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How do the Quarks and Gluons spin in the Proton ? The View from HERMES E.C. Aschenauer DESY E.C. Aschenauer Pan Pacific, Tokyo, July 2005 1

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  • How do the Quarks and Gluons spin in theProton ?

    — The View from HERMES —

    E.C. Aschenauer

    DESY

    E.C. Aschenauer Pan Pacific, Tokyo, July 2005 1

  • The Spin Structure of the Nucleon

    Naive Parton Model:∆uv + ∆dv = 1

    =⇒ ∆uv =4

    3,∆dv =

    −13

    BUT

    1988 EMC measured:Σ = 0.123 ± 0.013 ± 0.019

    =⇒ Spin Puzzle

    1

    2=

    1

    2(∆uv + ∆dv)

    F2 from HERA tells:

    Gluons are important !

    =⇒ sea quarks ∆qs=⇒ ∆G

    1

    2=

    1

    2(∆uv + ∆dv + ∆qs

    ︸︷︷︸) + ∆G

    ∆us,∆ds,∆ū,∆d̄,∆s,∆s̄

    Full description of Jq & Jgneeds

    orbital angular momentum1

    2=

    1

    2(∆uv + ∆dv + ∆qs)︸ ︷︷ ︸

    +Lq + (∆G + Lg)

    ∆Σ

    E.C. Aschenauer Pan Pacific, Tokyo, July 2005 2

  • The Spin Structure of the Nucleon

    Naive Parton Model:∆uv + ∆dv = 1

    =⇒ ∆uv =4

    3,∆dv =

    −13

    BUT

    1988 EMC measured:Σ = 0.123 ± 0.013 ± 0.019

    =⇒ Spin Puzzle

    1

    2=

    1

    2(∆uv + ∆dv)

    F2 from HERA tells:

    Gluons are important !

    =⇒ sea quarks ∆qs=⇒ ∆G

    1

    2=

    1

    2(∆uv + ∆dv + ∆qs

    ︸︷︷︸) + ∆G

    ∆us,∆ds,∆ū,∆d̄,∆s,∆s̄

    Full description of Jq & Jgneeds

    orbital angular momentum1

    2=

    1

    2(∆uv + ∆dv + ∆qs)︸ ︷︷ ︸

    +Lq + (∆G + Lg)

    ∆Σ

    E.C. Aschenauer Pan Pacific, Tokyo, July 2005 2

  • The Spin Structure of the Nucleon

    Naive Parton Model:∆uv + ∆dv = 1

    =⇒ ∆uv =4

    3,∆dv =

    −13

    BUT

    1988 EMC measured:Σ = 0.123 ± 0.013 ± 0.019

    =⇒ Spin Puzzle

    1

    2=

    1

    2(∆uv + ∆dv)

    F2 from HERA tells:

    Gluons are important !

    =⇒ sea quarks ∆qs=⇒ ∆G

    1

    2=

    1

    2(∆uv + ∆dv + ∆qs

    ︸︷︷︸) + ∆G

    ∆us,∆ds,∆ū,∆d̄,∆s,∆s̄

    Full description of Jq & Jgneeds

    orbital angular momentum1

    2=

    1

    2(∆uv + ∆dv + ∆qs)︸ ︷︷ ︸

    +Lq + (∆G + Lg)

    ∆Σ

    E.C. Aschenauer Pan Pacific, Tokyo, July 2005 2

  • HERA at DESY

    E.C. Aschenauer Pan Pacific, Tokyo, July 2005 3

  • HERA at DESY

    BeamDirection

    Polarimeter

    TransversePolarimeter

    Spin Rotator

    Spin Rotator

    pe

    Spin RotatorSpin Rotator

    Spin Rotator

    Spin Rotator

    Longitudinal

    � � �� � �

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    • HERA-e self-polarizing by emissionof synchrotron radiation−→ Transverse Polarization

    • Longitudinal polarization at HERMESvia spin-rotators

    • Online measurement of beampolarization with two Comptonback scattering polarimeters

    Comparison of rise time curves

    0

    20

    40

    60

    80

    6 6.5 7 7.5 8Time [hours]

    Pol

    ariz

    atio

    n [%

    ]

    Transverse Polarimeter

    Longitudinal Polarimeter

    Beam Polarisation < PB >∼ 55%∆PB/PB = 1.8− 3.4%

    E.C. Aschenauer Pan Pacific, Tokyo, July 2005 3

  • The HERMES Detector

    E.C. Aschenauer Pan Pacific, Tokyo, July 2005 4

  • The HERMES Detector

    1

    0

    2

    −1

    −2

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    CHAMBERSDRIFT

    FC 1/2

    TARGETCELL

    DVC

    MC 1−3

    HODOSCOPE H0

    MONITOR

    BC 1/2

    BC 3/4 TRD

    PROP.CHAMBERS

    FIELD CLAMPS

    PRESHOWER (H2)

    STEEL PLATE CALORIMETER

    DRIFT CHAMBERS

    TRIGGER HODOSCOPE H1

    0 1 2 3 4 5 6 7 8 9 10

    RICH

    SILICON

    270 mrad

    270 mrad

    MUON HODOSCOPEWIDE ANGLE

    FRONTMUONHODO

    MAGNET

    m

    IRON WALL

    MUON HODOSCOPES

    e+

    27.5 GeV

    140 mrad

    170 mrad

    170 mrad

    140 mrad

    Kinematic Range: 0.02 ≤ x ≤ 0.8 at Q2 ≥ 1GeV2 and W ≥ 2GeVΘx ≤ 175 mrad, 40 mrad ≤ Θy ≤ 140 mrad

    Reconstruction: δp/p 1.0 - 2.0%, δΘ ≤ 1.0mrad

    E.C. Aschenauer Pan Pacific, Tokyo, July 2005 4

  • The HERMES Detector

    1

    0

    2

    −1

    −2

    � � � � �

    � � � � �

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    m

    LUMINOSITY

    CHAMBERSDRIFT

    FC 1/2

    TARGETCELL

    DVC

    MC 1−3

    HODOSCOPE H0

    MONITOR

    BC 1/2

    BC 3/4 TRD

    PROP.CHAMBERS

    FIELD CLAMPS

    PRESHOWER (H2)

    STEEL PLATE CALORIMETER

    DRIFT CHAMBERS

    TRIGGER HODOSCOPE H1

    0 1 2 3 4 5 6 7 8 9 10

    RICH

    SILICON

    270 mrad

    270 mrad

    MUON HODOSCOPEWIDE ANGLE

    FRONTMUONHODO

    MAGNET

    m

    IRON WALL

    MUON HODOSCOPES

    e+

    27.5 GeV

    140 mrad

    170 mrad

    170 mrad

    140 mrad

    Kinematic Range: 0.02 ≤ x ≤ 0.8 at Q2 ≥ 1GeV2 and W ≥ 2GeVΘx ≤ 175 mrad, 40 mrad ≤ Θy ≤ 140 mrad

    Reconstruction: δp/p 1.0 - 2.0%, δΘ ≤ 1.0mrad

    Internal Gas Target:−→He ,

    −→D ,

    −→H ,H↑ unpol: H2, D2, He, N2, Ne, Ar, Kr, Xe

    E.C. Aschenauer Pan Pacific, Tokyo, July 2005 4

  • The HERMES Detector

    1

    0

    2

    −1

    −2

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    m

    LUMINOSITY

    CHAMBERSDRIFT

    FC 1/2

    TARGETCELL

    DVC

    MC 1−3

    HODOSCOPE H0

    MONITOR

    BC 1/2

    BC 3/4 TRD

    PROP.CHAMBERS

    FIELD CLAMPS

    PRESHOWER (H2)

    STEEL PLATE CALORIMETER

    DRIFT CHAMBERS

    TRIGGER HODOSCOPE H1

    0 1 2 3 4 5 6 7 8 9 10

    RICH

    SILICON

    270 mrad

    270 mrad

    MUON HODOSCOPEWIDE ANGLE

    FRONTMUONHODO

    MAGNET

    m

    IRON WALL

    MUON HODOSCOPES

    e+

    27.5 GeV

    140 mrad

    170 mrad

    170 mrad

    140 mrad

    Kinematic Range: 0.02 ≤ x ≤ 0.8 at Q2 ≥ 1GeV2 and W ≥ 2GeVΘx ≤ 175 mrad, 40 mrad ≤ Θy ≤ 140 mrad

    Reconstruction: δp/p 1.0 - 2.0%, δΘ ≤ 1.0mrad

    Internal Gas Target:−→He ,

    −→D ,

    −→H ,H↑ unpol: H2, D2, He, N2, Ne, Ar, Kr, Xe

    Particle ID: TRD, Preshower, Calorimeter⇒ 1997: Čerenkov 1998 ⇒: RICH + Muon-ID

    E.C. Aschenauer Pan Pacific, Tokyo, July 2005 4

  • DIS Kinematics

    Inclusive Scattering:

    u

    u

    (E’, p’)

    d

    e

    q

    (E, p)

    N

    detect scattered lepton

    Q2lab= 4EE′ sin2( θ2) ν

    lab= E − E′

    W 2lab= M2 + 2Mν − Q2

    xlab= Q

    2

    2Mν ylab= ν

    E= p·q

    p·k

    Q2 determines what can be resolved in theproton

    Semi-Inclusive Scattering:

    u

    π+

    u

    (E’, p’)

    d

    e

    q

    π

    (E, p)

    p

    KN

    detect scattered lepton and

    produced hadrons

    η =log(Ehcm−p

    h||)

    2∗(Ehcm+ph||)

    zlab= Eh

    ν

    E.C. Aschenauer Pan Pacific, Tokyo, July 2005 5

  • DIS Kinematics

    Inclusive Scattering:

    u

    u

    (E’, p’)

    d

    e

    q

    (E, p)

    N

    detect scattered lepton

    Q2lab= 4EE′ sin2( θ2) ν

    lab= E − E′

    W 2lab= M2 + 2Mν − Q2

    xlab= Q

    2

    2Mν ylab= ν

    E= p·q

    p·k

    Q2 determines what can be resolved in theproton

    Semi-Inclusive Scattering:

    u

    π+

    u

    (E’, p’)

    d

    e

    q

    π

    (E, p)

    p

    KN

    detect scattered lepton and

    produced hadrons

    η =log(Ehcm−p

    h||)

    2∗(Ehcm+ph||)

    zlab= Eh

    ν

    E.C. Aschenauer Pan Pacific, Tokyo, July 2005 5

  • Deep Inelastic Scattering

    Cross Section: d2σ

    dΩdE2= α

    2E′

    Q2ELµν(k, q, s)︸ ︷︷ ︸

    Wµν(P, q, S)︸ ︷︷ ︸

    leptonic hadronic

    Lµν : purely electromagnetic =⇒ calculable in QED

    Wµν = −gµνF1(x,Q2

    )+p

    µpν

    νF2

    (x,Q2

    )

    +i�µνλσ qλν

    (Sσg1

    (x,Q2

    )+ 1

    ν(p · qSσ − S · qpσ)g2

    (x,Q2

    ))

    (for spin 1) −b1(x,Q2

    )rµν +

    16b2

    (x,Q2

    )(sµν + tµν + uµν)

    +12b3

    (x,Q2

    )(sµν − uµν) + 12b4

    (x,Q2

    )(sµν − tµν)

    F1,F2: Unpolarized Structure Functions=⇒ describe momentum distribution of quarks

    g1,g2: Polarized Structure Functions=⇒ describe helicity distribution of quarks

    E.C. Aschenauer Pan Pacific, Tokyo, July 2005 6

  • Virtual Photon Asymmetry

    σ3/2 ∼ q−(x)

    ~Sγ + ~SN = 3/2

    ~SN = − ~Sq

    • Virtual photon γ∗ can only couple to quarks of opposite helicity

    E.C. Aschenauer Pan Pacific, Tokyo, July 2005 7

  • Virtual Photon Asymmetry

    σ3/2 ∼ q−(x)

    ~Sγ + ~SN = 3/2

    ~SN = − ~Sq

    σ1/2 ∼ q+(x)

    ~Sγ + ~SN = 1/2

    ~SN = ~Sq

    • Virtual photon γ∗ can only couple to quarks of opposite helicity• Select q+(x) or q−(x) by changing the orientation of target nucleon

    spin or helicity of incident lepton beam

    E.C. Aschenauer Pan Pacific, Tokyo, July 2005 7

  • Virtual Photon Asymmetry

    σ3/2 ∼ q−(x)

