Generalized Form Factors, Generalized Patron Distributions, and Spin Contents of the Nucleon
The Spin Structure of the Nucleon - University of VirginiaThe Spin Structure of the Nucleon EE.C....
Transcript of The Spin Structure of the Nucleon - University of VirginiaThe Spin Structure of the Nucleon EE.C....
The Spin Structure of the NucleonThe Spin Structure of the Nucleon
11SFU, VanCouver, March 2007SFU, VanCouver, March 2007EE.C. Aschenauer.C. Aschenauer
Experimental PrerequisitesExperimental Prerequisites
longitudinally polarized lepton beamlongitudinally polarized lepton beam
longitudinally polarized nuclear targetlongitudinally polarized nuclear target
large geometrical acceptancelarge geometrical acceptancesmall anglessmall angleslimited by synchrotron radiationlimited by synchrotron radiation
big anglesbig angles
(E’, p’)
e(E, p)
(E’, p’)
e(E, p)
*γ
(E’, p’)
e
q
(E, p)
*γ
(E’, p’)
e
q
(E, p)
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big anglesbig angleslimited by moneylimited by money
good particle identificationgood particle identification
So far only So far only “fixed target”“fixed target” experiments atexperiments at::
*γ
e
q*γ
ud
u
e
q
N
u
*γ
ud
q
Nu
*γ
π+
ud
q
π
p
KN
and polarized ppand polarized pp--collider atcollider at
The The contemporarycontemporary experimentsexperiments
GEM MWPC&Scifi
Target
Trigger Hodoscopes
SM1
ECal1/2 & HCal1/2
−Filterµ
SM2
RICH
MWPC
Two highTwo high--resolution resolution 4 GeV spectrometers4 GeV spectrometers
Hall A
Large acceptance spect. Large acceptance spect. electron/photon beamselectron/photon beams
Hall B
Beam: ≤6 GeV eBeam: ≤6 GeV e--; 85% polarization; 85% polarization
STARSTAR
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Beam: 27.5 GeV eBeam: 27.5 GeV e±±; <50>% polarization; <50>% polarizationTarget: (un)Target: (un)--polarized gas targets; <85%> polarizationpolarized gas targets; <85%> polarization
SiliconScifi
beamStraws
Drift chamber
MicroMegas
Beam: 160 GeV Beam: 160 GeV µµµµµµµµ; 75% polarization; 75% polarizationTarget: Target: 66LiD; 50% polarizationLiD; 50% polarization
7 GeV spectrometer, 7 GeV spectrometer, 1.8 GeV spectrometer, 1.8 GeV spectrometer,
large installation experimentslarge installation experiments
Hall CBeam: ≤6 GeV eBeam: ≤6 GeV e--; 85% polarization; 85% polarizationTarget: polarized targets Target: polarized targets 33He, He, 66LiD, NHLiD, NH3 3
Beams: 250 GeV pp; <60>% polarizationBeams: 250 GeV pp; <60>% polarizationLumi: 1.2 10Lumi: 1.2 103131cmcm--22ss--11
HERA @ DESYHERA @ DESYHERMES @ HERAHERMES @ HERA
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HERA: eHERA: e++/e/e-- (27GeV) (27GeV) -- proton (920 GeV) colliderproton (920 GeV) collider
The HERMES SpectrometerThe HERMES Spectrometer
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Internal Gas Target: He , H , D , H unpol: H2,D2,He,N2,Ne,Kr,Xe
The HERMES polarized gas targetThe HERMES polarized gas target
BRPABS
TGA
1st sexp. magn. syst.
collimator
discharge tube
SFTMFT
2nd sexp. magn. syst.
