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DVCS at HERMES

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					                    DVCS at HERMES

                       Frank Ellinghaus
                   University of Colorado
             Exclusive Reactions, JLab, USA, May 2007



• The GPD H via:
 – Beam-Spin Asymmetry (BSA)
 – Beam-Charge Asymmetry (BCA)

• The GPD E via transverse Target-Spin Asymmetry (TTSA)

• DVCS on Nuclei
          Parameterization of the Nucleon Structure




                 FF                        PDF      GPD

• Form Factors → Transverse position ← Elastic scattering

• PDFs → Longitudinal momentum distribution ← DIS

• GPDs → Access to transverse position and longitudinal momen-
  tum distr. at the SAME time, 3-D picture ← Exclusive reactions

                 Frank Ellinghaus, JLab, May 2007
 hermes
                                                               2
          Generalized Parton Distributions (GPDs)

Simplest/cleanest hard exclusive process:
Deeply-virtual electroproduction of real photons: e p → e p γ
Deeply-virtual Compton Scattering (DVCS):

                                                          • Longitudinal momentum
                             t                  q’          fractions:
                q
                                                            x ∈ [−1, 1] (not accessible)
                                                            ξ ≈ xB /(2 − xB )
          x+ ξ                                   x- ξ     • t = (q − q )2
                                        2
                                                            (γ ∗ → γ Momentum transfer)
                    GPDs (x, ξ, t, Q )
                                                          • Q2 = −q 2
            P                                        P’

⇒ Measurements as function of xB , t, Q2

                 DVCS: Access to all four GPDs H, H, E, E
                 Mesons: Access to H, E (VM) and H, E (PS)

                       Frank Ellinghaus, JLab, May 2007
 hermes
                                                                                           3
                                                               Overview GPDs
                                                                                           PDFs: GPDs in the limit t → 0
                            wide angle
                                                    form                                          H q (x, 0, 0) = q(x),
      deeply virtual        Compton
        Compton             scattering
                                                   factors
                                                                                               H q (x, 0, 0) = ∆q(x), . . .
        scattering
                                                                                            FFs: First moments of GPDs
                                                                                               1
                                                                                               −1
                                                                                                  dx H(x, ξ, t) = F1(t), . . .
   timelike
  Compton                                                           orbital angular
  scattering                        GPDs                              momentum
                                                              transverse localisation
                                                                                             Only known (quantitative)
  p¯ annihilation
   p
                                                                                                 access to (total)
  γγ → ππ, . . .                                                                            Orbital angular momentum:
                             exclusive             deep inelastic                                  1
                        meson production             scattering                                1
                       deep virtual / large t          PDFs                       Jq,g   = lim          dx x [H q,g (x, ξ, t)+E q,g (x, ξ, t)]
                                                                                           t→0 2   −1
                                                                                                                             (X. Ji, 97)

Original (HERMES) Motivation:
                                                                                                           ∼30%               ?       ?
Nucleon (Long.) Spin Structure: 1/2 = 1/2(∆u + ∆d + ∆s) + Lq + Jg
                                                                                                             Jq =?

                                            Frank Ellinghaus, JLab, May 2007
 hermes
                                                                                                                                          4
                   HowTo Access GPDs via DVCS?

DVCS final state e + p → e + p + γ is indistinguishable from the
Bethe-Heitler Process (BH) → Amplitudes add coherently
                                                                                       e
              e’                                                      e
                                                e            e’
 e                                                                                                   γ
              γ∗     γ                                                        γ   *

                                                    γ∗            γ



          p                  p’             p                 p           p                      p


              Fixed-Target, Collider                                                  Collider

Photon-Production cross section:
                         2                  2 ∗          2
                                                         ∗
     dσ ∝ |τDVCS + τBH| = |τDVCS| + |τBH| + (τDVCSτBH + τBHτDVCS)
                                                                              I


                    Frank Ellinghaus, JLab, May 2007
 hermes
                                                                                                     5
                          DVCS Measurements

          2    ∗          ∗                                2
dσ ∝ |τBH| + (τDVCSτBH + τBHτDVCS) + |τDVCS |
                            I
      2
|τBH| calculable in QED with the knowledge of the form factors
              3                                3
I ∝ ± cI +
       0         cI
              n=1 n    cos(nφ) + λ             n=1   sI sin(nφ)
                                                      n


 DVCS cross section (H1, Zeus):
 Measurement integrated over φ
 → I = 0 (at Twist–2), subtract |τBH|2                                            k
 (GPDs enter in quadratic combinations)
                                                                              q
                                                                  k                                uli
                                                                                      pγ   φ
 Azimuthal asymmetries                                            y
 (HERMES, JLab):                                                          x

 DVCS amplitudes directly accessible                                  z

 via I ⇒ Magnitude + Phase!!!
 (GPDs enter in linear combinations)

                  Frank Ellinghaus, JLab, May 2007
 hermes
                                                                                               6
                        Azimuthal Asymmetries