    ~Sγ + ~SN = 3/2

    ~SN = − ~Sq

    σ1/2 ∼ q+(x)

    ~Sγ + ~SN = 1/2

    ~SN = ~Sq

    • Virtual photon γ∗ can only couple to quarks of opposite helicity• Select q+(x) or q−(x) by changing the orientation of target nucleon

    spin or helicity of incident lepton beam

    • Different targets =⇒ sensitivity to different quark flavors

    E.C. Aschenauer Pan Pacific, Tokyo, July 2005 7

  • Virtual Photon Asymmetry

    σ3/2 ∼ q−(x)

    ~Sγ + ~SN = 3/2

    ~SN = − ~Sq

    σ1/2 ∼ q+(x)

    ~Sγ + ~SN = 1/2

    ~SN = ~Sq

    • Virtual photon γ∗ can only couple to quarks of opposite helicity• Select q+(x) or q−(x) by changing the orientation of target nucleon

    spin or helicity of incident lepton beam

    • Different targets =⇒ sensitivity to different quark flavors

    Quark Helicity Distributions:

    ∆qf (x) := q+f (x) − q−f (x) ( f : u,d, s,u,d, s )

    E.C. Aschenauer Pan Pacific, Tokyo, July 2005 7

  • F1(x) = 12∑

    i e2i (q

    +i (x) + q

    i (x)) =12

    i e2qi(x)

    momentum distribution of quarks

    g1(x) = 12∑

    i e2i (q

    +i (x) − q−i (x)) = 12

    i e2∆qi(x)

    helicity distribution of quarks

    Virtual Photon Asymmetries:

    A1 =σ 1

    2−σ 3

    2

    σ 12+σ 3

    2

    = g1−γ2g2

    F1A2 =

    σTLσT

    = γ(g1+g2)F1

    Measurable Asymmetries:

    A‖ =σ→⇐−σ

    →⇒

    σ→⇐+σ

    →⇒

    A⊥ =σ↑→−σ↑←σ↑→+σ↑←

    A‖ = D(A1 + ηA2) A⊥ = d(A2 + ξA1)

    With: D, d,R, �, γ, ξ, η being kinematic factorsE.C. Aschenauer Pan Pacific, Tokyo, July 2005 8

  • World data on g1/F1Proton > Deuterium

    0

    0.2

    0.4

    0.6

    0.8

    1

    10-4

    10-3

    10-2

    10-1

    1

    E 143

    E 155 (Q2-averaged by HERMES)

    SMC

    HERMES

    g1p /

    F1p

    x

    /GeV

    2

    10-1

    1

    10

    10-4

    10-3

    10-2

    10-1

    1

    -0.1

    0

    0.1

    0.2

    0.3

    0.4

    0.5

    0.6

    10-4

    10-3

    10-2

    10-1

    1

    HERMES

    E 143

    E 155 (Q2-averaged by HERMES)

    SMC

    COMPASS

    g1d /

    F1d

    x

    /GeV

    2

    10-1

    1

    10

    10-4

    10-3

    10-2

    10-1

    1

    Data given at measured < Q2 >: 0.02 - 58 GeV2

    A|| =1

    PbPt

    N→⇐L

    →⇒

    − N→⇒L

    →⇐

    N→⇐L

    →⇒ + N

    →⇒L

    →⇐

    g1

    F1=

    1

    1 + γ2

    »

    A||

    D+ (γ − η)A2

    E.C. Aschenauer Pan Pacific, Tokyo, July 2005 9

  • World data on xg1(x,Q2)

    0

    0.02

    0.04

    0.06

    10-4

    10-3

    10-2

    10-1

    0

    0.02

    0.04

    10-4

    10-3

    10-2

    10-1

    -0.04

    -0.02

    0

    0.02

    10-4

    10-3

    10-2

    10-1

    xg1

    HERMESSMCE155E143

    proton

    COMPASS

    deuteron

    E142E154JLAB

    neutron (3He)

    x

    gp1 > g

    D1 > g

    3He1

    very precise proton data

    most precise deuteron data

    0

    0.02

    0.04

    0.06

    10-4

    10-3

    10-2

    10-1

    0

    0.02

    0.04

    10-4

    10-3

    10-2

    10-1

    -0.04

    -0.02

    0

    0.02

    10-4

    10-3

    10-2

    10-1

    xg1

    HERMESSMCE155E143

    proton

    COMPASS

    deuteron

    x

    neutron (from g1p and g1

    d)

    gp1 > g

    D1 > g

    n1

    very precise proton data

    most precise deuteron data

    most precise neutron data

    gd1 =1

    2(1− 3

    2wD)(g

    p1 + g

    n1)

    in measured range (0.021-0.9):∫

    gp1 = 0.1246 ± 0.0032 ± 0.0074

    gd1 = 0.0452 ± 0.0015 ± 0.0017

    E.C. Aschenauer Pan Pacific, Tokyo, July 2005 10

  • World data on xg1(x,Q2)

    0

    0.02

    0.04

    0.06

    10-4

    10-3

    10-2

    10-1

    0

    0.02

    0.04

    10-4

    10-3

    10-2

    10-1

    -0.04

    -0.02

    0

    0.02

    10-4

    10-3

    10-2

    10-1

    xg1

    HERMESSMCE155E143

    proton

    COMPASS

    deuteron

    E142E154JLAB

    neutron (3He)

    x

    gp1 > g

    D1 > g

    3He1

    very precise proton data

    most precise deuteron data

    0

    0.02

    0.04

    0.06

    10-4

    10-3

    10-2

    10-1

    0

    0.02

    0.04

    10-4

    10-3

    10-2

    10-1

    -0.04

    -0.02

    0

    0.02

    10-4

    10-3

    10-2

    10-1

    xg1

    HERMESSMCE155E143

    proton

    COMPASS

    deuteron

    x

    neutron (from g1p and g1

    d)

    gp1 > g

    D1 > g

    n1

    very precise proton data

    most precise deuteron data

    most precise neutron data

    gd1 =1

    2(1− 3

    2wD)(g

    p1 + g

    n1)

    in measured range (0.021-0.9):∫

    gp1 = 0.1246 ± 0.0032 ± 0.0074

    gd1 = 0.0452 ± 0.0015 ± 0.0017

    E.C. Aschenauer Pan Pacific, Tokyo, July 2005 10

  • The structure function b1(x,Q2)

    Tensor structure function:

    b1 =1

    2

    q

    e2q(2q0 − (q+ + q−))

    Adzz =(σ

    →⇐ + σ

    →⇒) − 2σ0

    σ→⇐ + σ

    →⇒ + σ0

    = −32

    b1

    F1

    L µν

    Wµν

    k

    e

    k’e’

    γ∗ q

    p

    d

    Θ

    γ∗

    z q q+ 0q

    E.C. Aschenauer Pan Pacific, Tokyo, July 2005 11

  • The structure function b1(x,Q2)

    • First measurement of Adzz and bd1• Adzz 6= 0• Adzz ∼ 1%

    • bd1 > 0 at small x• in measured range (0.002-0.85):∫

    bd1 = (1.05± 0.34± 0.35) · 10−2

    • Qualitative agreement withcoherent double-scatteringmodels

    -0.02

    -0.01

    0

    0.01

    0.02

    10-2

    10-1

    1x

    Azzd

    -0.05

    0

    0.05

    0.1

    0.15

    10-2

    10-1

    1

    b1d

    10-1

    1

    10-2

    10-1

    1x

    〈Q2 〉

    /GeV

    2

    E.C. Aschenauer Pan Pacific, Tokyo, July 2005 12

  • The structure function b1(x,Q2)

    • First measurement of Adzz and bd1• Adzz 6= 0• Adzz ∼ 1%• bd1 > 0 at small x• in measured range (0.002-0.85):∫

    bd1 = (1.05± 0.34± 0.35) · 10−2

    • Qualitative agreement withcoherent double-scatteringmodels

    -0.02

    -0.01

    0

    0.01

    0.02

    10-2

    10-1

    1x

    Azzd

    -0.05

    0

    0.05

    0.1

    0.15

    10-2

    10-1

    1

    b1d

    10-1

    1

    10-2

    10-1

    1x

    〈Q2 〉

    /GeV

    2

    E.C. Aschenauer Pan Pacific, Tokyo, July 2005 12

  • Semi-inclusive DIS

    String Breaking

    u_

    d_

    π0

    u_

    u_

    u_

    ρ−

    ud0

    ud0

    π0

    π+

    π0

    −π

    u_

    u

    ud

    u

    d

    u

    uu

    u

    p

    incoming leptonscattered lepton

    virtual photon

    uud

    target nucleon

    E.C. Aschenauer Pan Pacific, Tokyo, July 2005 13

  • Semi-inclusive DIS

    String Breaking

    u_

    d_

    π0

    u_

    u_

    u_

    ρ−

    ud0

    ud0

    π0

    π+

    π0

    −π

    u_

    u

    ud

    u

    d

    u

    uu

    u

    p

    incoming leptonscattered lepton

    virtual photon

    uud

    target nucleon

    Correlation between detected hadron and struck qf=⇒ ’Flavor - Separation’

    Inclusive DIS:∆Σ = (∆u + ∆ū + ∆d + ∆d̄ + ∆s + ∆s̄)Semi-inclusive DIS:∆u,∆ū,∆d,∆d̄,∆s,∆s̄

    In LO-QCD:

    Ah1(x,Q2) =

    σh1/2 − σh3/2

    σh1/2 + σ

    h3/2

    =1 + R(x,Q2)

    1 + γ2·∑

    f e2f ∆qf (x,Q

    2)∫

    dzDhf (z,Q2)

    f e2f qf (x,Q

    2)∫

    dzDhf (z,Q2)

    (∆qf ),qf (Polarized) quark distributionsDhf (z) fragmentation functions giving the probability that a (struck) quark

    of flavor f fragments into a hadron of type h

    E.C. Aschenauer Pan Pacific, Tokyo, July 2005 14

  • ∆q-Extraction• Rewrite Photon-Nucleon Asymmetry

    Ah1(x)g2=0' C ·

    q

    e2qq(x)∫

    dzDhq (z)∑

    q′ e2q′q′(x)

    ∫dzDhq′(z)

    ︸ ︷︷ ︸

    ∆q(x)

    q(x)

    Phq (x, z)

    • Purity P hq (x, z): probability hadron h originates from an event with struckquark f; completely unpolarized quantity

    • Extract ∆q by solving:

    ~A = P ~Q

    ~A= (A1,p(x),A1,d(x),Aπ±

    1,p(x),Aπ±

    1,d(x),AK±

    1,d(x))

    ~Q= (∆uu

    , ∆dd

    , ∆ūū

    , ∆d̄d̄

    , ∆ss

    , ∆s̄s̄

    )