SFT / WFTQMS
chopper
storage cellSFT
MFT
QMS
choppersexp. magn. syst.
beam blockernozzle
Atomic Beam SourceAtomic Beam Source Breit Rabi PolarimeterBreit Rabi Polarimeter
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HERA beam
sample tubeextension tube
beam shutter
SFT
injection tube
ADVANTAGES:ADVANTAGES:no dilution; all the material is polarizedno dilution; all the material is polarizedno radiation damage no radiation damage rapid inversion of polarization direction every 90s in less than 0.5srapid inversion of polarization direction every 90s in less than 0.5s
The HERA PolarimetersThe HERA Polarimeters
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HeraHera--e selfe self--polarizing due to Sokolovpolarizing due to Sokolov--Ternov effectTernov effect
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The HERMES SpectrometerThe HERMES Spectrometer
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Kinematic Range: 0.02 < x < 0.8 at Q2 > 1 GeV2 and W > 2 GeV
Reconstruction:∆∆∆∆p/p < 2%, ∆θ∆θ∆θ∆θ < 1 mrad
Particle ID: TRD, Preshower, Calorimeter
֏1997: Cherenkov, 1998֏: RICH + Muon-ID
Internal Gas Target: unpol: H2,D2,He,N,Ne,Kr, Xe He , H , D , H
hadron/positron separationhadron/positron separationcombining signals from: combining signals from: TRD, calorimeter, preshowerTRD, calorimeter, preshower
hadron separationhadron separationDual radiator RICH forDual radiator RICH for ππππππππ, K, pK, p
Which Hadron (Which Hadron (ππππππππ,K,p) is Which,K,p) is Which
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Aerogel; n=1.03
C4F10; n=1.0014
ππππ
K
News on the spin structure of the nucleonNews on the spin structure of the nucleon
Naïve parton modelNaïve parton model
43∆ =∆ =∆ =∆ =vu 1
3∆ = −∆ = −∆ = −∆ = −vd Unpolarised structure fct.Unpolarised structure fct.
1010SFU, VanCouver, March 2007SFU, VanCouver, March 2007EE.C. Aschenauer.C. Aschenauer
1 1( )
2 2 v vu d++++ ∆∆∆∆∆∆∆∆====1 1( )
2 2 v gsv qLd LGqu= + + + += + + + += + + + += + + + +∆∆∆∆∆∆∆∆ ++++∆∆∆∆∆∆∆∆
∆Σ∆Σ∆Σ∆Σ
1 1( )
2 2 v svu q Gd∆∆∆∆ ∆∆∆∆+ ++ ++ ++ +∆∆∆∆ ++++ ∆∆∆∆====
( )∆ + ∆ + ∆ + ∆ + ∆ + ∆∆ + ∆ + ∆ + ∆ + ∆ + ∆∆ + ∆ + ∆ + ∆ + ∆ + ∆∆ + ∆ + ∆ + ∆ + ∆ + ∆s su d u d s s
43∆ =∆ =∆ =∆ =vu 1
3∆ = −∆ = −∆ = −∆ = −vdBUTBUT
1989 EMC measured1989 EMC measuredΣΣΣΣΣΣΣΣ = 0.120 0.094 0.138= 0.120 0.094 0.138± ±
Spin PuzzleSpin Puzzle
Unpolarised structure fct.Unpolarised structure fct.
Gluons are important !Gluons are important !
Sea quarksSea quarks ∆∆∆∆∆∆∆∆qq ss
∆∆∆∆∆∆∆∆GG Full description of JFull description of Jqq and Jand Jggneedsneeds
orbital angular momentumorbital angular momentum
−1Lg ====1f ====
{{{{ }}}}112 ( ) ( ) ( ) ( )1 1 5 1 52
Tw x f x S g x h x S nCorr L T
++++Φ = + γ + γ γΦ = + γ + γ γΦ = + γ + γ γΦ = + γ + γ γ
The quark content of the nucleonThe quark content of the nucleon
1111SFU, VanCouver, March 2007SFU, VanCouver, March 2007EE.C. Aschenauer.C. Aschenauer
HERA F2
0
1
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5
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103
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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-5x=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
How to measure Quark PolarizationsHow to measure Quark Polarizations
3/ 2 (~ )q xσσσσ −−−−
* 3/ 2NSSγγγγ + =+ =+ =+ =rrrr rrrr
N qSS ==== −−−−rrrr rrrr
1/ 2 (~ )q xσσσσ ++++
* 1/ 2NSSγγγγ + =+ =+ =+ =rrrr rrrr
N qSS ====rrrr rrrr
Virtual photon Virtual photon γγγγγγγγ** can only couple to quarks of opposite helicitycan only couple to quarks of opposite helicitySelect Select qq++(x)(x) or or qq--(x)(x) by changing the orientation of by changing the orientation of