                  I ∝ ±(cI +
                         0                 [cI cos(nφ) + λsI sin(nφ)])
                                             n             n
                                       n

Beam–Spin Asymmetry (BSA) and Beam–Charge Asymmetry (BCA)
on unpolarized target:
               →
               −       ←−
                +
    BSA : dσ(e p) − dσ(e+p) ∼ sI
                               1,unp
                                                           1,1
                                     sin(φ) ∼ sin(φ) × Im Munp
      BCA :   dσ(e+p) − dσ(e−p) ∼ cI
                                   1,unp
                                                               1,1
                                         cos(φ) ∼ cos(φ) × Re Munp

(Higher Twist/Order → cos 2φ, cos 3φ, sin 2φ)


Longitudinal Target–Spin Asymmetry (LTSA)
                −         →
   LTSA : dσ(e+←) − dσ(e+− ) ∼ sI
                p         p       sin(φ) ∼ sin(φ) × Im M 1,1
                                                      1,LP               LP

(Higher Twist/Order → sin 2φ, sin 3φ)



                   Frank Ellinghaus, JLab, May 2007
  hermes
                                                                              7
                     From Amplitudes to GPDs

 1,1                     xB                              t
Munp = F1(t) H1(ξ, t) + 2−xB (F1(t) + F2(t)) H1(ξ, t) − 4M 2 F2(t) E1(ξ, t)
xB , −t ≈ 0.1 ⇒ Compton Form-Factor H1

            Im H1 ∼ −π              e2 (H q (ξ, ξ, t) − H q (−ξ, ξ, t))
                                     q
                                q
                                         1
                                                                           
                                                               1   1
            Re H1 ∼           e2 P
                               q              H q (x, ξ, t)      +        dx
                          q
                                                              x−ξ x+ξ
                                        −1


              1,1
BSA: Im Munp mainly accesses the GPD H q (x, ξ, t) at x = ξ ⇒ measures
H q (ξ, ξ, t)
           1,1
BCA: Re Munp contains full x–dependence of the GPD H q (x, ξ, t),
x is not accessible ⇒
GPD Model → Observables ← Measurement

                    Frank Ellinghaus, JLab, May 2007
  hermes
                                                                                8
                                               HERMES Event Selection
HERA Beam: 27.6 GeV, e+ and e−, P ≈ 35 − 55%
pol. + unpol. Gas Targets: H/D/Ne/Kr/..
                                                   FIELD CLAMPS                        TRIGGER HODOSCOPE H1
          m
                             FRONT                                    DRIFT CHAMBERS
          2                  MUON
                             HODO
                                                                                                        PRESHOWER (H2)




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          −2
                                                                                          WIDE ANGLE
                                                                                                                         MUON HODOSCOPES
                                                                                        MUON HODOSCOPE
                                                                      MAGNET

                   0              1            2          3       4            5           6            7         8               9                               10 m



Events with exactly one DIS-positron/DIS-electron and exactly
one photon in the calorimeter
Data shown taken before installation of recoil detctor ⇒
                                          Frank Ellinghaus, JLab, May 2007
 hermes
                                                                                                                                                                                     9
                           Exclusivity for DVCS via Missing Mass

 2
Mx ≡ (q + p − pγ )2 ⇒ MC for background and cuts (→ resolution)!

                                                                      • elastic BH (e p → e p γ)
 1000*N/ NDIS




                                             elastic BH
                0.3
                                             associated BH            • associated BH
                                             semi-inclusive             (mainly e p → e ∆+ γ)
                0.2
                                             HERMES
                                                                      • semi–inclusive
                0.1                                                     (mainly e p → e π 0 X)
                 0                                                    • exclusive π 0 (e p → e π 0)
                      -5   0   5      10       15       20       25
                                                        2
                                                      M (GeV )
                                                                 2      not shown (small)
                                                        X


Not simulated: DVCS process (DVCS c.s. “unknown”, DVCS << BH)
+Radiative corrections to BH (→ excl. peak overestimated, BG
underestimated)
⇒ “Exclusive” bin (-1.5 < Mx < 1.7 GeV)
⇒ Overall background contribution ≈ 15%
                                   Frank Ellinghaus, JLab, May 2007
  hermes
                                                                                                      10
                                    Beam–Spin Asymmetry (BSA)
                                                                                        −
                                                                                        →     ←−
                                                                                  1     N (φ)− N (φ)
                                                     ALU(φ) =                           −      −
                                                                                <|Pb |> →(φ)+←(φ)
                                                                                        N      N
          0.8                                                                                   0.3




                                                                                        φ
   ALU




                                                                                          LU
                                                                                         Asin
                        →+                                                                                         →+
                        e p→e γX               (Mx< 1.7 GeV)
                                    +
                                                                                                                   e p→e γX
                                                                                                                                    +

          0.6                                                                                   0.2
                        HERMES PREL. 2000                   (refined)
                                                                                                                   HERMES PRELIMINARY 2000
                             P1 + P2 sin φ + P3 sin 2φ                                          0.1
          0.4                                                                                                      (refined analysis)