    E.C. Aschenauer Pan Pacific, Tokyo, July 2005 15

  • Measured Hadron Asymmetries

    -0.1

    0

    0.1

    0.2

    0.3

    0.4

    0.5

    10 -1

    0.03 0.1

    x

    -0.1

    0

    0.1

    0.2

    0.3

    0.4

    0.5A1

    A1,d

    -0.1

    0

    0.1

    0.2

    0.3

    0.4

    0.5

    10 -1

    A1,dAh+

    SMC

    -0.1

    0

    0.1

    0.2

    0.3

    0.4

    0.5

    10 -1

    A1,dAπ+

    -0.1

    0

    0.1

    0.2

    0.3

    0.4

    0.5

    10 -1

    A1,dAK+

    -0.1

    0

    0.1

    0.2

    0.3

    0.4

    0.5

    10 -1

    0.03 0.1 0.4

    x

    -0.1

    0

    0.1

    0.2

    0.3

    0.4

    0.5A1,dA

    h−

    SMC

    -0.1

    0

    0.1

    0.2

    0.3

    0.4

    0.5

    10 -1

    0.03 0.1 0.4

    x

    A1,dAπ−

    -0.1

    0

    0.1

    0.2

    0.3

    0.4

    0.5

    10 -1

    0.03 0.1 0.4x

    A1,dAK−

    0

    0.2

    0.4

    0.6

    0.8

    10 -1

    0.03 0.1

    x

    A1

    A1,p

    0

    0.2

    0.4

    0.6

    0.8

    10 -1

    A1,pAh+

    SMC

    0

    0.2

    0.4

    0.6

    0.8

    10 -1

    A1,pAπ+

    0

    0.2

    0.4

    0.6

    0.8

    10 -1

    0.03 0.1 0.4

    x

    A1,pAh−

    SMC

    0

    0.2

    0.4

    0.6

    0.8

    10 -1

    0.03 0.1 0.4x

    A1,pAπ−

    Deuterium

    Proton

    -0.1

    0

    0.1

    0.2

    0.3

    0.4

    0.5

    10 -1

    0.03 0.1

    x

    -0.1

    0

    0.1

    0.2

    0.3

    0.4

    0.5A1

    A1,d

    -0.1

    0

    0.1

    0.2

    0.3

    0.4

    0.5

    10 -1

    A1,dAh+

    SMC

    -0.1

    0

    0.1

    0.2

    0.3

    0.4

    0.5

    10 -1

    A1,dAπ+

    -0.1

    0

    0.1

    0.2

    0.3

    0.4

    0.5

    10 -1

    A1,dAK+

    -0.1

    0

    0.1

    0.2

    0.3

    0.4

    0.5

    10 -1

    0.03 0.1 0.4

    x

    -0.1

    0

    0.1

    0.2

    0.3

    0.4

    0.5A1,dA

    h−

    SMC

    -0.1

    0

    0.1

    0.2

    0.3

    0.4

    0.5

    10 -1

    0.03 0.1 0.4

    x

    A1,dAπ−

    -0.1

    0

    0.1

    0.2

    0.3

    0.4

    0.5

    10 -1

    0.03 0.1 0.4x

    A1,dAK−

    0

    0.2

    0.4

    0.6

    0.8

    10 -1

    0.03 0.1

    x

    A1

    A1,p

    0

    0.2

    0.4

    0.6

    0.8

    10 -1

    A1,pAh+

    SMC

    0

    0.2

    0.4

    0.6

    0.8

    10 -1

    A1,pAπ+

    0

    0.2

    0.4

    0.6

    0.8

    10 -1

    0.03 0.1 0.4

    x

    A1,pAh−

    SMC

    0

    0.2

    0.4

    0.6

    0.8

    10 -1

    0.03 0.1 0.4x

    A1,pAπ−

    Deuterium

    Proton

    • AK−1 (x) ≈ 0 !! =⇒ K− = (ūs)is an all–sea object

    • statistics sufficient for5-parameter fit

    Q̃ = (∆u

    u,∆d

    d,∆ū

    ū,∆d̄

    d̄,∆s

    s,∆s̄

    s̄= 0)

    E.C. Aschenauer Pan Pacific, Tokyo, July 2005 16

  • Measured Hadron Asymmetries

    -0.1

    0

    0.1

    0.2

    0.3

    0.4

    0.5

    10 -1

    0.03 0.1

    x

    -0.1

    0

    0.1

    0.2

    0.3

    0.4

    0.5A1

    A1,d

    -0.1

    0

    0.1

    0.2

    0.3

    0.4

    0.5

    10 -1

    A1,dAh+

    SMC

    -0.1

    0

    0.1

    0.2

    0.3

    0.4

    0.5

    10 -1

    A1,dAπ+

    -0.1

    0

    0.1

    0.2

    0.3

    0.4

    0.5

    10 -1

    A1,dAK+

    -0.1

    0

    0.1

    0.2

    0.3

    0.4

    0.5

    10 -1

    0.03 0.1 0.4

    x

    -0.1

    0

    0.1

    0.2

    0.3

    0.4

    0.5A1,dA

    h−

    SMC

    -0.1

    0

    0.1

    0.2

    0.3

    0.4

    0.5

    10 -1

    0.03 0.1 0.4

    x

    A1,dAπ−

    -0.1

    0

    0.1

    0.2

    0.3

    0.4

    0.5

    10 -1

    0.03 0.1 0.4x

    A1,dAK−

    0

    0.2

    0.4

    0.6

    0.8

    10 -1

    0.03 0.1

    x

    A1

    A1,p

    0

    0.2

    0.4

    0.6

    0.8

    10 -1

    A1,pAh+

    SMC

    0

    0.2

    0.4

    0.6

    0.8

    10 -1

    A1,pAπ+

    0

    0.2

    0.4

    0.6

    0.8

    10 -1

    0.03 0.1 0.4

    x

    A1,pAh−

    SMC

    0

    0.2

    0.4

    0.6

    0.8

    10 -1

    0.03 0.1 0.4x

    A1,pAπ−

    Deuterium

    Proton

    -0.1

    0

    0.1

    0.2

    0.3

    0.4

    0.5

    10 -1

    0.03 0.1

    x

    -0.1

    0

    0.1

    0.2

    0.3

    0.4

    0.5A1

    A1,d

    -0.1

    0

    0.1

    0.2

    0.3

    0.4

    0.5

    10 -1

    A1,dAh+

    SMC

    -0.1

    0

    0.1

    0.2

    0.3

    0.4

    0.5

    10 -1

    A1,dAπ+

    -0.1

    0

    0.1

    0.2

    0.3

    0.4

    0.5

    10 -1

    A1,dAK+

    -0.1

    0

    0.1

    0.2

    0.3

    0.4

    0.5

    10 -1

    0.03 0.1 0.4

    x

    -0.1

    0

    0.1

    0.2

    0.3

    0.4

    0.5A1,dA

    h−

    SMC

    -0.1

    0

    0.1

    0.2

    0.3

    0.4

    0.5

    10 -1

    0.03 0.1 0.4

    x

    A1,dAπ−

    -0.1

    0

    0.1

    0.2

    0.3

    0.4

    0.5

    10 -1

    0.03 0.1 0.4x

    A1,dAK−

    0

    0.2

    0.4

    0.6

    0.8

    10 -1

    0.03 0.1

    x

    A1

    A1,p

    0

    0.2

    0.4

    0.6

    0.8

    10 -1

    A1,pAh+

    SMC

    0

    0.2

    0.4

    0.6

    0.8

    10 -1

    A1,pAπ+

    0

    0.2

    0.4

    0.6

    0.8

    10 -1

    0.03 0.1 0.4

    x

    A1,pAh−

    SMC

    0

    0.2

    0.4

    0.6

    0.8

    10 -1

    0.03 0.1 0.4x

    A1,pAπ−

    Deuterium

    Proton

    • AK−1 (x) ≈ 0 !! =⇒ K− = (ūs)is an all–sea object

    • statistics sufficient for5-parameter fit

    Q̃ = (∆u

    u,∆d

    d,∆ū

    ū,∆d̄

    d̄,∆s

    s,∆s̄

    s̄= 0)

    E.C. Aschenauer Pan Pacific, Tokyo, July 2005 16

  • Quark Polarizations0

    0.5

    10-1

    ∆u/u

    -0.5

    0

    10-1

    ∆d/d

    -1

    0

    1

    10-1

    ∆u–/u–

    -1

    0

    1

    10-1

    ∆d–/d–

    -1

    0

    1

    10-1

    ∆s/s

    0

    5

    10

    10-1

    〈Q2〉/GeV2

    0.03 0.1 0.6

    x

    ∆qf (x)

    qf (x):=

    q+f (x)

    qf (x)− q

    −f (x)

    qf (x)

    • ∆u(x)/u(x) > 0=⇒ polarized parallel to theproton spin

    • ∆d(x)/d(x) < 0=⇒ polarized opposite tothe proton spin

    • ∆ūū

    ∼ ∆d̄d̄

    ∼ ∆ss

    ∼ 0

    E.C. Aschenauer Pan Pacific, Tokyo, July 2005 17

  • Quark Polarizations0

    0.5

    10-1

    ∆u/u

    -0.5

    0

    10-1

    ∆d/d

    -1

    0

    1

    10-1

    ∆u–/u–

    -1

    0

    1

    10-1

    ∆d–/d–

    -1

    0

    1

    10-1

    ∆s/s

    0

    5

    10

    10-1

    〈Q2〉/GeV2

    0.03 0.1 0.6

    x

    ∆qf (x)

    qf (x):=

    q+f (x)

    qf (x)− q

    −f (x)

    qf (x)

    • ∆u(x)/u(x) > 0=⇒ polarized parallel to theproton spin

    • ∆d(x)/d(x) < 0=⇒ polarized opposite tothe proton spin

    • ∆ūū

    ∼ ∆d̄d̄

    ∼ ∆ss

    ∼ 0

    E.C. Aschenauer Pan Pacific, Tokyo, July 2005 17

  • Quark Polarizations0

    0.5

    10-1

    ∆u/u

    -0.5

    0

    10-1

    ∆d/d

    -1

    0

    1

    10-1

    ∆u–/u–

    -1

    0

    1

    10-1

    ∆d–/d–

    -1

    0

    1

    10-1

    ∆s/s

    0

    5

    10

    10-1

    〈Q2〉/GeV2

    0.03 0.1 0.6

    x

    ∆qf (x)

    qf (x):=

    q+f (x)

    qf (x)− q

    −f (x)

    qf (x)

    • ∆u(x)/u(x) > 0=⇒ polarized parallel to theproton spin

    • ∆d(x)/d(x) < 0=⇒ polarized opposite tothe proton spin

    • ∆ūū

    ∼ ∆d̄d̄

    ∼ ∆ss

    ∼ 0

    E.C. Aschenauer Pan Pacific, Tokyo, July 2005 17

  • Quark Polarizations0

    0.5

    10-1

    ∆u/u

    -0.5

    0

    10-1

    ∆d/d

    -1

    0

    1

    10-1

    ∆u–/u–

    -1

    0

    1

    10-1

    ∆d–/d–

    -1

    0

    1

    10-1

    ∆s/s

    0

    5

    10

    10-1

    〈Q2〉/GeV2

    0.03 0.1 0.6

    x

    ∆qf (x)

    qf (x):=

    q+f (x)

    qf (x)− q

    −f (x)

    qf (x)

    • ∆u(x)/u(x) > 0=⇒ polarized parallel to theproton spin

    • ∆d(x)/d(x) < 0=⇒ polarized opposite tothe proton spin

    • ∆ūū

    ∼ ∆d̄d̄

    ∼ ∆ss

    ∼ 0

    E.C. Aschenauer Pan Pacific, Tokyo, July 2005 17

  • Polarized Quark Densities

    0

    0.2

    10-1

    x⋅∆u

    -0.2

    0

    10-1

    x⋅∆d

    -0.1

    0

    10-1

    GRSV 2000LO val

    BB 01 LOx⋅∆u

    Q2=2.5GeV2

    -0.1

    0

    10-1

    x⋅∆d–

    -0.1

    0

    10-1

    x⋅∆s

    0.03 0.1 0.6

    x

    ∆qf (x) := q+f (x) − q−f (x)

    • ∆u(x) and ∆d(x)good agreement with NLO-QCD fit

    • ∆ū(x),∆d̄(x) ∼ 0

    • No indication for ∆s(x) < 0• in measured range (0.023-0.6):

    ∆ū = -0.002 ± 0.043∫

    ∆d̄ = -0.054 ± 0.035∫

    ∆s = +0.028 ± 0.034

    E.C. Aschenauer Pan Pacific, Tokyo, July 2005 18

  • Polarized Quark Densities

    0

    0.2

    10-1

    x⋅∆u

    -0.2

    0

    10-1

    x⋅∆d

    -0.1

    0

    10-1

    GRSV 2000LO val

    BB 01 LOx⋅∆u

    Q2=2.5GeV2

    -0.1

    0

    10-1

    x⋅∆d–

    -0.1

    0

    10-1

    x⋅∆s

    0.03 0.1 0.6

    x

    ∆qf (x) := q+f (x) − q−f (x)

    • ∆u(x) and ∆d(x)good agreement with NLO-QCD fit

    • ∆ū(x),∆d̄(x) ∼ 0

    • No indication for ∆s(x) < 0• in measured range (0.023-0.6):

    ∆ū = -0.002 ± 0.043∫

    ∆d̄ = -0.054 ± 0.035∫

    ∆s = +0.028 ± 0.034

    E.C. Aschenauer Pan Pacific, Tokyo, July 2005 18

  • Polarized Quark Densities

    0

    0.2

    10-1

    x⋅∆u

    -0.2

    0

    10-1

    x⋅∆d

    -0.1

    0

    10-1

    GRSV 2000LO val

    BB 01 LOx⋅∆u

    Q2=2.5GeV2

    -0.1

    0

    10-1

    x⋅∆d–

    -0.1

    0

    10-1

    x⋅∆s

    0.03 0.1 0.6

    x

    ∆qf (x) := q+f (x) − q−f (x)

    • ∆u(x) and ∆d(x)good agreement with NLO-QCD fit

    • ∆ū(x),∆d̄(x) ∼ 0

    • No indication for ∆s(x) < 0• in measured range (0.023-0.6):

    ∆ū = -0.002 ± 0.043∫

    ∆d̄ = -0.054 ± 0.035∫

    ∆s = +0.028 ± 0.034

    E.C. Aschenauer Pan Pacific, Tokyo, July 2005 18

  • SU(2)-Flavor Symmetry Breaking(?)

