1. HERMESでのHard Exclusive生成過程による 核子内クォーク全角運動量についての研究
Generalized Parton Distribution
GPD and Jq
Target Transverse Spin Asymmetry
Deeply Virtual Compton Scattering
Exclusive ρ production
HERMES results
Summary
宮地義之(東工大理)，今津義充，小林知洋，長谷川大樹，柴田利明
他 HERMES collaboration

2. Generalized Parton Distributionq P P’ p p’
Form Factor: F(t), G(t)
Elastic scattering t q P p p’
Deep Inelastic Scattering
Parton distribution: q(x), Δq(x), δq(x)
𝑄 2 =− 𝑞 2 1 GeV 2
Hard Exclusive Production: q q' P P’ p p’ t
𝑒𝑁𝑒′𝑁′ ,,,...
𝑄 2 =− 𝑞 2 1 GeV 2
Generalized Parton Distribution:
𝐻,𝐸, 𝐻  , 𝐸 

3. Generalized Parton Distribution
Forward Limit: ξ→0, t→0
𝐻 𝑞 𝑥,0,0=𝑞𝑥 𝐻  𝑞 𝑥,0,0=𝑞𝑥
Generalized Paton Distributions
Vector
𝐻𝑥,,𝑡
Tensor
𝐸𝑥,,𝑡
Form Factors:
Axial vector
𝐻  𝑥,,𝑡
−1 1 𝑑𝑥 𝐻 𝑞 𝑥,,𝑡= 𝐹 1 𝑞 𝑡 −1 1 𝑑𝑥 𝐸 𝑞 𝑥,,𝑡= 𝐹 2 𝑞 𝑡 −1 1 𝑑𝑥 𝐻  𝑞 𝑥,,𝑡= 𝑔 𝐴 𝑞 𝑡 −1 1 𝑑𝑥 𝐸  𝑞 𝑥,,𝑡= ℎ 𝐴 𝑞 𝑡
Dirac
Pauli
Axial vector
Pseudoscala r
Pseudo scalar
𝐸  𝑥,,𝑡
for quarks and gluon
GPD and total angular momentum of parton
𝐽 q,g = 1 2 −1 1 𝑑𝑥 𝑥 𝐻 q,g 𝑥,,𝑡0 𝐸 q,g 𝑥,,𝑡0

4. Hard Exclusive Production and GPD
Deeply Virtual Compton Scattering: (DVCS) q q' P P’ t
𝑒𝑁𝑒′𝑁′
Involved GPDs:
clean reaction
𝐻,𝐸, 𝐻  , 𝐸 
Hard exclusive meson production:
𝑒𝑁𝑒′𝑁′ ,,... q q' P P’ t
vector meson:
pseudo-scalar meson:
𝐻,𝐸
𝐻  , 𝐸 
Factorization for longitudinal photons only
Meson Amplitude should be taken care
Quark flavor sensitivity

5. HERMES spectrometer q q' ex.) DVCS P e+,- Exclusive reaction:
via missing mass
𝑀 𝑋 2 = 𝑞𝑃−𝑞′ 2
No recoil detection
Exclusive production events
were selected with a Mx cut

6. Target Spin Asymmetry: AUT
Transversely hydrogen gas target
2002 – 2005
analysis are based on data.
<|PT|> ~ 80%
Two azimuthal angles:
Angle of the target spin direction
Between the lepton and photon (meson) planes
𝐴 𝑈𝑇 ,  𝑆 = 1 𝑆 ⊥ 𝑑,  𝑆 −𝑑,  𝑆  𝑑,  𝑆 𝑑,  𝑆 

7. DVCS Target Spin Asymmetry
𝐴 𝑈𝑇 ,  𝑆 ∝ 𝐴 𝑈𝑇 sin−  𝑆 cos sin−  𝑆 cos 𝐴 𝑈𝑇 cos−  𝑆 cos cos−  𝑆 cos
~− 𝑡 4M 2 ⋅ 𝐹 2 𝐻− 𝐹 1 𝐸 Jq
~− 𝑡 4M 2 ⋅ 𝐹 2 𝐻  − 𝐹 1  𝐸 

8. Exclusive ρ Target Spin Asymmetry
𝐴 𝑈𝑇 sin −  𝑆  ~𝐸⋅𝐻
ex.) Goeke et. al., Prog. Part. Nucl. Phys. 47 (2001) 401
access to Jq
(hep-ph/ )
Including 2005 data doubles the total statistic of DVCS and ρ production.

9. Summary Generalized Parton Distribution Connect PDFs and Form factors
Access to the total angular moment
Single Spin Asymmetry in Hard Exclusive Production
DVCS is clean process to access GPD
Transverse Target Spin Asymmetry is sensitive to Jq
HERMES measured
non-zero TSA in DVCS and Exclusive ρ production
Data taken in 2005 doubles the statistic.