          0.2                                                                                     0

           0                                                                                    -0.1

      -0.2                                                                                      -0.2

      -0.4                                                                                      -0.3
                        P1 = -0.04 ± 0.02 (stat)
      -0.6              P2 = -0.18 ± 0.03 (stat)                                                -0.4
                        P3 = 0.00 ± 0.03 (stat)                                                        Asin φ
                                                                                                        LU      M x < 1.7 GeV   = -0.18 ± 0.03 (stat) ± 0.03 (sys)
      -0.8                                                                                      -0.5
                                                                                                       <-t > = 0.18 GeV , <xB> = 0.12, <Q > = 2.5 GeV
                                                                                                                                2                    2            2
                <-t > = 0.18 GeV , <xB> = 0.12, <Q > = 2.5 GeV
                                2                       2                   2

           -1                                                                                   -0.6
                 -3     -2     -1          0        1         2         3                                -1        0       1            2   3    4        5   6
                                                                  φ (rad)                                                                                Mx (GeV)

  ALU in exclusive bin: Expected                                                       sin(φ)–Moment in non–exclusive
                             1,1                                                          region: small and slightly
   sin(φ) dependence ⇒ Im Munp
                                                                                                positive (→ π 0)
(Results from 1996/97 → PRL 87, 182001 (2001))
                                        Frank Ellinghaus, JLab, May 2007
 hermes
                                                                                                                                                                      11
Kinematic dependences of Beam–Spin Asymmetry (BSA)

Kinematic dependence of combined 96/97 (published, PRL) and 2000
(preliminary, hep-ex/0212019) data, reanalyzed with common cuts
               0.6                                                                                                                                                                        −
                                                                                                                                                                                          →     ←−
                                                                                                                                                                                    1     N (φ)− N (φ)
               0.4
                                                                                                                                                                       ALU(φ) =           −      −
                                                                                                                                                                                  <|Pb |> →(φ)+←(φ)
                                                                                                                                                                                          N      N
               0.2          e+p → e+ γ X                            HERMES PRELIMINARY
     sin(Φ)




                                                                                                                                                                       Asinφ ≤ 0.2
         ALU




                 0


                                                                                                                                                                        LU
               -0.2



               -0.4



               0.6

               0.5

               0.4




                                                                                                                                                                       Asin2φ consistent with zero
               0.3
     sin(2Φ)




               0.2
                                                                                                                                                                        LU
         ALU




                0.1

                 0

               -0.1

               -0.2

               -0.3
                   0   0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 1    1.5   2   2.5       3   3.5   4   4.5   5   0.06   0.08   0.1   0.12   0.14   0.16   0.18   0.2


                                              2                                      2        2                                       Xbj
                                 -tc(GeV )                                     Q (GeV )



⇒ Weak kinematic dependence (kinematics correlated!)
Compare to calculations at average x, Q2, t per bin →

                                                            Frank Ellinghaus, JLab, May 2007
 hermes
                                                                                                                                                                                                         12
Kinematic dependences of Beam–Spin Asymmetry (BSA)
                0.3                                                                      0.3
      sinφ
          ALU




                                                                                  sinφ
                                                                                   ALU
                0.2                                                                      0.2
                0.1                                                                      0.1
                0                                                                           0
             -0.1                                                                        -0.1
             -0.2                                                  A/B                   -0.2
                                                                   C/D
             -0.3                                                  E
                                                                                         -0.3
             -0.4                                                                        -0.4
             -0.5                                                                        -0.5
                          0     0.1    0.2    0.3   0.4    0.5   0.6     0.7                    0   2   4   6   8       10
                                                                           2                                        2        2
                                                                 -t (GeV )                                      Q (GeV )
                                                                                • Model calculations using VGG
                0.3
                                                                                  code give too large asymme-
      sinφ
          ALU




                0.2
                0.1                                                               tries compared to perliminary
                0                                                                 HERMES (blue) and published
             -0.1
             -0.2
                                                                                  CLAS (green , PRL) data
             -0.3                                                               • similar magnitude seen in
             -0.4                                                                 other model calculations
             -0.5
                      0       0.05    0.1 0.15      0.2   0.25   0.3     0.35   • Flat kinematic dependence
                                                                          xB
                                                                                  well described by models


                                             Frank Ellinghaus, JLab, May 2007
 hermes
                                                                                                                                 13
  Kinematic dependences of Beam–Spin Asymmetry (BSA)

  The models (Guzey/Teckentrup, PRD 74, 2006) are in agreement with
  “all” other dvcs data so far:
  → Cross section at H1/ZEUS
  → BCA at HERMES (→ later...)
  → published average BSA values from HERMES+CLAS (PRL, 2001)
          0                                                                       0                                                                      0
Asinφ




                                                                        Asinφ




                                                                                                                                               Asinφ
 LU




                                                                         LU




                                                                                                                                                LU
        -0.1                                                                    -0.1                                                                   -0.1