    Unpolarized

    0

    0.5

    1

    0 0.05 0.1 0.15 0.2 0.25 0.3 0.35

    Systematic Error

    x

    d_ -

    u_

    CTEQ5M CTEQ4M

    MRST GRV98

    HermesE866

    Strong breaking of SU(2)-Flavor Symmetry

    Polarized

    -0.2

    -0.15

    -0.1

    -0.05

    0

    0.05

    0.1

    0.15

    0.2

    10 -1

    0.03 0.1 0.6

    x

    χQSMmeson cloud

    x(∆u–-∆d

    –)

    Q2 = 2.5 GeV2

    No significant breaking ofSU(2)-Flavor Symmetry ∆ū ∼ ∆d̄More Data needed

    E.C. Aschenauer Pan Pacific, Tokyo, July 2005 19

  • SU(2)-Flavor Symmetry Breaking(?)

    Unpolarized

    0

    0.5

    1

    0 0.05 0.1 0.15 0.2 0.25 0.3 0.35

    Systematic Error

    x

    d_ -

    u_

    CTEQ5M CTEQ4M

    MRST GRV98

    HermesE866

    Strong breaking of SU(2)-Flavor Symmetry

    Polarized

    -0.2

    -0.15

    -0.1

    -0.05

    0

    0.05

    0.1

    0.15

    0.2

    10 -1

    0.03 0.1 0.6

    x

    χQSMmeson cloud

    x(∆u–-∆d

    –)

    Q2 = 2.5 GeV2

    No significant breaking ofSU(2)-Flavor Symmetry ∆ū ∼ ∆d̄More Data needed

    E.C. Aschenauer Pan Pacific, Tokyo, July 2005 19

  • How to measure ∆G• ”Indirect” from scaling violation

    Remember unpolarized case:HERA F2

    0

    1

    2

    3

    4

    5

    1 10 102

    103

    104

    105

    F2 em

    -log

    10(x

    )

    Q2(GeV2)

    ZEUS NLO QCD fit

    H1 PDF 2000 fit

    H1 94-00

    H1 (prel.) 99/00

    ZEUS 96/97

    BCDMS

    E665

    NMC

    x=6.32E-5 x=0.000102x=0.000161

    x=0.000253

    x=0.0004x=0.0005

    x=0.000632x=0.0008

    x=0.0013

    x=0.0021

    x=0.0032

    x=0.005

    x=0.008

    x=0.013

    x=0.021

    x=0.032

    x=0.05

    x=0.08

    x=0.13

    x=0.18

    x=0.25

    x=0.4

    x=0.65

    Remember unpolarized case:HERA F2

    0

    1

    2

    3

    4

    5

    1 10 102

    103

    104

    105

    F2 em

    -log

    10(x

    )

    Q2(GeV2)

    ZEUS NLO QCD fit

    H1 PDF 2000 fit

    H1 94-00

    H1 (prel.) 99/00

    ZEUS 96/97

    BCDMS

    E665

    NMC

    x=6.32E-5 x=0.000102x=0.000161

    x=0.000253

    x=0.0004x=0.0005

    x=0.000632x=0.0008

    x=0.0013

    x=0.0021

    x=0.0032

    x=0.005

    x=0.008

    x=0.013

    x=0.021

    x=0.032

    x=0.05

    x=0.08

    x=0.13

    x=0.18

    x=0.25

    x=0.4

    x=0.65

    =⇒ big Q2 − xbj lever arm=⇒ very accurate G(x)

    0

    5

    10

    15

    20

    -410 -310 -210 -110 10

    5

    10

    15

    20

    x

    xg

    2 = 5 GeV2Q

    2 = 20 GeV2Q

    2 = 200 GeV2Q

    0

    5

    10

    15

    20 ZEUS-JETS (prel.) 94-00

    H1 PDF 2000

    total uncert.

    exp. uncert.

    total uncert.

    H1+ZEUS

    Remember unpolarized case:HERA F2

    0

    1

    2

    3

    4

    5

    1 10 102

    103

    104

    105

    F2 em

    -log

    10(x

    )

    Q2(GeV2)

    ZEUS NLO QCD fit

    H1 PDF 2000 fit

    H1 94-00

    H1 (prel.) 99/00

    ZEUS 96/97

    BCDMS

    E665

    NMC

    x=6.32E-5 x=0.000102x=0.000161

    x=0.000253

    x=0.0004x=0.0005

    x=0.000632x=0.0008

    x=0.0013

    x=0.0021

    x=0.0032

    x=0.005

    x=0.008

    x=0.013

    x=0.021

    x=0.032

    x=0.05

    x=0.08

    x=0.13

    x=0.18

    x=0.25

    x=0.4

    x=0.65

    =⇒ big Q2 − xbj lever arm=⇒ very accurate G(x)

    0

    5

    10

    15

    20

    -410 -310 -210 -110 10

    5

    10

    15

    20

    x

    xg

    2 = 5 GeV2Q

    2 = 20 GeV2Q

    2 = 200 GeV2Q

    0

    5

    10

    15

    20 ZEUS-JETS (prel.) 94-00

    H1 PDF 2000

    total uncert.

    exp. uncert.

    total uncert.

    H1+ZEUS

    Polarized case:

    10-4

    10-3

    10-2

    10-1

    1

    10

    10 2

    10 3

    10 4

    10-1

    1 10 102

    E143

    Q2, GeV2

    HERMES

    E155

    EMC

    SMC

    • fixed target experiments=⇒ small Q2 − xbj lever arm

    • determines only sign of ∆G(x)

    -0.4

    -0.2

    0

    0.2

    0.4

    0.6

    0.8

    10-3

    10-2

    10-1

    1x

    E.C. Aschenauer Pan Pacific, Tokyo, July 2005 20

  • How to measure ∆G• ”Indirect” from scaling violation

    Remember unpolarized case:HERA F2

    0

    1

    2

    3

    4

    5

    1 10 102

    103

    104

    105

    F2 em

    -log

    10(x

    )

    Q2(GeV2)

    ZEUS NLO QCD fit

    H1 PDF 2000 fit

    H1 94-00

    H1 (prel.) 99/00

    ZEUS 96/97

    BCDMS

    E665

    NMC

    x=6.32E-5 x=0.000102x=0.000161

    x=0.000253

    x=0.0004x=0.0005

    x=0.000632x=0.0008

    x=0.0013

    x=0.0021

    x=0.0032

    x=0.005

    x=0.008

    x=0.013

    x=0.021

    x=0.032

    x=0.05

    x=0.08

    x=0.13

    x=0.18

    x=0.25

    x=0.4

    x=0.65

    Remember unpolarized case:HERA F2

    0

    1

    2

    3

    4

    5

    1 10 102

    103

    104

    105

    F2 em

    -log

    10(x

    )

    Q2(GeV2)

    ZEUS NLO QCD fit

    H1 PDF 2000 fit

    H1 94-00

    H1 (prel.) 99/00

    ZEUS 96/97

    BCDMS

    E665

    NMC

    x=6.32E-5 x=0.000102x=0.000161

    x=0.000253

    x=0.0004x=0.0005

    x=0.000632x=0.0008

    x=0.0013

    x=0.0021

    x=0.0032

    x=0.005

    x=0.008

    x=0.013

    x=0.021

    x=0.032

    x=0.05

    x=0.08

    x=0.13

    x=0.18

    x=0.25

    x=0.4

    x=0.65

    =⇒ big Q2 − xbj lever arm=⇒ very accurate G(x)

    0

    5

    10

    15

    20

    -410 -310 -210 -110 10

    5

    10

    15

    20

    x

    xg

    2 = 5 GeV2Q

    2 = 20 GeV2Q

    2 = 200 GeV2Q

    0

    5

    10

    15

    20 ZEUS-JETS (prel.) 94-00

    H1 PDF 2000

    total uncert.

    exp. uncert.

    total uncert.

    H1+ZEUS

    Remember unpolarized case:HERA F2

    0

    1

    2

    3

    4

    5

    1 10 102

    103

    104

    105

    F2 em

    -log

    10(x

    )

    Q2(GeV2)

    ZEUS NLO QCD fit

    H1 PDF 2000 fit

    H1 94-00

    H1 (prel.) 99/00

    ZEUS 96/97

    BCDMS

    E665

    NMC

    x=6.32E-5 x=0.000102x=0.000161

    x=0.000253

    x=0.0004x=0.0005

    x=0.000632x=0.0008

    x=0.0013

    x=0.0021

    x=0.0032

    x=0.005

    x=0.008

    x=0.013

    x=0.021

    x=0.032

    x=0.05

    x=0.08

    x=0.13

    x=0.18

    x=0.25

    x=0.4

    x=0.65

    =⇒ big Q2 − xbj lever arm=⇒ very accurate G(x)

    0

    5

    10

    15

    20

    -410 -310 -210 -110 10

    5

    10

    15

    20

    x

    xg

    2 = 5 GeV2Q

    2 = 20 GeV2Q

    2 = 200 GeV2Q

    0

    5

    10

    15

    20 ZEUS-JETS (prel.) 94-00

    H1 PDF 2000

    total uncert.

    exp. uncert.

    total uncert.

    H1+ZEUS

    Polarized case:

    10-4

    10-3

    10-2

    10-1

    1

    10

    10 2

    10 3

    10 4

    10-1

    1 10 102

    E143

    Q2, GeV2

    HERMES

    E155

    EMC

    SMC

    • fixed target experiments=⇒ small Q2 − xbj lever arm

    • determines only sign of ∆G(x)

    -0.4

    -0.2

    0

    0.2

    0.4

    0.6

    0.8

    10-3

    10-2

    10-1

    1x

    E.C. Aschenauer Pan Pacific, Tokyo, July 2005 20

  • How to measure ∆G• ”Indirect” from scaling violation

    Remember unpolarized case:HERA F2

    0

    1

    2

    3

    4

    5

    1 10 102

    103

    104

    105

    F2 em

    -log

    10(x

    )

    Q2(GeV2)

    ZEUS NLO QCD fit

    H1 PDF 2000 fit

    H1 94-00

    H1 (prel.) 99/00

    ZEUS 96/97

    BCDMS

    E665

    NMC

    x=6.32E-5 x=0.000102x=0.000161

    x=0.000253

    x=0.0004x=0.0005

    x=0.000632x=0.0008

    x=0.0013

    x=0.0021

    x=0.0032

    x=0.005

    x=0.008

    x=0.013

    x=0.021

    x=0.032

    x=0.05

    x=0.08

    x=0.13

    x=0.18

    x=0.25

    x=0.4

    x=0.65

    Remember unpolarized case:HERA F2

    0

    1

    2

    3

    4

    5

    1 10 102

    103

    104

    105

    F2 em

    -log

    10(x

    )

    Q2(GeV2)

    ZEUS NLO QCD fit

    H1 PDF 2000 fit

    H1 94-00

    H1 (prel.) 99/00

    ZEUS 96/97

    BCDMS

    E665

    NMC

    x=6.32E-5 x=0.000102x=0.000161

    x=0.000253

    x=0.0004x=0.0005

    x=0.000632x=0.0008

    x=0.0013

    x=0.0021

    x=0.0032

    x=0.005

    x=0.008

    x=0.013

    x=0.021

    x=0.032

    x=0.05

    x=0.08

    x=0.13

    x=0.18

    x=0.25

    x=0.4

    x=0.65

    =⇒ big Q2 − xbj lever arm=⇒ very accurate G(x)

    0

    5

    10

    15

    20

    -410 -310 -210 -110 10

    5

    10

    15

    20

    x

    xg

    2 = 5 GeV2Q

    2 = 20 GeV2Q

    2 = 200 GeV2Q

    0

    5

    10

    15

    20 ZEUS-JETS (prel.) 94-00

    H1 PDF 2000

    total uncert.

    exp. uncert.

    total uncert.