1212SFU, VanCouver, March 2007SFU, VanCouver, March 2007EE.C. Aschenauer.C. Aschenauer
Select Select qq++(x)(x) or or qq--(x)(x) by changing the orientation of by changing the orientation of target nucleon spin or helicity of incident lepton beamtarget nucleon spin or helicity of incident lepton beam
', ','||
', '
1 e h e he h
B T e h e h
N L N LA
P P N L N L
→ → → →→ → → →→ → → →→ → → →⇐⇐⇐ ⇐ ⇒ ⇒⇒ ⇒⇒ ⇒⇒ ⇒ ⇐⇐⇐ ⇐
→ → → →→ → → →→ → → →→ → → →⇐⇐⇐ ⇐ ⇒ ⇒⇒ ⇒⇒ ⇒⇒ ⇒ ⇐⇐⇐ ⇐
−−−−====
++++
', ',', 1 / 2 3 / 2
|| ', ',1/ 2 3 / 2
~e h e h
e he h e hA
σ − σσ − σσ − σσ − σσ + σσ + σσ + σσ + σ
Asymmetry definition:Asymmetry definition:qq q−−−−++++∆ = −∆ = −∆ = −∆ = −
inclusiveinclusive DIS: only DIS: only e’e’ info usedinfo used semisemi--inclusiveinclusive DIS: DIS: e’+he’+h info usedinfo used
World data on inclusive DISWorld data on inclusive DIS
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HERMES (⟨Q2⟩< 1 GeV2)HERMES (⟨Q2⟩> 1 GeV2)E 143E 155
SMCSMC (low x - low Q 2)
CLAS
COMPASSCOMPASS (low x - low Q 2)A
1d
x
⟨Q2 ⟩(
GeV
2 )
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New data from COMPASS, New data from COMPASS, HERMES & JLab very preciseHERMES & JLab very precisehigh xhigh x--behaviour consistent withbehaviour consistent withAA��������1 with x1 with x��������11AA11
d d consistent with zero consistent with zero for x < 0.05for x < 0.05
ProtonProton DeuteriumDeuterium(Hall(Hall--A)A)
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HERMES (⟨Q2⟩< 1 GeV2)HERMES (⟨Q2⟩> 1 GeV2)E 143E 155
SMCSMC (low x - low Q 2)
CLAS
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1d
x
⟨Q2 ⟩(
GeV
2 )
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CLAS PLB 641, 11 (2006)AA11
nn from from 33HeHe
COMPASS PRD75(2007)012007COMPASS PRD75(2007)012007
World data on inclusive DISWorld data on inclusive DIS
1 1 1
1 3( )(1 )
2 2d p n
Dg g g w= + −= + −= + −= + −Combine p and d to get n:Combine p and d to get n:
or or 33HeHe3
1 1 12He np
pnP Pg g g++++����
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SMCSMC (low x - low Q 2)
CLAS
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1d
x
⟨Q2 ⟩(
GeV
2 )
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HERMES (Q2 < 1 GeV2)HERMES (Q2 > 1 GeV2)SMC (low x - low Q 2)SMCE 143E 155
xg1p
x
xg1d
COMPASSCOMPASS (low x - low Q 2)
41 22 2 21 / 2 ( )
22 2( , ) (( , ) , )1
2
2/ 4 8 2
dunpolQ y
y yg x Q g x Qx
dA Q
y dx Qγγγγ
γ παγ παγ παγ πα
σσσσ = += += += +
− −− −− −− −
����
-0.1
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xg1n from p,d:HERMES (Q2< 1 GeV2)HERMES (Q2> 1 GeV2)E155E143SMC
xg1n
E154E142JLABHERMES
xg1n from 3He:
xg1n
x
⟨Q2 ⟩ (
GeV
2 )
1
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10-2
10-1
1
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1 1 12 pnP Pg g g++++����
What can we learn on the PDFsWhat can we learn on the PDFs
21 ~ [ Ge C GCg ΣΣΣΣ ∆∆∆∆ + ∆+ ∆+ ∆+ ∆ΣΣΣΣ⊗ ⊗⊗ ⊗⊗ ⊗⊗ ⊗ ∆∆∆∆∆ +∆ +∆ +∆ +
LO-QCD2 ,1
2p nNSe q∆Σ∆Σ∆Σ∆Σ = + ∆= + ∆= + ∆= + ∆
, ]p nNS NSC q∆ ⊗ ∆∆ ⊗ ∆∆ ⊗ ∆∆ ⊗ ∆
Compass: hepCompass: hep--ex/0609038ex/0609038Hermes: hepHermes: hep--ex/0609039ex/0609039
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HERMES (Q2 < 1 GeV2)HERMES (Q2 > 1 GeV2)SMC (low x - low Q 2)SMCE 143E 155
xg1p
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COMPASSCOMPASS (low x - low Q 2)
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xg1n
E154E142JLABHERMES
xg1n from 3He:
xg1n
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⟨Q2 ⟩ (
GeV
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HERMES: IntegralsHERMES: Integrals
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x
∫ x g
1dx
0.