        -0.2                                                                    -0.2                                                                   -0.2



        -0.3                                                                    -0.3                                                                   -0.3



        -0.4                                                                    -0.4                                                                   -0.4
                               Regge                                                                   Regge                                                                  Regge
                         exponential                                                             exponential                                                            exponential
                   HERMES preliminary                                                      HERMES preliminary                                                     HERMES preliminary
        -0.5                                                                    -0.5                                                                   -0.5
               0       0.1     0.2      0.3   0.4   0.5    0.6    0.7                  0   0.05     0.1         0.15   0.2   0.25        0.3                  0   1      2      3      4   5   6     7     8
                                                                 2
                                                          -t [GeV ]                                                                 xB                                                             Q2 [GeV2]

  The size and kinematic dependence of the asymmetry is reproduced
  (except maybe at small Q2).
  More data with improved systematics to come, but BSA less sensi-
  tive to models when compared to BCA.

                                                     Frank Ellinghaus, JLab, May 2007
          hermes
                                                                                                                                                                                                    14
    BCA: Beam–Charge Asymmetry                                                              (hep-ex/0605108, PRD 2007)

                 N + (φ)−N −(φ)                                           3                               2
AC(φ) =          N + (φ)+N −(φ)
                                           ∝ I ∝ ±(cI +
                                                    0
                                                                               I
                                                                          n=1 cn cos(nφ)       +λ              I
                                                                                                          n=1 sn sin(nφ))


⇒ Calculate “symmetrized” BCA (φ → |φ|) to get rid of all sin(φ)–
dependences due to polarized beam.
                                                                                     0.3




                                                                              cosφ
   AC




                                                                               AC
                                                                                                                 ±       ±
          0.2
                     HERMES
                                       ±         ±
                                      e p → e ’ γ X (Mx< 1.7 GeV)                                  HERMES       e p → e ’γ X
                                                                                     0.2
          0.1


            0                                                                        0.1


          -0.1                                                                         0
                       P1 cos φ
          -0.2         P1 + P2 cos φ + P3 cos 2φ + P4 cos 3φ
                                                                                     -0.1
                                                                                              -1      0     1        2        3   4
                 0     0.5        1        1.5       2    2.5     3
                                                                                                                             MX (GeV)
                                                           |φ| (rad)
   AC in exclusive bin: Expected                                              cos(φ)–Moments zero at higher
                             1,1
    cos(φ) dependence ⇒ Re Munp                                                        missing mass


                                       Frank Ellinghaus, JLab, May 2007
 hermes
                                                                                                                                      15
            Beam-Charge Asymmetry versus −t (PRD 2007)
 cosφ
                          ±          ±                                           0.6
                      e p/d → e ’ γ X           (Mx< 1.7 GeV)
  AC
                                                                                                Regge




                                                                         Acosφ
                                                                                            exponential




                                                                          C
         0.6          (in HERMES acceptance)
                                                                                 0.5          HERMES
                    proton
                    deuteron (preliminary)                                       0.4
         0.4
                                                Regge, D-term                    0.3

                                                Regge, no D-term
         0.2                                                                     0.2

                                                fac., D-term                     0.1
                                                fac., no D-term
           0
                                                                                   0

                                                                                 -0.1
         -0.2                                                                           0          0.1    0.2   0.3   0.4               0.5
                                                                                                                                   2
                                                                                                                            -t [GeV ]
                0   0.1       0.2   0.3   0.4    0.5   0.6   0.7   0.8

                                                       -t (GeV )
                                                                   2     Guzey/Teckentrup, PRD 74, 2006
 VGG                                                                     ⇒ Both in agreement
 ⇒ Regge+D-Term disfavored

tiny e−p sample (only ≈ 700 events) ⇒ Now ≈ 20 times more on disk!
        ⇒ t–dependence of BCA has high sensitivity to GPD models!

                                      Frank Ellinghaus, JLab, May 2007
  hermes
                                                                                                                                   16
      Utilize both charges for BSA: A closer look . . .
                                    2    ∗          ∗  2
                dσ |τDVCS| ∝ + |τBH| + (τDVCSτBH + τBHτDVCS)
                                                                              I


Fourier expansion (unpolarized p target):
                                            2
                       2          BH                BH
                                            X
              |τBH |       ∝     c0     +         cn       cos(nφ)
                                            n=1
                                              2
                       2         DV CS                 DV CS                      DV CS
                                              X
             |τDV CS | ∝        c0        +         cn         cos(nφ) + λ s1             sin(φ)
                                              n=1
                                               3                            2
                                                                                               !
                                        cI +           cI cos(nφ) + λ             sI sin(nφ)
                                               X                            X
                   I ∝ ±                 0              n                          n
                                               n=1                          n=1