    H1+ZEUS

    Remember unpolarized case:HERA F2

    0

    1

    2

    3

    4

    5

    1 10 102

    103

    104

    105

    F2 em

    -log

    10(x

    )

    Q2(GeV2)

    ZEUS NLO QCD fit

    H1 PDF 2000 fit

    H1 94-00

    H1 (prel.) 99/00

    ZEUS 96/97

    BCDMS

    E665

    NMC

    x=6.32E-5 x=0.000102x=0.000161

    x=0.000253

    x=0.0004x=0.0005

    x=0.000632x=0.0008

    x=0.0013

    x=0.0021

    x=0.0032

    x=0.005

    x=0.008

    x=0.013

    x=0.021

    x=0.032

    x=0.05

    x=0.08

    x=0.13

    x=0.18

    x=0.25

    x=0.4

    x=0.65

    =⇒ big Q2 − xbj lever arm=⇒ very accurate G(x)

    0

    5

    10

    15

    20

    -410 -310 -210 -110 10

    5

    10

    15

    20

    x

    xg

    2 = 5 GeV2Q

    2 = 20 GeV2Q

    2 = 200 GeV2Q

    0

    5

    10

    15

    20 ZEUS-JETS (prel.) 94-00

    H1 PDF 2000

    total uncert.

    exp. uncert.

    total uncert.

    H1+ZEUS

    Polarized case:

    10-4

    10-3

    10-2

    10-1

    1

    10

    10 2

    10 3

    10 4

    10-1

    1 10 102

    E143

    Q2, GeV2

    HERMES

    E155

    EMC

    SMC

    • fixed target experiments=⇒ small Q2 − xbj lever arm

    • determines only sign of ∆G(x)

    -0.4

    -0.2

    0

    0.2

    0.4

    0.6

    0.8

    10-3

    10-2

    10-1

    1x

    E.C. Aschenauer Pan Pacific, Tokyo, July 2005 20

  • How to measure ∆G• ”Indirect” from scaling violation

    Remember unpolarized case:HERA F2

    0

    1

    2

    3

    4

    5

    1 10 102

    103

    104

    105

    F2 em

    -log

    10(x

    )

    Q2(GeV2)

    ZEUS NLO QCD fit

    H1 PDF 2000 fit

    H1 94-00

    H1 (prel.) 99/00

    ZEUS 96/97

    BCDMS

    E665

    NMC

    x=6.32E-5 x=0.000102x=0.000161

    x=0.000253

    x=0.0004x=0.0005

    x=0.000632x=0.0008

    x=0.0013

    x=0.0021

    x=0.0032

    x=0.005

    x=0.008

    x=0.013

    x=0.021

    x=0.032

    x=0.05

    x=0.08

    x=0.13

    x=0.18

    x=0.25

    x=0.4

    x=0.65

    Remember unpolarized case:HERA F2

    0

    1

    2

    3

    4

    5

    1 10 102

    103

    104

    105

    F2 em

    -log

    10(x

    )

    Q2(GeV2)

    ZEUS NLO QCD fit

    H1 PDF 2000 fit

    H1 94-00

    H1 (prel.) 99/00

    ZEUS 96/97

    BCDMS

    E665

    NMC

    x=6.32E-5 x=0.000102x=0.000161

    x=0.000253

    x=0.0004x=0.0005

    x=0.000632x=0.0008

    x=0.0013

    x=0.0021

    x=0.0032

    x=0.005

    x=0.008

    x=0.013

    x=0.021

    x=0.032

    x=0.05

    x=0.08

    x=0.13

    x=0.18

    x=0.25

    x=0.4

    x=0.65

    =⇒ big Q2 − xbj lever arm=⇒ very accurate G(x)

    0

    5

    10

    15

    20

    -410 -310 -210 -110 10

    5

    10

    15

    20

    x

    xg

    2 = 5 GeV2Q

    2 = 20 GeV2Q

    2 = 200 GeV2Q

    0

    5

    10

    15

    20 ZEUS-JETS (prel.) 94-00

    H1 PDF 2000

    total uncert.

    exp. uncert.

    total uncert.

    H1+ZEUS

    Remember unpolarized case:HERA F2

    0

    1

    2

    3

    4

    5

    1 10 102

    103

    104

    105

    F2 em

    -log

    10(x

    )

    Q2(GeV2)

    ZEUS NLO QCD fit

    H1 PDF 2000 fit

    H1 94-00

    H1 (prel.) 99/00

    ZEUS 96/97

    BCDMS

    E665

    NMC

    x=6.32E-5 x=0.000102x=0.000161

    x=0.000253

    x=0.0004x=0.0005

    x=0.000632x=0.0008

    x=0.0013

    x=0.0021

    x=0.0032

    x=0.005

    x=0.008

    x=0.013

    x=0.021

    x=0.032

    x=0.05

    x=0.08

    x=0.13

    x=0.18

    x=0.25

    x=0.4

    x=0.65

    =⇒ big Q2 − xbj lever arm=⇒ very accurate G(x)

    0

    5

    10

    15

    20

    -410 -310 -210 -110 10

    5

    10

    15

    20

    x

    xg

    2 = 5 GeV2Q

    2 = 20 GeV2Q

    2 = 200 GeV2Q

    0

    5

    10

    15

    20 ZEUS-JETS (prel.) 94-00

    H1 PDF 2000

    total uncert.

    exp. uncert.

    total uncert.

    H1+ZEUS

    Polarized case:

    10-4

    10-3

    10-2

    10-1

    1

    10

    10 2

    10 3

    10 4

    10-1

    1 10 102

    E143

    Q2, GeV2

    HERMES

    E155

    EMC

    SMC

    • fixed target experiments=⇒ small Q2 − xbj lever arm

    • determines only sign of ∆G(x)

    -0.4

    -0.2

    0

    0.2

    0.4

    0.6

    0.8

    10-3

    10-2

    10-1

    1x

    E.C. Aschenauer Pan Pacific, Tokyo, July 2005 20

  • Direct Measurements of ∆G/G

    Isolate the photon-gluon fusion process (PGF)

    • Select pairs of high-PT oppositely charged hadronsOR

    Select single high-PT hadrons

    • Reaction: γ∗p → h±1 + h∓2 + X OR γ∗p → h±1 + X

    • A|| =N

    →⇐h

    ±1h

    ∓2

    −N→⇒h

    ±1h

    ∓2

    N→⇐h

    ±1h

    ∓2

    + N→⇒h

    ±1h

    ∓2

    vs. pT(h±1 ,h∓2 ); A|| =

    N→⇐h

    ±1

    − N→⇒h

    ±1

    N→⇐h

    ±1

    + N→⇒h

    ±1

    vs. pT(h±1 )

    • low Q2 range (Q2 > 0 GeV2)=⇒ increase statistics=⇒ scale of hard sub-processes p̂2T

    • require pT (h1,h2) > 0.5 GeV,M(2π) > 1.0 GeV =⇒ removes resonances ρ and φ

    E.C. Aschenauer Pan Pacific, Tokyo, July 2005 21

  • Direct Measurements of ∆G/G

    Isolate the photon-gluon fusion process (PGF)

    • Select pairs of high-PT oppositely charged hadronsOR

    Select single high-PT hadrons

    • Reaction: γ∗p → h±1 + h∓2 + X OR γ∗p → h±1 + X

    • A|| =N

    →⇐h

    ±1h

    ∓2

    −N→⇒h

    ±1h

    ∓2

    N→⇐h

    ±1h

    ∓2

    + N→⇒h

    ±1h

    ∓2

    vs. pT(h±1 ,h∓2 ); A|| =

    N→⇐h

    ±1

    − N→⇒h

    ±1

    N→⇐h

    ±1

    + N→⇒h

    ±1

    vs. pT(h±1 )

    • low Q2 range (Q2 > 0 GeV2)=⇒ increase statistics=⇒ scale of hard sub-processes p̂2T

    • require pT (h1,h2) > 0.5 GeV,M(2π) > 1.0 GeV =⇒ removes resonances ρ and φ

    E.C. Aschenauer Pan Pacific, Tokyo, July 2005 21

  • Interpretation ?!

    Four different processes can contribute:

    γ

    T T

    e+

    e+’

    q

    V

    h,v

    *q

    h,

    q

    +

    l

    +

    lt

    VMDAVMD = 0 DIS

    ADIS ∼∆q

    q

    QCDC

    AQCDC ∼∆q

    q

    PGF

    APGF ∼∆G

    G

    A‖ ∼4∑

    i=1

    fi ·Ai ∼ (fQCDCAQCDC + fPGFAPGF + fDISADIS + fXAX)

    APGF ≈ 〈â(γg → qq̄)〉〈∆G

    G

    〉= 〈âPGF〉

    ︸ ︷︷ ︸

    〈∆G

    G

    -1

    AQCDC ≈ 〈â(γq → qg)〉〈∆q

    q

    〉= 〈âQCDC〉

    ︸ ︷︷ ︸

    〈∆q

    q

    + 12

    .. estimate theirrelative contributions fiusing Monte Carlo (PYTHIA-6)=⇒ ∆G/G

    E.C. Aschenauer Pan Pacific, Tokyo, July 2005 22

  • Interpretation ?!

    Four different processes can contribute:

    γ

    T T

    e+

    e+’

    q

    V

    h,v

    *q

    h,

    q

    +

    l

    +

    lt

    VMDAVMD = 0 DIS

    ADIS ∼∆q

    q

    QCDC

    AQCDC ∼∆q

    q

    PGF

    APGF ∼∆G

    G

    A‖ ∼4∑

    i=1

    fi ·Ai ∼ (fQCDCAQCDC + fPGFAPGF + fDISADIS + fXAX)

    APGF ≈ 〈â(γg → qq̄)〉〈∆G

    G

    〉= 〈âPGF〉

    ︸ ︷︷ ︸

    〈∆G

    G

    -1

    AQCDC ≈ 〈â(γq → qg)〉〈∆q

    q

    〉= 〈âQCDC〉

    ︸ ︷︷ ︸

    〈∆q

    q

    + 12

    .. estimate theirrelative contributions fiusing Monte Carlo (PYTHIA-6)=⇒ ∆G/G

    E.C. Aschenauer Pan Pacific, Tokyo, July 2005 22

  • Interpretation ?!

    Four different processes can contribute:

    γ

    T T

    e+

    e+’

    q

    V

    h,v

    *q

    h,

    q

    +

    l

    +

    lt

    VMDAVMD = 0 DIS

    ADIS ∼∆q

    q

    QCDC

    AQCDC ∼∆q

    q

    PGF

    APGF ∼∆G

    G

    A‖ ∼4∑

    i=1

    fi ·Ai ∼ (fQCDCAQCDC + fPGFAPGF + fDISADIS + fXAX)

    APGF ≈ 〈â(γg → qq̄)〉〈∆G

    G

    〉= 〈âPGF〉

    ︸ ︷︷ ︸

    〈∆G

    G

    -1

    AQCDC ≈ 〈â(γq → qg)〉〈∆q

    q

    〉= 〈âQCDC〉

    ︸ ︷︷ ︸

    〈∆q

    q

    + 12

    .. estimate theirrelative contributions fiusing Monte Carlo (PYTHIA-6)=⇒ ∆G/G

    E.C. Aschenauer Pan Pacific, Tokyo, July 2005 22

  • Interpretation ?!

