Quark Orbital Angular Momentum

35 Pages·2015·6 MB·English

by  Matthias Burkardt

Quark Orbital Angular Momentum
Matthias Burkardt
NMSU
May 29, 2015
Outline 2
3D imaging of the nucleon
(cid:44)→ Single-Spin Asymmetries (SSAs)
quark-gluon correlations → color force
angular momentum decompositions (Jaffe v. Ji)
(cid:44)→ change in OAM due to FSI
Summary
Deeply Virtual Compton Scattering (DVCS) 3
Compton scattering
form factor
electron hits nucleon, nucleon
electron hits nucleon & remains intact & photon gets
nucleon remains intact emitted
study amplitude that nucleon study both energy & q2
remains intact as function of dependence
momentum transfer →F(q2) (cid:44)→ additional information about
F(q2)=(cid:82) dxGPD(x,q2) momentum fraction x of
active quark
(cid:44)→ GPDs provide momentum
disected form factors (cid:44)→ generalized parton
distributions GPD(x,q2)
Physics of GPDs: 3D Imaging of the Nucleon 4
MB, PRD62, 071503 (2000)
FT
form factors:←→ρ((cid:126)r)
GPDs(x,0,−∆2): form factor for quarks with momentum fractionx
⊥
(cid:44)→ suitable FT of GPDs should provide spatial distribution of quarks
with momentum fraction x
Impact Parameter Dependent Quark Distributions
(cid:90) d2∆
q(x,b⊥)= (2π)⊥2GPD(x,0,−∆2⊥)e−ib⊥·∆⊥
q(x,b )= parton distribution as a function of the separation b from
⊥ ⊥
(cid:80)
the transverse center of momentum R ≡ r x
⊥ i∈q,g ⊥,i i
probabilistic interpretation!
no relativistic corrections: Galilean subgroup! (MB,2000)
(cid:44)→ corollary: interpretation of 2d-FT of F (Q2) as charge density in
1
transverse plane also free from relativistic corrections
(MB,2003;G.A.Miller, 2007)
Impact parameter dependent quark distributions 5
unpolarized proton
q(x,b⊥)=(cid:82) d(22π∆)⊥2H(x,0,−∆2⊥)e−ib⊥·∆⊥
F (−∆2)=(cid:82) dxH(x,0,−∆2)
1 ⊥ ⊥
x= momentum fraction of the quark
b relative to ⊥ center of momentum
⊥
small x: large ’meson cloud’
larger x: compact ’valence core’
x→1: active quark becomes center of
momentum
(cid:44)→ (cid:126)b →0 (narrow distribution) for x→1
⊥
Impact parameter dependent quark distributions 6
proton polarized in +xˆ direction
no axial symmetry!
(cid:90) d2∆
q(x,b⊥)= (2π)⊥2Hq(x,0,−∆2⊥)e−ib⊥·∆⊥
1 ∂ (cid:90) d2∆
−2M ∂b (2π)⊥2Eq(x,0,−∆2⊥)e−ib⊥·∆⊥
y
Physics: relevant density in DIS is
j+ ≡j0+j3 and left-right asymmetry
from j3
intuitive explanation
moving Dirac particle with
anomalous magnetic moment has
electric dipole moment ⊥ to p(cid:126) and ⊥
magnetic moment
(cid:44)→ γ∗ ’sees’ flavor dipole moment of
oncoming nucleon
Impact parameter dependent quark distributions 6
proton polarized in +xˆ direction
no axial symmetry!
(cid:90) d2∆
q(x,b⊥)= (2π)⊥2Hq(x,0,−∆2⊥)e−ib⊥·∆⊥
1 ∂ (cid:90) d2∆
−2M ∂b (2π)⊥2Eq(x,0,−∆2⊥)e−ib⊥·∆⊥
y
Physics: relevant density in DIS is
j+ ≡j0+j3 and left-right asymmetry
from j3
Impact parameter dependent quark distributions 7
proton polarized in +xˆ direction
(cid:90) d2∆
q(x,b⊥)= (2π)⊥2Hq(x,0,−∆2⊥)e−ib⊥·∆⊥
1 ∂ (cid:90) d2∆
−2M ∂b (2π)⊥2Eq(x,0,−∆2⊥)e−ib⊥·∆⊥
y
sign & magnitude of the average shift
model-independently related to p/n
anomalous magnetic moments:
(cid:104)bq(cid:105) ≡(cid:82)dx(cid:82)d2b q(x,b )b
y ⊥ ⊥ y
= 1 (cid:82) dxE (x,0,0)= κq
2M q 2M
Impact parameter dependent quark distributions 7
sign & magnitude of the average shift
model-independently related to p/n
anomalous magnetic moments:
(cid:104)bq(cid:105) ≡(cid:82)dx(cid:82)d2b q(x,b )b
y ⊥ ⊥ y
= 1 (cid:82) dxE (x,0,0)= κq
2M q 2M
κp =1.913= 2κp − 1κp+...
3 u 3 d
u-quarks: κp =2κ +κ =1.673
u p n
(cid:44)→ shift in +yˆdirection
d-quarks: κp =2κ +κ =−2.033
u n p
(cid:44)→ shift in −yˆdirection
(cid:104)bq(cid:105)=O(±0.2fm) !!!!
y
GPD ←→ Single Spin Asymmetries (SSA) 8
example: γp→πX
u,d distributions in ⊥ polarized proton have left-right asymmetry
in ⊥ position space (T-even!); sign “determined” by κ & κ
u d
attractive final state interaction (FSI) deflects active quark
towards the center of momentum
(cid:44)→ FSI translates position space distortion (before the quark is
knocked out) in +yˆ-direction into momentum asymmetry that
favors −yˆdirection→ chromodynamic lensing
⇒ κ ,κ ←→ sign of SSA!!!!!!!! (MB,2004)
p n
confirmed by Hermes & Compass data