                                                                     −
                                                                     →     ←−
                                      e−/e+                    1     N (φ)− N (φ)         ±sI sin φ
The approximation:                   ALU (φ)             =   <|Pb |> →(φ)+←(φ)
                                                                     −      −
                                                                                             1
                                                                                           |τBH |2
                                                                     N      N
is too simple . . .
                                       −
                                       →     ←−
            e−/e+                1     N (φ)− N (φ)                                     DV
                                                                             ±sI sin φ+s1 CS sin φ
           ALU (φ)         =   <|Pb |> →(φ)+←(φ)
                                       −      −
                                                                               1
                                                                  |τBH |2 +cDV CS +cDV CS cos φ±cI ±cI cos φ
                                       N      N                             0         1            0 1


                               Frank Ellinghaus, JLab, May 2007
  hermes
                                                                                                               17
              Using both beam charges for the BSA:
                                −
                                →     ←−
           e−/e+          1     N (φ)− N (φ)                                     DV
                                                                      ±sI sin φ+s1 CS sin φ
          ALU (φ)   =   <|Pb |> →(φ)+←(φ)
                                −      −
                                                                        1
                                                           |τBH |2 +cDV CS +cDV CS cos φ±cI ±cI cos φ
                                N      N                             0         1            0 1

sin φ amplitude of the “usual” BSA is not only sensitive to the
interference term, but gets contributions from the DVCS term
The “usual” BSA is complicated, it depends on the beam-charge
and on the size of the BCA
⇒ Disentangle contributions from the interference term and the
DVCS term by measuring two new asymmetries:
The “Interference” BSA:
                          −
                          −→      ←−
                                   −     ←−
                                          −      −
                                                 −→
                    1     N + (φ)+N −(φ)−N + (φ)−N −(φ)                              −sI sin φ
     AI (φ)
      LU      =   <|Pb |> − +
                          −→      ←−
                                   −     ←−
                                          −      −
                                                 −→
                                                                         |τBH |
                                                                                       1
                                                                                2 +cDV CS +cDV CS cos φ
                                    −      +
                          N (φ)+N (φ)+N (φ)+N −(φ)                                  0        1

The “DVCS” BSA:
                            −
                            −→    ←−
                                   −     ←−
                                          −     −
                                                −→
                      1     N (φ)−N (φ)−N (φ)+N −(φ)
                              +     −      +                                         DV
                                                                                    s1 CS sin φ
  ADV CS (φ)
   LU          =            −→
                    <|Pb |> − +   ←−
                                   −     ←−
                                          −     −
                                                −→                                           DV
                                                                           |τBH |2 +cDV CS +c1 CS cos φ
                            N (φ)+N −(φ)+N +(φ)+N −(φ)                               0

⇒ New asymmetries can disentangle (both charges needed) the
contributions from interference and DVCS2 term
                        Frank Ellinghaus, JLab, May 2007
 hermes
                                                                                                          18
                                                           More on H to come
                                                                                                                        Iron Shielding

                                                                                                                        Cryostat


    Recoil Detector and unpol.                                                                                          SC Coils

                                                                                                                        SciFi

    Targets (2006/2007)                                                                                                 Connector Plate

                                                                                                                                                        Photon

    • ensures exclusivity of events                                                                 C3 Collimator                                       Detector

                                                                                                                                                        SciFi
                                                                                                    Si Detector                                         Detector
                                                                                                    Cooling
                                                                                                                                                        Silicon
                – Semi–inclusive background                                                         Si Detector
                                                                                                    Connectors
                                                                                                                                                        Detector

                                                                                                                                                        Target Cell

                  5% ⇒     1%                                                                       Hybrid
                                                                                                                                                        Flange


                – Associated background 10%
                  ⇒ ≈ 1%
                                                                                                                                            0.1   0.2      0.3 m

               1                                  1                                        1
Fraction fi




                                   Fraction fi




                                                                            Fraction fi
              0.9                                0.9                                      0.9
              0.8                                0.8                                      0.8
              0.7                                0.7                                      0.7
              0.6                                0.6                                      0.6
              0.5                                0.5                                      0.5                                  ⇒ Essential at
              0.4                                0.4                                      0.4
              0.3                                0.3                                      0.3
                                                                                                                               larger −t values
              0.2                                0.2                                      0.2
              0.1                                0.1                                      0.1
               0                                  0                                        0
                                                                                                                               ⇒ Talk by
                    0   0.2                            0      5        10                       0   0.5             1
                              xB                             Q2 (GeV2)                              -tc (GeV2)                  R. Perez-Benito

                                                 Frank Ellinghaus, JLab, May 2007
        hermes
                                                                                                                                                                 19
                               What about the GDP E ?