    Four different processes can contribute:

    γ

    T T

    e+

    e+’

    q

    V

    h,v

    *q

    h,

    q

    +

    l

    +

    lt

    VMDAVMD = 0 DIS

    ADIS ∼∆q

    q

    QCDC

    AQCDC ∼∆q

    q

    PGF

    APGF ∼∆G

    G

    A‖ ∼4∑

    i=1

    fi ·Ai ∼ (fQCDCAQCDC + fPGFAPGF + fDISADIS + fXAX)

    APGF ≈ 〈â(γg → qq̄)〉〈∆G

    G

    〉= 〈âPGF〉

    ︸ ︷︷ ︸

    〈∆G

    G

    -1

    AQCDC ≈ 〈â(γq → qg)〉〈∆q

    q

    〉= 〈âQCDC〉

    ︸ ︷︷ ︸

    〈∆q

    q

    + 12

    .. estimate theirrelative contributions fiusing Monte Carlo (PYTHIA-6)=⇒ ∆G/G

    E.C. Aschenauer Pan Pacific, Tokyo, July 2005 22

  • Pairs of high-PT Hadrons

    pTh2 (GeV/c)

    f i (i

    = Q

    CD

    C, P

    GF

    , VM

    D)

    pTh1>1.5 GeV/c

    fPGFfQCDCfVMD

    0

    0.2

    0.4

    0.6

    0.8

    1

    0.6 0.8 1 1.2 1.4 1.6 1.8-1

    -0.8

    -0.6

    -0.4

    -0.2

    0

    0.2

    0.4

    0.6

    0.6 0.8 1 1.2 1.4 1.6 1.8 2

    GSA ( ~ 0.4)GSB ( ~ 0.3)GSC ( ~ -0.1)

    pTh2 (GeV/c)

    A||(

    pTh

    1 ,p

    Th2 )

    pTh1>1.5 GeV/c ∆G/G=-1

    ∆G/G=0

    ∆G/G=+1

    ∆G/G=0.41

    Published: within LO pQCD and PYTHIA5 MC model

    ∆G/G = 0.41 ± 0.18 (stat.) ± 0.03 (exp.syst.)at 〈xG〉 = 0.17 and 〈p̂2T 〉 = 2.1 GeV2

    6 x more data on polarized Deuterium and new Pythia modified for HERMES

    SMC Q2 > 1 GeV2

    COMPASS Q2 < 1 GeV2

    COMPASS Q2 > 1 GeV2

    HERMES Q2

  • Pairs of high-PT Hadrons

    pTh2 (GeV/c)

    f i (i

    = Q

    CD

    C, P

    GF

    , VM

    D)

    pTh1>1.5 GeV/c

    fPGFfQCDCfVMD

    0

    0.2

    0.4

    0.6

    0.8

    1

    0.6 0.8 1 1.2 1.4 1.6 1.8-1

    -0.8

    -0.6

    -0.4

    -0.2

    0

    0.2

    0.4

    0.6

    0.6 0.8 1 1.2 1.4 1.6 1.8 2

    GSA ( ~ 0.4)GSB ( ~ 0.3)GSC ( ~ -0.1)

    pTh2 (GeV/c)

    A||(

    pTh

    1 ,p

    Th2 )

    pTh1>1.5 GeV/c ∆G/G=-1

    ∆G/G=0

    ∆G/G=+1

    ∆G/G=0.41

    Published: within LO pQCD and PYTHIA5 MC model

    ∆G/G = 0.41 ± 0.18 (stat.) ± 0.03 (exp.syst.)at 〈xG〉 = 0.17 and 〈p̂2T 〉 = 2.1 GeV2

    6 x more data on polarized Deuterium and new Pythia modified for HERMES

    SMC Q2 > 1 GeV2

    COMPASS Q2 < 1 GeV2

    COMPASS Q2 > 1 GeV2

    HERMES Q2

  • Why is a FF extraction important for HERMES

    • enter in ∆q, δq and f⊥1T extraction• test factorization at HERMES

    energies√

    s ∼ 7GeV• are the FF from e+e− applicable at ep

    and/or〈Q2

    〉= 2.5GeV

    Extract π,K,p multiplicities:

    1

    NDIS· dN

    h(z,Q2)

    dz=

    f

    e2f∫ 1

    0dxqf (x,Q

    2)Dhf (z,Q2)

    f

    e2f∫ 1

    0dxqf (x,Q2)

    E.C. Aschenauer Pan Pacific, Tokyo, July 2005 24

  • Why is a FF extraction important for HERMES

    • enter in ∆q, δq and f⊥1T extraction• test factorization at HERMES

    energies√

    s ∼ 7GeV• are the FF from e+e− applicable at ep

    and/or〈Q2

    〉= 2.5GeV

    Extract π,K,p multiplicities:

    1

    NDIS· dN

    h(z,Q2)

    dz=

    f

    e2f∫ 1

    0dxqf (x,Q

    2)Dhf (z,Q2)

    f

    e2f∫ 1

    0dxqf (x,Q2)

    E.C. Aschenauer Pan Pacific, Tokyo, July 2005 24

  • How to extract FF/Multiplicities at HERMESunpolarisedH & D data

    experimentalmultiplicitiesin acceptance

    unpolarisedH & D data

    e+

    e−c.s. background

    correction

    experimentalmultiplicitiesin acceptance

    γ

    T T

    e+

    e+’

    q

    V

    h,v

    *q

    h,

    q

    +

    l

    +

    lt

    excl. VM correction

    PID using RICH

    MC

    unpolarisedH & D data

    e+

    e−c.s. background

    correction

    experimentalmultiplicitiesin acceptance

    born levelmultiplicities

    γ

    T T

    e+

    e+’

    q

    V

    h,v

    *q

    h,

    q

    +

    l

    +

    lt

    excl. VM correction

    PID using RICH

    MC

    1

    2

    3

    4

    5

    6

    7

    8

    9

    10

    11

    12

    13

    14

    15

    16

    1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16Born level z bin (j)

    Exp

    erim

    enta

    l bin

    (i)

    n(i,j) for all pions

    0.04

    0.05

    0.060.070.080.090.1

    0.2

    0.3

    0.4

    0.5

    0.60.70.80.9

    1

    2

    0 20 40 60 80 100

    Q2 (GeV2/c2)

    Du

    π+ in

    PK

    H p

    aram

    etri

    sati

    on

    z = 0.3

    z = 0.7

    LONLO

    unpolarisedH & D data

    e+

    e−c.s. background

    correction

    experimentalmultiplicitiesin acceptance

    born levelmultiplicities

    Q − Evolution2

    acceptance correctionradiative unfolding

    γ

    T T

    e+

    e+’

    q

    V

    h,v

    *q

    h,

    q

    +

    l

    +

    lt

    excl. VM correction

    PID using RICH

    MC

    E.C. Aschenauer Pan Pacific, Tokyo, July 2005 25

  • How to extract FF/Multiplicities at HERMES

    unpolarisedH & D data

    experimentalmultiplicitiesin acceptance

    unpolarisedH & D data

    e+

    e−c.s. background

    correction

    experimentalmultiplicitiesin acceptance

    γ

    T T

    e+

    e+’

    q

    V

    h,v

    *q

    h,

    q

    +

    l

    +

    lt

    excl. VM correction

    PID using RICH

    MC

    unpolarisedH & D data

    e+

    e−c.s. background

    correction

    experimentalmultiplicitiesin acceptance

    born levelmultiplicities

    γ

    T T

    e+

    e+’

    q

    V

    h,v

    *q

    h,

    q

    +

    l

    +

    lt

    excl. VM correction

    PID using RICH

    MC

    1

    2

    3

    4

    5

    6

    7

    8

    9

    10

    11

    12

    13

    14

    15

    16

    1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16Born level z bin (j)

    Exp

    erim

    enta

    l bin

    (i)

    n(i,j) for all pions

    0.04

    0.05

    0.060.070.080.090.1

    0.2

    0.3

    0.4

    0.5

    0.60.70.80.9

    1

    2

    0 20 40 60 80 100

    Q2 (GeV2/c2)

    Du

    π+ in

    PK

    H p

    aram

    etri

    sati

    on

    z = 0.3

    z = 0.7

    LONLO

    unpolarisedH & D data

    e+

    e−c.s. background

    correction

    experimentalmultiplicitiesin acceptance

    born levelmultiplicities

    Q − Evolution2

    acceptance correctionradiative unfolding

    γ

    T T

    e+

    e+’

    q

    V

    h,v

    *q

    h,

    q

    +

    l

    +

    lt

    excl. VM correction

    PID using RICH

    MC

    E.C. Aschenauer Pan Pacific, Tokyo, July 2005 25

  • How to extract FF/Multiplicities at HERMES

    unpolarisedH & D data

    experimentalmultiplicitiesin acceptance

    unpolarisedH & D data

    e+

    e−c.s. background

    correction

    experimentalmultiplicitiesin acceptance

    γ

    T T

    e+

    e+’

    q

    V

    h,v

    *q

    h,

    q

    +

    l

    +

    lt

    excl. VM correction

    PID using RICH

    MC

    unpolarisedH & D data

    e+

    e−c.s. background

    correction

    experimentalmultiplicitiesin acceptance

    born levelmultiplicities

    γ

    T T

    e+

    e+’

    q

    V

    h,v

    *q

    h,

    q

    +

    l

    +

    lt

    excl. VM correction

    PID using RICH

    MC

    1

    2

    3

    4

    5

    6

    7

    8

    9

    10

    11

    12

    13

    14

    15

    16

    1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16Born level z bin (j)

    Exp

    erim

    enta

    l bin

    (i)

    n(i,j) for all pions

    0.04

    0.05

    0.060.070.080.090.1

    0.2

    0.3

    0.4

    0.5

    0.60.70.80.9

    1

    2

    0 20 40 60 80 100

    Q2 (GeV2/c2)

    Du

    π+ in

    PK

    H p

    aram

    etri

    sati

    on

    z = 0.3

    z = 0.7

    LONLO

    unpolarisedH & D data

    e+

    e−c.s. background

    correction

    experimentalmultiplicitiesin acceptance

    born levelmultiplicities

    Q − Evolution2

    acceptance correctionradiative unfolding

    γ

    T T

    e+

    e+’

    q

    V

    h,v

    *q

    h,

    q

    +

    l

    +

    lt

    excl. VM correction

    PID using RICH

    MC

    E.C. Aschenauer Pan Pacific, Tokyo, July 2005 25

  • How to extract FF/Multiplicities at HERMES

    unpolarisedH & D data

    experimentalmultiplicitiesin acceptance

    unpolarisedH & D data

    e+

    e−c.s. background

    correction

    experimentalmultiplicitiesin acceptance

    γ

    T T

    e+

    e+’

    q

    V

    h,v

    *q

    h,

    q

    +

    l

    +

    lt

    excl. VM correction

    PID using RICH

    MC

    unpolarisedH & D data

    e+

    e−c.s. background

    correction

    experimentalmultiplicitiesin acceptance

    born levelmultiplicities

    γ

    T T

    e+

    e+’

    q

    V

    h,v

    *q

    h,

    q

    +

    l

    +

    lt

    excl. VM correction

    PID using RICH

    MC

    1

    2

    3

    4

    5

    6

    7

    8

    9

    10

    11

    12

    13

    14

    15

    16

    1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16Born level z bin (j)

    Exp

    erim

    enta

    l bin

    (i)

    n(i,j) for all pions

    0.04

    0.05

    0.060.070.080.09

    0.1

    0.2

    0.3

    0.4

    0.5

    0.60.70.80.9

    1

    2

    0 20 40 60 80 100

    Q2 (GeV2/c2)

    Du

    π+ in

    PK

    H p

    aram

    etri

    sati

    on

    z = 0.3

    z = 0.7

    LONLO

    unpolarisedH & D data

    e+

    e−c.s. background

    correction

    experimentalmultiplicitiesin acceptance

    born levelmultiplicities

    Q − Evolution2

    acceptance correctionradiative unfolding

    γ

    T T

    e+

    e+’

    q

    V

    h,v

    *q

    h,

    q

    +

    l

    +

    lt

    excl. VM correction

    PID using RICH

    MC

    E.C. Aschenauer Pan Pacific, Tokyo, July 2005 25

  • Data - MC Agreement• MC: Lepto in combination with JETSET; PDF: CTEQ-6L

    Fragmentation parameters tuned to HERMES multiplicities in acceptance

    • Data: Q2 > 1GeV2,W2 > 10GeV2, z > 0.2,2GeV < p(π,K,p)± < 15GeVPID and background corrections as described before applied

    0

    0.1

    0.2

    0.3

    0 0.25 0.5 0.75 1 1.25

    pt

    Mu

    ltip

    licit

    y

    pip

    0

    0.1

    0.2

    0.3

    0 0.25 0.5 0.75 1 1.25

    pt

    Mu

    ltip

    licit

    y

    pim

    0

    0.02

    0.04

    0.06

    0 0.25 0.5 0.75 1 1.25

    pt

    Mu

    ltip

    licit

    y

    kp

    0

    0.01

    0.02

    0.03

    0 0.25 0.5 0.75 1 1.25

    pt

    Mu

    ltip

    licit

    y

    km

    0

    0.05

    0.1

    0.15

    0 0.25 0.5 0.75 1 1.25

    pt

    Mu

    ltip

    licit

    y

    pp

    0

    0.005

    0.01

    0.015

    0 0.25 0.5 0.75 1 1.25

    pt

    Mu

    ltip

    licit

    y

    pm

    Exp.

