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1 Flavor Symmetry of Parton Distributions and Fragmentation Functions Jen-Chieh Peng Workshop on “Future Prospects in QCD at High Energy” BNL, July 17-22, 2006 University of Illinois at Urbana-Champaign

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2 Outline

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3 Is in the proton? Test of the Gottfried Sum Rule New Muon Collaboration (NMC) obtains S G = 0.235 ± 0.026 ( Significantly lower than 1/3 ! ) =

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4 Drell-Yan Measurements

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5 Unpolarized Semi-Inclusive DIS Use SIDIS to extract parton distribution functions Universality of fragmentation functions (hep-ph/0011155)

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6 Flavor structure of sea-quark distribution via SIDIS Assuming factorization is valid Require knowledge on the fragmentation function D’(z) SIDIS from HERMESDrell-Yan vs SIDIS

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7 Future experiments to measure at large x

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8 Future SIDIS for at small x ? HERMES: Semi-Inclusive DIS

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9 Independent of nuclear effect in deuteron!

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10 Garvey and Peng, nucl-ex/0109010

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11 Models for asymmetry Meson Cloud ModelsChiral-Quark Soliton ModelInstantons Quark degrees of freedom in a pion mean-field nucleon = chiral soliton expand in 1/Nc Theses models also have implications on asymmetry between and flavor structure of the polarized sea

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12 Meson cloud model Signal and Thomas Brodsky and Ma Melnitchouk and Malheiro Christiansen and Magnin Analysis of neutrino DIS data Barone et al.

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13 Result from NuTeV D. Mason, DIS 2005 talk s(x)s-bar(x)

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14 Spin and flavor are closely connected Meson Cloud Model Pauli Blocking Model A spin-up valence quark would inhibit the probability of generating a spin-down antiquark Instanton Model Chiral-Quark Soliton Model Statistical Model

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15 JCP, Eur. Phys. J. A18 (2003) 395

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16 Flavor Structure of the Helicity Distributions No evidence for Measurement of W ± production at RHIC-spin would provide new information

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17 Drell-Yan decay angular distributions Collins-Soper frame Θ and Φ are the decay polar and azimuthal angles of the μ + in the dilepton rest-frame A general expression for Drell-Yan decay angular distributions: In general :

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18 Drell-Yan decay angular distributions Collins-Soper frame Θ and Φ are the decay polar and azimuthal angles of the μ + in the dilepton rest-frame A general expression for Drell-Yan decay angular distributions:

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19 Decay angular distributions in pion-induced Drell-Yan Z. Phys. 37 (1988) 545 Dashed curves are from pQCD calculations NA10 π - +W

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20 Decay angular distributions in pion-induced Drell-Yan Data from NA10 (Z. Phys. 37 (1988) 545) Is the Lam-Tung relation violated? 140 GeV/c194 GeV/c286 GeV/c

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21 Boer-Mulders function h 1 ┴ 1 =0.47, M C =2.3 GeV Boer, PRD 60 (1999) 014012

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22 Motivation for measuring decay angular distributions in p+p and p+d Drell-Yan No proton-induced Drell-Yan azimuthal decay angular distribution data Provide constraints on models explaining the pion-induced Drell-Yan data. (h 1 ┴ is expected to be small for sea quarks. The vacuum effects should be similar for p+N and π+N ) Test of the Lam-Tung relation in proton-induced Drell-Yan Compare the decay angular distribution of p+p versus p+d

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23 E866 Preliminary <λ><λ>1.07±0.07 0.04±0.013 <ν><ν>0.03±0.01 -0.13±0.07 p+d at 800 GeV/c Decay angular distributions for p+d Drell-Yan at 800 GeV/c

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24 Comparison of NA10 versus E866 Sea-quark Boer-Mulders function is relatively small

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25 Comparison of p+d versus p+p

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26 Many Quark Distributions Are Probed in Semi-Inclusive DIS Unpolarized Polarized target Polarzied beam and target S L and S T : Target Polarizations; λe: Beam Polarization Sivers Transversity Boer-Mulders

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27 for large x S = 0 dominance d/u→0 S Z = 0 dominance d/u→1/5 SU(6) symmetry d/u →1/2

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28 Can one probe the meson cloud directly? Scattering of electron off virtual pion was studied at HERA by tagging forward-going proton/neutron Pion structure functions at 10 -4 < x < 10 -2 were measured

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29 BONUS at Hall-B Tagging slow-moving spectator protons This setup is ideal for detecting the scattering off the meson cloud: a) ep→e’pX (π 0 cloud) b) ep→e’ΛX (K + cloud)

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30 Connections between parton distribution functions and fragmentation functions

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32 Ma, Schmidt, Soffer, Yang assumes the following relations between fragmentation function and parton distributions: CTEQ5 PDFBSB PDF (hep-ph/0208122) Precise e + e - data at large z from Belle could shed light on the connection between PDF and fragmentation functions

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33 Connection between PDF and FF for mesons? SMRS pion PDFKretzer pion fragmentation function

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34 Connection between PDF and FF for mesons? Kretzer pion fragmentation function

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35 Flavor structure of the fragmentation functions 1) Hyperons (Alberg et al. hep-ph/9809243) Can be measured with Drell-Yan using Σ + beam. Difficult experiment! 2) Pions Σ + contains uus valence quarks X

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36 Flavor structure of the fragmentation functions 3) Kaons Difficult to measure sea-quark distributions in K + !

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37 What is known about kaon fragmentation functions? KKP global fit: This implies: Lingyan Zhu (PR-04-114) Connections between the parton distribution and fragmentation functions?

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38 Summary The flavor asymmetry of light sea quarks provides insight on nucleon sea. Future measurements of the sea quarks at higher and lower x and polarized sea are anticipated. Flavor and spin structure of the nucleon are connected. Complementarity between electron and hadron probes. Connection between the parton distribution function and the parton fragmentation functions need to be better understood. The flavor structure of nucleon and meson fragmentation functions could be an interesting area for further investigations.

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