Remember:                                   1
                           1
                  Jq = lim                      dx x [H q (x, ξ, t) + E q (x, ξ, t)]
                       t→0 2              −1




GPD E (on p target) is al-                                                         k
ways kinematically suppressed,                                                          φS
                                                                       k       q
except in:
                                                                   y               pγ
AU T : unpolarized beam,
       transversely pol. target                                            x                 φ   uli
                                                                  z



                   1         dσ ⇑ (φ,φs)−dσ ⇓ (φ,φs)
AU T (φ, φs) =   |PT |   ·   dσ ⇑ (φ,φs)+dσ ⇓ (φ,φs)

∝ Im[F2H − F1E] · sin (φ − φS ) cos φ + Im[F2H − F1ξ E] · cos (φ − φS ) sin φ


                             Frank Ellinghaus, JLab, May 2007
  hermes
                                                                                                       20
    DVCS TTSA compared to the Model Calculations!

Data taking with transverse Hydrogen target finished
≈ 10 million on tape, half the data (2002-2004) analyzed
                                            0.4




                                                   HERMES




                       sin(φ-φs)cos(φ)
                                          0.2 PRELIMINARY
                                            0.2
                                                                               e+ p⇑ → e+ γ X
                                              (in HERMES acceptance)            (Mx < 1.7 GeV)
                                           0  0




                                         -0.2
                                            -0.2




                           AUT           -0.4
                                            -0.4




                                         -0.6
                                            -0.6




                                             0.4
                                            -0.8




                                                   0            0.5        0          0.2          0
                                                                                                  0.4       5               10
                       cos(φ-φs)sin(φ)




                                          0.2
                                            0.2




                                           0  0




                                         -0.2
                                            -0.2




                                                                                                                Ju=0
                           AUT




                                                                                                                Ju=0.2
                                         -0.4
                                            -0.4




                                                                                                                Ju=0.4
                                         -0.6
                                            -0.6




                                                                                                         (hep-ph/0506264)
                                            -0.8




                                                   0            0.5        0          0.2          0
                                                                                                  0.4       5               10




                                                   0   0.25   0.5          0   0.1 0.2 0.3        0     2.5 5       7.5 10
                                                          -t (GeV )
                                                                       2                         xB             2
                                                                                                           Q (GeV )
                                                                                                                         2


  sin(φ−φs ) cos φ
AU T                 largely independent on all model parameters but Ju
(F.E., Nowak, Vinnikov, Ye, EPJ C46 (2006), hep-ph/0506264)

⇒ First model dependent extraction of Ju possible!

                                         Frank Ellinghaus, JLab, May 2007
  hermes
                                                                                                                                 21
           First Constraint on Angular Momentum !


         Ju
                    HERMES 2002-04 Preliminary                                        e+ p ⇑ → e+ γ X (MX<1.7 GeV)
              1                                                             sin ( φ- φS ) cos φ
                                                                           AUT                    = -0.149 ± 0.058(stat) ± 0.033(syst)
                                                                                                    2                     2         2
                                                                           <-t> = 0.12 GeV , <x> = 0.095, <Q > = 2.5 GeV

          0.8                                                                    GPD Model: LO/Regge/D-term=0
                                                                            [Goeke et al., Prog.Part.Nucl.Phys.47(2001),401]
                                                                           Code: VGG [Vanderhaeghen et al., priv. comm.]
                                         Ju +J
          0.6                                   d   /2.9 VGG
                                                          = 0
                                                              .42
                                                                    ± 0.2
                                                                          1 (e
                                                                               xp
          0.4                                                                      tot ) ±
                                                                                             0.06
                                                                                                        (bVGG
                                                                                                          v,s ∈[
                                                                                                                1,∞ ]
                                                                                                                      )
          0.2                             val                 2
                      Lattice QCDSF J q (µ 2= 4GeV )
                      stat. uncertainty only        [PRL92(2004),042002]

              0
               -1     -0.8      -0.6      -0.4          -0.2          -0         0.2                0.4         0.6           0.8        1
                                                                                                                                    Jd

⇒ First model dependent constraint on total quark angular
                     momentum Ju, Jd.


                             Frank Ellinghaus, JLab, May 2007
hermes
                                                                                                                                             22
         Second comparison to model calculations . . .
                                                                 0.3
                                                                                                     E=0
                                                                                                    u
                                                                                                   J =0




                                                    Asinϕ cosφ
                                                                 0.2            Regge             u
                                                                                                 J =0.2
                                                                                                  u
                                                                                                J =0.4




                                                     UT
                                                                 0.1                     HERMES prelim.

• On the other hand, the mo-                                         0

  dels (Guzey/Teckentrup, PRD 74,                                -0.1

  2006) suggest a small value for                                -0.2

  Ju under the assumption that                                   -0.3

  Jd = 0.                                                        -0.4

                                                                 -0.5
                                                                           0   0.1      0.2    0.3      0.4      0.5
                                                                                                              2
• The way to go: Constrain mo-                                      0.3
                                                                                                       -t [GeV ]


  dels for GPD H by BSA/BCA




                                                       Asinϕ cosφ
                                                                    0.2

  (first). Some model parameters




                                                        UT
                                                                    0.1         Exponential

  might be the same for the GPD                                       0

  E ...                                                             -0.1

  ⇒ Compare the remaining mo-                                       -0.2

  dels to the TTSA and learn                                        -0.3

  about the GPD E (Ju, Jd)                                          -0.4

                                                                    -0.5
                                                                           0   0.1      0.2    0.3      0.4      0.5
                                                                                                       -t [GeV2]