    2004c

    2004a

    F. all W2

    Jetset

    0

    0.02

    0.04

    0.06

    0.08

    0.1

    0 1 2 3

    rap

    Mu

    ltip

    licit

    y

    pip

    0

    0.02

    0.04

    0.06

    0.08

    0.1

    0 1 2 3

    rap

    Mu

    ltip

    licit

    y

    pim

    0

    0.01

    0.02

    0.03

    0.04

    0 1 2 3

    rap

    Mu

    ltip

    licit

    y

    kp

    0

    0.005

    0.01

    0.015

    0.02

    0 1 2 3

    rap

    Mu

    ltip

    licit

    y

    km

    0

    0.02

    0.04

    0.06

    0.08

    0.1

    0 1 2 3

    rap

    Mu

    ltip

    licit

    y

    pp

    0

    0.002

    0.004

    0.006

    0 1 2 3

    rap

    Mu

    ltip

    licit

    y

    pm

    Exp.

    2004c

    2004a

    F. all W2

    Jetset

    Excellent agreement; also on cross section level (Data/MC < 10%)

    E.C. Aschenauer Pan Pacific, Tokyo, July 2005 26

  • Data - MC Agreement• MC: Lepto in combination with JETSET; PDF: CTEQ-6L

    Fragmentation parameters tuned to HERMES multiplicities in acceptance

    • Data: Q2 > 1GeV2,W2 > 10GeV2, z > 0.2,2GeV < p(π,K,p)± < 15GeVPID and background corrections as described before applied

    0

    0.1

    0.2

    0.3

    0 0.25 0.5 0.75 1 1.25

    pt

    Mu

    ltip

    licit

    y

    pip

    0

    0.1

    0.2

    0.3

    0 0.25 0.5 0.75 1 1.25

    pt

    Mu

    ltip

    licit

    y

    pim

    0

    0.02

    0.04

    0.06

    0 0.25 0.5 0.75 1 1.25

    pt

    Mu

    ltip

    licit

    y

    kp

    0

    0.01

    0.02

    0.03

    0 0.25 0.5 0.75 1 1.25

    pt

    Mu

    ltip

    licit

    y

    km

    0

    0.05

    0.1

    0.15

    0 0.25 0.5 0.75 1 1.25

    pt

    Mu

    ltip

    licit

    y

    pp

    0

    0.005

    0.01

    0.015

    0 0.25 0.5 0.75 1 1.25

    pt

    Mu

    ltip

    licit

    y

    pm

    Exp.

    2004c

    2004a

    F. all W2

    Jetset

    0

    0.02

    0.04

    0.06

    0.08

    0.1

    0 1 2 3

    rap

    Mu

    ltip

    licit

    y

    pip

    0

    0.02

    0.04

    0.06

    0.08

    0.1

    0 1 2 3

    rap

    Mu

    ltip

    licit

    y

    pim

    0

    0.01

    0.02

    0.03

    0.04

    0 1 2 3

    rap

    Mu

    ltip

    licit

    y

    kp

    0

    0.005

    0.01

    0.015

    0.02

    0 1 2 3

    rap

    Mu

    ltip

    licit

    y

    km

    0

    0.02

    0.04

    0.06

    0.08

    0.1

    0 1 2 3

    rap

    Mu

    ltip

    licit

    y

    pp

    0

    0.002

    0.004

    0.006

    0 1 2 3

    rap

    Mu

    ltip

    licit

    y

    pm

    Exp.

    2004c

    2004a

    F. all W2

    Jetset

    Excellent agreement; also on cross section level (Data/MC < 10%)

    E.C. Aschenauer Pan Pacific, Tokyo, July 2005 26

  • Exclusive VM Contamination

    • exclusive VM production:totally different process than SIDIS

    • estimate contribution from PYTHIA-6:changes: QED-radiation, VMD-model,...

    • ratio: Nhexcl.VM(z)/NhSIDIS(z)• large contribution for π at high z

    contribution for K moderate vs z• contribution growing for small xbj for

    both π and K

    00.5

    11.5

    22.5

    33.5

    44.5

    0 5 10 15

    ∆E (GeV)

    σ (p

    b)

    00.20.40.60.8

    11.21.41.61.8

    2

    0 5 10 15

    ∆E (GeV)

    σ Dat

    a/σ M

    C

    0

    0.2

    0.4

    0.6

    0.8

    1

    1.2

    0.4 0.6 0.8 1

    M(π+π-) (GeV)

    σ (p

    b)

    00.20.40.60.8

    11.21.41.61.8

    2

    0.4 0.6 0.8 1

    M(π+π-) (GeV)

    σ Dat

    a/σ M

    C

    zN

    h V

    M(z

    )/N

    h(z

    )

    0

    0.2

    0.4

    0.6

    0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

    0

    0.2

    0.4

    0.6

    0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

    π+ Target:ProtonNeutronDeuterium

    0

    0.2

    0.4

    0.6

    0.8

    0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

    0

    0.2

    0.4

    0.6

    0.8

    0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

    π-

    0

    0.025

    0.05

    0.075

    0.1

    0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

    0

    0.025

    0.05

    0.075

    0.1

    0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

    K+

    0

    0.1

    0.2

    0.3

    0.4

    0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

    0.1

    0.2

    0.3

    0.4

    0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

    K-

    xBjN

    h V

    M(x

    Bj)/

    Nh(x

    Bj)

    0

    0.2

    0.4

    0.6

    10 -1 1

    0

    0.2

    0.4

    0.6

    10-1

    1

    π+ Target:ProtonNeutronDeuterium

    0.25 < z < 0.350.60 < z < 0.75

    0

    0.2

    0.4

    0.6

    10-1

    1

    0

    0.2

    0.4

    0.6

    10-1

    1

    π-

    0

    0.025

    0.05

    0.075

    0.1

    10-1

    1

    0

    0.025

    0.05

    0.075

    0.1

    10-1

    1

    K+

    0

    0.025

    0.05

    0.075

    0.1

    10-1

    10

    0.025

    0.05

    0.075

    0.1

    10-1

    1

    K-

    E.C. Aschenauer Pan Pacific, Tokyo, July 2005 27

  • Exclusive VM Contamination

    • exclusive VM production:totally different process than SIDIS

    • estimate contribution from PYTHIA-6:changes: QED-radiation, VMD-model,...

    • ratio: Nhexcl.VM(z)/NhSIDIS(z)• large contribution for π at high z

    contribution for K moderate vs z

    • contribution growing for small xbj forboth π and K

    00.5

    11.5

    22.5

    33.5

    44.5

    0 5 10 15

    ∆E (GeV)

    σ (p

    b)

    00.20.40.60.8

    11.21.41.61.8

    2

    0 5 10 15

    ∆E (GeV)

    σ Dat

    a/σ M

    C

    0

    0.2

    0.4

    0.6

    0.8

    1

    1.2

    0.4 0.6 0.8 1

    M(π+π-) (GeV)

    σ (p

    b)

    00.20.40.60.8

    11.21.41.61.8

    2

    0.4 0.6 0.8 1

    M(π+π-) (GeV)

    σ Dat

    a/σ M

    C

    zN

    h V

    M(z

    )/N

    h(z

    )

    0

    0.2

    0.4

    0.6

    0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

    0

    0.2

    0.4

    0.6

    0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

    π+ Target:ProtonNeutronDeuterium

    0

    0.2

    0.4

    0.6

    0.8

    0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

    0

    0.2

    0.4

    0.6

    0.8

    0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

    π-

    0

    0.025

    0.05

    0.075

    0.1

    0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

    0

    0.025

    0.05

    0.075

    0.1

    0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

    K+

    0

    0.1

    0.2

    0.3

    0.4

    0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

    0.1

    0.2

    0.3

    0.4

    0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

    K-

    xBj

    Nh V

    M(x

    Bj)/

    Nh(x

    Bj)

    0

    0.2

    0.4

    0.6

    10 -1 1

    0

    0.2

    0.4

    0.6

    10-1

    1

    π+ Target:ProtonNeutronDeuterium

    0.25 < z < 0.350.60 < z < 0.75

    0

    0.2

    0.4

    0.6

    10-1

    1

    0

    0.2

    0.4

    0.6

    10-1

    1

    π-

    0

    0.025

    0.05

    0.075

    0.1

    10-1

    1

    0

    0.025

    0.05

    0.075

    0.1

    10-1

    1

    K+

    0

    0.025

    0.05

    0.075

    0.1

    10-1

    10

    0.025

    0.05

    0.075

    0.1

    10-1

    1

    K-

    E.C. Aschenauer Pan Pacific, Tokyo, July 2005 27

  • Exclusive VM Contamination

    • exclusive VM production:totally different process than SIDIS

    • estimate contribution from PYTHIA-6:changes: QED-radiation, VMD-model,...

    • ratio: Nhexcl.VM(z)/NhSIDIS(z)• large contribution for π at high z

    contribution for K moderate vs z• contribution growing for small xbj for

    both π and K

    00.5

    11.5

    22.5

    33.5

    44.5

    0 5 10 15

    ∆E (GeV)

    σ (p

    b)

    00.20.40.60.8

    11.21.41.61.8

    2

    0 5 10 15

    ∆E (GeV)

    σ Dat

    a/σ M

    C

    0

    0.2

    0.4

    0.6

    0.8

    1

    1.2

    0.4 0.6 0.8 1

    M(π+π-) (GeV)

    σ (p

    b)

    00.20.40.60.8

    11.21.41.61.8

    2

    0.4 0.6 0.8 1

    M(π+π-) (GeV)

    σ Dat

    a/σ M

    C

    zN

    h V

    M(z

    )/N

    h(z

    )

    0

    0.2

    0.4

    0.6

    0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

    0

    0.2

    0.4

    0.6

    0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

    π+ Target:ProtonNeutronDeuterium

    0

    0.2

    0.4

    0.6

    0.8

    0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

    0

    0.2

    0.4

    0.6

    0.8

    0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

    π-

    0

    0.025

    0.05

    0.075

    0.1

    0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

    0

    0.025

    0.05

    0.075

    0.1

    0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

    K+

    0

    0.1

    0.2

    0.3

    0.4

    0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

    0.1

    0.2

    0.3

    0.4

    0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

    K-

    xBjN

    h V

    M(x

    Bj)/

    Nh(x

    Bj)

    0

    0.2

    0.4

    0.6

    10 -1 1

    0

    0.2

    0.4

    0.6

    10-1

    1

    π+ Target:ProtonNeutronDeuterium

    0.25 < z < 0.350.60 < z < 0.75

    0

    0.2

    0.4

    0.6

    10-1

    1

    0

    0.2

    0.4

    0.6

    10-1

    1

    π-

    0

    0.025

    0.05

    0.075

    0.1

    10-1

    1

    0

    0.025

    0.05

    0.075

    0.1

    10-1

    1

    K+

    0

    0.025

    0.05

    0.075

    0.1

    10-1

    10

    0.025

    0.05

    0.075

    0.1

    10-1

    1

    K-

    E.C. Aschenauer Pan Pacific, Tokyo, July 2005 27

  • π± - Multiplicity vs. z

    10-2

    10-1

    1

    0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1z

    mu

    ltip

    licit

    y

    HERMES Preliminary

    π+

    excl. VM substractedexcl. VM included

    proton target

    Q2=2.5 GeV2/c210

    -2

    10-1

    1

    0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1z

    mu

    ltip

    licit

    y

    HERMES Preliminary

    π-

    excl. VM substractedexcl. VM included

    proton target

    Q2=2.5 GeV2/c2

    • Systematic uncertainty mainly from hadron PID correction• Q2 > 1GeV2,W2 > 10GeV2

