 Countries Study of nucleon structure double spin asymmetries (inclusive, seminclusive) single spin asymmetries (seminclusive, transversity and exclusive processes) Data taking since 1995

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The Nucleon Spin Polarised Deep Inelastic Scattering (DIS) HERMES (√s=7 GeV): Q 2 max = 20 GeV 2

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Characteristiques of the HERMES experiment Characteristiques of the HERMES experiment Stern-Gerlach separation resolution: p/p~2%, <1 mrad PID: leptons with ~98%, contam. <1% hadrons dual RICH: , K,p 2

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hadron/positron separation combining signals from:TRD-Calorimeter-Preshower-RICH Aerogel; n=1.03 C 4 F 10 ; n=1.0014 hadron separation Dual radiator RICH for , K, p Particle Identification K

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Polarized quark distributions Inclusive DIS: p,d, 3 He Measurements of g 1 on p,d, 3 He provides PDF through the Q 2 evolution

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Polarised Structure Functions : g 1 g 1 corrected for instrumental smearing (unfolded) and QED radiative effects measured on neutron ( 3 He, 1995), proton and deuteron targets Better precision for g 1 n from g 1 d -g 1 p Data can be used in NLO QCD fits to obtain polarized PDFs –Two methods will be used g 1 and QCD fit papers under preparation g 1 (x) world data (at measured Q 2 ) Measured Q 2

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Polarised semi-inclusive DIS - ud K - us Flavor tagging + ud z=E h /(E E’) Partonic Distribution Function (PDF) Fragmentation Function (FF)

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Polarised Quark Distribution Functions known quantities Polarised Parton Distribution Functions q f (x)=q + (x)-q - (x) Hadronic asymmetries to be measured Purity Functions Extract q by solving

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Measured Asymmetries Proton Deuteron statistics sufficient for 5 parameter fit:

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[PRL92(2004), PRD71(2005)] u quarks: large positive polarisation d quarks: negative polarisation sea quarks (u, d, s, s):compatibile with 0 --- Polarised Quark Distribution Functions First direct 5-flavor separation of polarised PDFs in measured range (0.023 – 0.6) :

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longitudinally polarised quarks and nucleons q(x): helicity difference axial charge known Nucleon quark structure unpolarised quarks and nucleons q(x): spin averaged vector charge well known transversely polarised quarks and nucleons q(x): helicity flip tensor charge measuring !

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Single helicity flip NOT allowed in e.m. & strong interactions Peculiarities of Transversity q Double helicity flip chiral-odd DF chiral-odd DF x chiral-odd FF “Collins” FF

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DIS + SIDIS cross section (Collins) (Sivers) Relativistic nature of quark. In absence of relativistic effects h 1 (x)=g 1 (x) Q 2 -evolution. Unlike for g 1 p (x), the gluon doesn’t mix with quark in h 1 p (x) High sensitivity to the valence quark polarization q and q have opposite sign. _ Tensor charge: first moment of h 1. Calculable by lattice QCD. Chiral-odd Distribution Function Chiral-even naïve T-odd DF Related to parton orbital momentum Violates naïve universality of PDF - Different sign of in DY Peculiarity of

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Transversity asymmetry [PRL94(2005)] Transversity asymmetry [PRL94(2005)] transversity x Collins FF Sivers DF x FF unpolarised Sivers DF connected to quark angular momentum

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No other assumption necessary !! Separation DF and FF weighting the events with their p hT Angles and Asymmetries Definitions Convolution Integral on initial quark transverse momentum p T and final k T Bi-dimensional fit of A( , s )

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T ransversity Asymmetries [PRL94(2005)] T ransversity Asymmetries [PRL94(2005)] positivo e negativo Significant non zero asymmetries A + >0, A - <0 |A | > |A | ? Possible evidence First measurement of naïve T-odd DF in DIS ?. Ferving activities STAR PHENIX Hall A CLAS COMPASS BELLE

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T ransversity Asymmetries on Kaons T ransversity Asymmetries on Kaons No Significant non zero amplitudes Systematic uncertainty: PID, Acceptance, Smearing, Unpolarised cosine moments A k+ > 0, A k- ≈ 0 Systematic uncertainty: PID, Acceptance, Smearing, Unpolarised cosine moments

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T ransversity Asymmetries on Kaons-Pions T ransversity Asymmetries on Kaons-Pions A k+ consistent with A + u quarks dominance Collins FF similar for and k ? A k+ larger than A + in some bins u quarks dominance Sea quarks contribution to Sivers moment important ?

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Conclusions Conclusions Polarised Structure Functions: 1.Precise and complete measurement of g 1 Polarised Quark Distributions: 1.First complete separation of pPDFs w/o assumption on sea polarization 2.No hint of negative strange sea Transversity: 1.First measurements of Collins and Sivers moments for pions in SIDIS 2.First measurements of Collins and Sivers moments for kaons in SIDIS 3.2005 data will double the statistics 4.Collins function estimation will allow extraction of the transversity distribution 5. Sivers function will be extracted in the next few years at HERMES

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Extra slides

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Results for Q and S Inclusive Asymmetry Kaon Asymmetry Need a longitudinal polarized deuterium target strange quark sea in proton and neutron identical fragmentation simplifies All needed information can be extracted from HERMES data alone inclusive A 1,d (x,Q 2 )and kaon A K 1,d (x,Q 2 ) double spin asym. Kaon multiplicities Only assumptions used: isospin symmetry between proton and neutron charge-conjugation invariance in fragmentation Fit x-dependence of multiplicities using PDFs from CTEQ-6 This Work Kretzer KKP This Work Kretzer KKP 0.379±0.002±0.009 1.103 1.111 1.722±0.024±0.108 0.783 0.296

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Results for Q and S Earlier HERMES conclusions of unpolarised strange sea confirmed factor 2 smaller error bars Errors very sensitive to FF input

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VM-Contribution basically no VM contribution for Kaons

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