                 Frank Ellinghaus, JLab, May 2007
hermes
                                                                                                                       23
           Investigate the internal structure of Nuclei

                                                                               0.3




                                                                        φ
                                                                         LU
                                                                        Asin
           0.8                                                                                    →+
     ALU
                         →+
                         e Ne → e γ X
                                     +
                                             (Mx< 1.7 GeV)                                        e Ne → e+ γ X
                                                                               0.2
           0.6           HERMES PRELIMINARY                                                       HERMES PRELIMINARY
                              P1 + P2 sin φ + P3 sin 2φ                        0.1
           0.4
                                                                                 0
           0.2
                                                                               -0.1
            0
                                                                               -0.2
          -0.2
                                                                               -0.3
          -0.4
                         P1 = 0.00 ± 0.02 (stat)                               -0.4
          -0.6           P2 = -0.22 ± 0.03 (stat)
                                                                                      Asin φ   M x < 1.7 GeV   = -0.22 ± 0.03 (stat) ± 0.03 (sys)
                         P3 = 0.04 ± 0.03 (stat)                               -0.5
                                                                                       LU

          -0.8                                                                        <-t > = 0.13 GeV , <xB> = 0.09, <Q > = 2.2 GeV
                                                                                                               2                    2            2

                 <-t > = 0.13 GeV , <xB> = 0.09, <Q > = 2.2 GeV
                                 2                  2               2
                                                                               -0.6
            -1                                                                          -1        0       1        2      3     4        5   6
                  -3     -2     -1       0      1       2       3
                                                                                                                                        Mx (GeV)
                                                             φ (rad)

DVCS on Neon (hep-ex/0212019) triggered first calculations for
DVCS on Nuclei
⇒ Possibility (?) to explore nuclear structure in terms of quarks
and gluons, EMC effect, (anti-)shadowing, color transparency, ...

                                     Frank Ellinghaus, JLab, May 2007
 hermes
                                                                                                                                                     24
   Contributions from different processes from MC


      Process Fraction :
                           20
                             Ne
                                                     • Coherent Bether-Heitler contribution
1.2                                                    Incoherent Bethe-Heitler contribution
                                                       semi-inclusive π 0
  1                                                    resonances

0.8                                                  • DVCS not simulated

0.6
                                                     • Task: Find upper (lower) −t cut for
                                                       each target in order to compare the
0.4
                                                       BSA for the coherent (incoherent) pro-
                                                       duction at similar average values of −t ,
0.2
                                                       xB , and Q2

   0         0.05          0.1        0.15     0.2       – coherent: −t = 0.018 GeV2
                    -t (GeV )     2
                                                         – incoherent: −t = 0.2 GeV2


                                  Frank Ellinghaus, JLab, May 2007
hermes
                                                                                            25
  Average kinematic values for coherent production

           Target         −t     = 0.018            %coherent    Q2     xB
           Proton         −t     < 0.030                0       1.68   0.068
          Deuterium       −t     < 0.030               56%      1.70   0.066
           Helium-4       −t     < 0.030               68%      1.74   0.066
          Nitrogen        −t     < 0.043               82%      1.77   0.064
            Neon          −t     < 0.050               82%      1.73   0.064
           Krypton        −t     < 0.081               82%      1.63   0.060
            Xenon         −t     < 0.085               82%      1.60   0.059

• Q2 and xB very similar.

• Fraction of coherent production is                     82% for all but light tar-
  gets




                 Frank Ellinghaus, JLab, May 2007
 hermes
                                                                                 26
                                 A-dependence of the BSA

                                   HERMES PRELIMINARY
                      0.5              Coherent enriched                Incoherent enriched



            Asin Φ
                                       〈 -t’ 〉 = 0.018 GeV2             〈 -t’ 〉 = 0.2 GeV2

             LU
                        0


                      -0.5
                       0.4

                      0.2
            Asin 2Φ




                        0
             LU




                      -0.2

                      -0.4
                             1              10                102   1         10              102
                                             A                                 A




• No obvious A-dependence seen.
  Consistent with Guzey/Siddikov (J.Phys.G:Nucl.Part.Phys.32(2006))

• Asin 2φ is consistent with zero for all targets
   LU


                             Frank Ellinghaus, JLab, May 2007
 hermes
                                                                                                    27
                                                Ratio AA /Ap
                                                       LU  LU

                                 4         HERMES PRELIMINARY




               ALU, A / ALU, H
                                           Coherent enriched




            sin φ
                                                                          Fit to a constant : 1.75 ± 0.39

                                 2




            sin φ
                                 0                            〈 -t’ 〉 = 0.018 GeV2

               ALU, A / ALU, H
            sin φ                4
                                           Incoherent enriched
                                 2
            sin φ




                                 0
                                                             〈 -t’ 〉 = 0.2 GeV2
                                                               10     A                             102