    E.C. Aschenauer Pan Pacific, Tokyo, July 2005 28

  • π± - Multiplicity vs. z

    10-2

    10-1

    1

    0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1z

    mu

    ltip

    licit

    y

    HERMES Preliminary

    π+

    excl. VM substractedexcl. VM includedEMC D(u→π+) FF

    proton target

    Q2=25.0 GeV2/c2

    10-3

    10-2

    10-1

    1

    0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1z

    mu

    ltip

    licit

    y

    HERMES Preliminary

    π-

    excl. VM substractedexcl. VM includedEMC D(u→π-) FF

    proton target

    Q2=25.0 GeV2/c2

    • Comparison with EMC, Nucl. Phys. B321 (1989) 541

    • EMC: Fragmentation Function Dπ±u

    E.C. Aschenauer Pan Pacific, Tokyo, July 2005 29

  • π± - Multiplicity vs. Q2 and xbj

    10-1

    1

    1 10 Q2

    (d2 N

    π /d

    z d

    Q2 )

    / (d

    Nd

    is/d

    Q2 )

    : 0.25 < z < 0.35: 0.35 < z < 0.45

    : 0.45 < z < 0.60: 0.60 < z < 0.75

    HERMES Preliminary

    π+/-

    excl. VM substractedexcl. VM included

    Kretzer FF

    proton target

    10-1

    1

    10

    10-1

    1xbj(d

    2 (N

    π++N

    π-)

    /dz

    dx)

    / (d

    Nd

    is/d

    x)

    : 0.25 < z < 0.35: 0.35 < z < 0.45

    : 0.45 < z < 0.60: 0.60 < z < 0.75

    HERMES 2000 Preliminary

    π

    excl. VM substractedexcl. VM includedEMC (charged had.)

    proton target

    Q2 = 2.5 GeV2/c2

    • Reasonable agreement with results using S. Kretzter FF• very weak xbj dependence

    E.C. Aschenauer Pan Pacific, Tokyo, July 2005 30

  • K± - Multiplicity vs. z

    10-2

    10-1

    1

    0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1z

    mu

    ltip

    licit

    y

    HERMES Preliminary

    K+

    excl. VM substractedexcl. VM included

    proton target

    Q2=2.5 GeV2/c2

    10-3

    10-2

    10-1

    0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1z

    mu

    ltip

    licit

    y

    HERMES Preliminary

    K-

    excl. VM substractedexcl. VM included

    proton target

    Q2=2.5 GeV2/c2

    • charge separated Kaon multiplicities• Systematic uncertainty mainly from hadron PID correction• low K− statistics =⇒ more statistics under way

    E.C. Aschenauer Pan Pacific, Tokyo, July 2005 31

  • and Summary

    • HERMES continues happily taking data with a transverse polarized p-target

    Integrated DIS HERA Run II (polarized)

    0

    500

    1000

    1500

    2000

    2500

    3000

    x 10 3

    0 50 100 150 200 250 300Day of Running

    Nu

    mb

    er o

    f p

    ol.

    DIS

    eve

    nts

    2002/03

    2003

    2004

    2005

    • Transversity, Sivers and friends =⇒ G. Schnell• Exclusive reactions =⇒ Lq

    DVCS: AUT =⇒ sensitive to GPD H + E =⇒ Ju =⇒ Y. Miyachiexclusive ρ0 / π+: AUT =⇒ sensitive to GPD E / H̃+ Ẽ =⇒ A. Rostomyan

    • finalize most of HERA-I analysis• gd1 ,gp1 ,gn1 ,b1,∆q

    • Extraction of FF very close• new Millennium extraction of ∆q (Purity free)• new ∆s + ∆s̄ extraction using isoscalor method

    • the nice description of HERMES data by Monte Carlo will allowa new extraction of ∆G/G

    Many more results to come from physics topics not touched in this talk

    E.C. Aschenauer Pan Pacific, Tokyo, July 2005 32

  • and Summary

    • HERMES continues happily taking data with a transverse polarized p-targetIntegrated DIS HERA Run II (polarized)

    0

    500

    1000

    1500

    2000

    2500

    3000

    x 10 3

    0 50 100 150 200 250 300Day of Running

    Nu

    mb

    er o

    f p

    ol.

    DIS

    eve

    nts

    2002/03

    2003

    2004

    2005

    • Transversity, Sivers and friends =⇒ G. Schnell• Exclusive reactions =⇒ Lq

    DVCS: AUT =⇒ sensitive to GPD H + E =⇒ Ju =⇒ Y. Miyachiexclusive ρ0 / π+: AUT =⇒ sensitive to GPD E / H̃+ Ẽ =⇒ A. Rostomyan

    • finalize most of HERA-I analysis• gd1 ,gp1 ,gn1 ,b1,∆q

    • Extraction of FF very close• new Millennium extraction of ∆q (Purity free)• new ∆s + ∆s̄ extraction using isoscalor method

    • the nice description of HERMES data by Monte Carlo will allowa new extraction of ∆G/G

    Many more results to come from physics topics not touched in this talk

    E.C. Aschenauer Pan Pacific, Tokyo, July 2005 32

  • and Summary

    • HERMES continues happily taking data with a transverse polarized p-target

    Integrated DIS HERA Run II (polarized)

    0

    500

    1000

    1500

    2000

    2500

    3000

    x 10 3

    0 50 100 150 200 250 300Day of Running

    Nu

    mb

    er o

    f p

    ol.

    DIS

    eve

    nts

    2002/03

    2003

    2004

    2005

    • Transversity, Sivers and friends =⇒ G. Schnell• Exclusive reactions =⇒ Lq

    DVCS: AUT =⇒ sensitive to GPD H + E =⇒ Ju =⇒ Y. Miyachiexclusive ρ0 / π+: AUT =⇒ sensitive to GPD E / H̃+ Ẽ =⇒ A. Rostomyan

    • finalize most of HERA-I analysis• gd1 ,gp1 ,gn1 ,b1,∆q

    • Extraction of FF very close• new Millennium extraction of ∆q (Purity free)• new ∆s + ∆s̄ extraction using isoscalor method

    • the nice description of HERMES data by Monte Carlo will allowa new extraction of ∆G/G

    Many more results to come from physics topics not touched in this talk

    E.C. Aschenauer Pan Pacific, Tokyo, July 2005 32

  • and Summary

    • HERMES continues happily taking data with a transverse polarized p-target

    Integrated DIS HERA Run II (polarized)

    0

    500

    1000

    1500

    2000

    2500

    3000

    x 10 3

    0 50 100 150 200 250 300Day of Running

    Nu

    mb

    er o

    f p

    ol.

    DIS

    eve

    nts

    2002/03

    2003

    2004

    2005

    • Transversity, Sivers and friends =⇒ G. Schnell• Exclusive reactions =⇒ Lq

    DVCS: AUT =⇒ sensitive to GPD H + E =⇒ Ju =⇒ Y. Miyachiexclusive ρ0 / π+: AUT =⇒ sensitive to GPD E / H̃+ Ẽ =⇒ A. Rostomyan

    • finalize most of HERA-I analysis• gd1 ,gp1 ,gn1 ,b1,∆q

    • Extraction of FF very close• new Millennium extraction of ∆q (Purity free)• new ∆s + ∆s̄ extraction using isoscalor method

    • the nice description of HERMES data by Monte Carlo will allowa new extraction of ∆G/G

    Many more results to come from physics topics not touched in this talk

    E.C. Aschenauer Pan Pacific, Tokyo, July 2005 32

  • and Summary

    • HERMES continues happily taking data with a transverse polarized p-target

    Integrated DIS HERA Run II (polarized)

    0

    500

    1000

    1500

    2000

    2500

    3000

    x 10 3

    0 50 100 150 200 250 300Day of Running

    Nu

    mb

    er o

    f p

    ol.

    DIS

    eve

    nts

    2002/03

    2003

    2004

    2005

    • Transversity, Sivers and friends =⇒ G. Schnell• Exclusive reactions =⇒ Lq

    DVCS: AUT =⇒ sensitive to GPD H + E =⇒ Ju =⇒ Y. Miyachiexclusive ρ0 / π+: AUT =⇒ sensitive to GPD E / H̃+ Ẽ =⇒ A. Rostomyan

    • finalize most of HERA-I analysis• gd1 ,gp1 ,gn1 ,b1,∆q

    • Extraction of FF very close• new Millennium extraction of ∆q (Purity free)• new ∆s + ∆s̄ extraction using isoscalor method

    • the nice description of HERMES data by Monte Carlo will allowa new extraction of ∆G/G

    Many more results to come from physics topics not touched in this talk

    E.C. Aschenauer Pan Pacific, Tokyo, July 2005 32

  • and Summary

    • HERMES continues happily taking data with a transverse polarized p-target

    Integrated DIS HERA Run II (polarized)

    0

    500

    1000

    1500

    2000

    2500

    3000

    x 10 3

    0 50 100 150 200 250 300Day of Running

    Nu

    mb

    er o

    f p

    ol.

    DIS

    eve

    nts

    2002/03

    2003

    2004

    2005

    • Transversity, Sivers and friends =⇒ G. Schnell• Exclusive reactions =⇒ Lq

    DVCS: AUT =⇒ sensitive to GPD H + E =⇒ Ju =⇒ Y. Miyachiexclusive ρ0 / π+: AUT =⇒ sensitive to GPD E / H̃+ Ẽ =⇒ A. Rostomyan

    • finalize most of HERA-I analysis• gd1 ,gp1 ,gn1 ,b1,∆q

    • Extraction of FF very close• new Millennium extraction of ∆q (Purity free)• new ∆s + ∆s̄ extraction using isoscalor method

    • the nice description of HERMES data by Monte Carlo will allowa new extraction of ∆G/G

    Many more results to come from physics topics not touched in this talk

    E.C. Aschenauer Pan Pacific, Tokyo, July 2005 32

  • and Summary

    • HERMES continues happily taking data with a transverse polarized p-target

    Integrated DIS HERA Run II (polarized)

    0

    500

    1000

    1500

    2000

    2500

    3000

    x 10 3

    0 50 100 150 200 250 300Day of Running

    Nu

    mb

    er o

    f p

    ol.

    DIS

    eve

    nts

    2002/03

    2003

    2004

    2005

    • Transversity, Sivers and friends =⇒ G. Schnell• Exclusive reactions =⇒ Lq

    DVCS: AUT =⇒ sensitive to GPD H + E =⇒ Ju =⇒ Y. Miyachiexclusive ρ0 / π+: AUT =⇒ sensitive to GPD E / H̃+ Ẽ =⇒ A. Rostomyan

    • finalize most of HERA-I analysis• gd1 ,gp1 ,gn1 ,b1,∆q

    • Extraction of FF very close• new Millennium extraction of ∆q (Purity free)• new ∆s + ∆s̄ extraction using isoscalor method

    • the nice description of HERMES data by Monte Carlo will allowa new extraction of ∆G/G

    Many more results to come from physics topics not touched in this talk

    E.C. Aschenauer Pan Pacific, Tokyo, July 2005 32

    The Spin Structure of the NucleonHERA at DESYThe HERMES DetectorDIS KinematicsDeep Inelastic Scattering Virtual Photon AsymmetryWorld data on $mathbf {g_1/F_1}$World data on $mathbf {xg_1(x,Q^2)}$The structure function $mathbf {b_1(x,Q^2)}$The structure function $mathbf {b_1(x,Q^2)}$Semi-inclusive DISSemi-inclusive DIS$Delta $q-ExtractionMeasured Hadron AsymmetriesQuark PolarizationsPolarized Quark DensitiesSU(2)-FlavorSymmetry Breaking(?)How to measure $Delta G$Direct Measurements of $displaystyle mathbf {Delta G/G}$ Interpretation ?!Pairs of high-$P_T$ HadronsWhy is a FF extraction important for HERMESHow to extract FF/Multiplicities at HERMESData - MC AgreementExclusive VM Contamination$displaystyle mathbf {pi ^{pm }}$ - Multiplicity vs. z$ displaystyle mathbf {pi ^{pm }}$ - Multiplicity vs. z$displaystyle mathbf {pi ^{pm }}$ - Multiplicity vs. $displaystyle mathbf {Q^2}$ and $displaystyle mathbf {x_{bj}}$ $ displaystyle mathbf {K^{pm }}$ - Multiplicity vs. zand Summary