• Coherent enriched: mean ratio deviates from unity by 2σ.
  – Consistent with prediction of R = 5/3 for Spin-0 and Spin-1/2
    targets (Kirchner/Mueller, Eur.Phys.J. 2003)
  – Calculation of R=1-1.1 for 4He (Liuti, Taneja, Phys.Rev.C 2005)
    consistent with measurement (large stat. error, calculations
    for heavier targets underway)
• Incoherent enriched: Consistent with unity as naively expected

                                 Frank Ellinghaus, JLab, May 2007
 hermes
                                                                                                            28
                                                   Ratio AA /Ap
                                                          LU  LU

                 Nucl proton            2
              ALU /ALU , t=-0.02 GeV , xBj=0.064

                      HERMES preliminary
                      Without mesons
                      With mesons, Model A
                      With mesons, Model B
          3




          2




          1




          1                        10                  100 A


 Consistent with two predicti-
 ons by Guzey/Siddikov, one dis-
                                 Consistent with predictions by
 favored (J.Phys.G, 2006)
                                 Guzey/Strikman (Phys.Rev.C, 2003)

⇒ Promising, more data needed . . .

                                    Frank Ellinghaus, JLab, May 2007
 hermes
                                                                       29
                     Summary and Outlook

• HERA/HERMES: End of data taking 7/2/2007:
  Goal: “map out” GPD H u via DVCS Beam-Spin and Beam-Charge
  Asymmetries

• Contributions form the Interference term and the DVCS2 term
  can be disentangeled by new asymmetries involving both beam
  charges

• First model dependent constraint on the total angular momen-
  tum of u-quarks (Ju) and d-quarks (Jd) in the nucleon.

• DVCS on Nuclei looks promising

• Final remark: Orbital angular momentum sum rule needs t → 0
  Hermes measurements on GPD E at “small” t will not be precise
  JLab@12 will yield precision measurements at “large” t ⇒ EIC

               Frank Ellinghaus, JLab, May 2007
 hermes
                                                             30
 The GPD H, Long. Target–Spin Asymmetry (LTSA)
                                                                     −
                                                                     ←     −
                                                                           →
                                                                1    N (φ)− N (φ)
                                  AUL(φ) =                   <|PT |> ←(φ)+→(φ)
                                                                     −     −        ∝ sin φ × ImH1
                                                                     N      N
           0.6
     AUL
                        HERMES PRELIMINARY                                                0.6




                                                                                    AUL
                          e p → e γ X (Mx<1.7 GeV)
                              +          +                                                           HERMES PRELIMINARY 99,00
                                                                                                         e d → e γ X (Mx<1.7 GeV)
                                                                                                             +          +
                                  (in HERMES acceptance)
           0.4                                                                                                   (in HERMES acceptance)
                                                                                          0.4
                                             A = s0 + s1 sin φ + s2 sin 2φ
                                                                                                             A = s0 + s1 sin φ + s2 sin 2φ
           0.2
                                                                                          0.2


            0
                                                                                           0


                        χ / ndf: 8.5/ 7
                          2
         -0.2
                                                                                                       χ / ndf: 6.2/ 7
                                                                                                         2
                        s0: -0.009 ± 0.024 (stat.)                                    -0.2
                        s1: -0.071 ± 0.034 (stat.)                                                     s0: 0.030 ± 0.017 (stat.)
                        s2: -0.113 ± 0.034 (stat.)                                                     s1: -0.036 ± 0.024 (stat.)
         -0.4                                                                                          s2: -0.039 ± 0.023 (stat.)
                      <-t>=0.12 GeV , <xB>=0.10, <Q >=2.5 GeV
                                         2               2           2
                                                                                      -0.4
                                                                                                     <-t>=0.13 GeV , <xB>=0.10, <Q >=2.5 GeV
                                                                                                                        2           2            2

                 -3     -2          -1         0        1        2           3
                                                               φ [rad]                          -3     -2          -1       0       1        2       3
                                                                                                                                             φ [rad]
    →
AUL(− ) in exclusive bin:
    p                                                                                    →
                                                                                         −
                                                                                     AUL( d ) in exclusive bin:
Expected sin(φ) dep. ⇒ GPD H,                                                        ⇒ consistent with zero
Unexpected sin(2φ) dependence

                                         Frank Ellinghaus, JLab, May 2007
hermes
                                                                                                                                                         31
  The GPD H, Long. Target–Spin Asymmetry (LTSA)




• No effect seen from 40% coherent contribution in first bin
• Difference at higher −t
  ⇒ Different asymmetry on the neutron when comp. to proton
• Asin 2φ ⇒ Difference due to missing qGq twist-3 in the models?
   UL
   sin 2φ
  AU L ⇒ Difference due to large sin 2φ (while sin φ is small) in π 0
  background (CLAS, hep–ex/0605012)?

                Frank Ellinghaus, JLab, May 2007
 hermes
                                                                   32

				
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