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pdnNS
Q2=5 GeV2 Saturation in deuteron integral is assumedSaturation in deuteron integral is assumeduse only deuteriumuse only deuterium
80191 1
[ ]3 4(1 )2
d
NSS
D
CC w
a a= − ∆= − ∆= − ∆= − ∆∆∆∆∆ −−−−
ΓΓΓΓ
From hyperon beta decayFrom hyperon beta decayaa88=0.586=0.586±±0.0310.031From neutron beta decayFrom neutron beta decay
aa33=1.269=1.269±±0.0030.0031
0.9
10.0210.0436 0.0012( ) 0.0018( ) 0.0008( ) 0.0026( )ddxg stat syst par evol= ± ± ± ±= ± ± ± ±= ± ± ± ±= ± ± ± ±∫∫∫∫
1515SFU, VanCouver, March 2007SFU, VanCouver, March 2007EE.C. Aschenauer.C. Aschenauer
-0.02
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∫ x g
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pdnNS
Q2=5 GeV2
QQ22=5 GeV=5 GeV22, NNLO in MS scheme, NNLO in MS scheme
80 3
1[2 3 ]
6au u aa∆ + ∆ = + +∆ + ∆ = + +∆ + ∆ = + +∆ + ∆ = + +
80 3
1[2 3 ]
6ad d aa∆ + ∆ = + −∆ + ∆ = + −∆ + ∆ = + −∆ + ∆ = + −
80
1[ ]
3as s a∆ + ∆ = −∆ + ∆ = −∆ + ∆ = −∆ + ∆ = −
COMPASS: COMPASS:
0.08 0.01 0.02s s = − ± ±= − ± ±= − ± ±= − ± ±∆ + ∆∆ + ∆∆ + ∆∆ + ∆0 0.33 0.03 0.05a = ± ±= ± ±= ± ±= ± ±
CLAS: CLAS: ∆∆∆∆∆∆∆∆qq
1616SFU, VanCouver, March 2007SFU, VanCouver, March 2007EE.C. Aschenauer.C. Aschenauer
Using:Using:
Polarised quark distributionsPolarised quark distributionsCorrelation between detected hadron and struck Correlation between detected hadron and struck qqff
“Flavor “Flavor –– Separation”Separation”
Inclusive DIS:Inclusive DIS:
SemiSemi--inclusive DIS:inclusive DIS:
( )u d u d s s∆Σ = ∆ + ∆ + ∆ + ∆ + ∆ + ∆∆Σ = ∆ + ∆ + ∆ + ∆ + ∆ + ∆∆Σ = ∆ + ∆ + ∆ + ∆ + ∆ + ∆∆Σ = ∆ + ∆ + ∆ + ∆ + ∆ + ∆
( , , , , , )u d u d s s∆ ∆ ∆ ∆ ∆ ∆∆ ∆ ∆ ∆ ∆ ∆∆ ∆ ∆ ∆ ∆ ∆∆ ∆ ∆ ∆ ∆ ∆In LOIn LO--QCD:QCD:
2 2 2 2( , ) ( , ) ( , )hh h e q x Q D z Q q x Qσ −σ −σ −σ − ∆∆∆∆σσσσ
∑∑∑∑
scattered lepton
u_
d_
u_
u_
u_
ρ−
u_
π0
π0
π+−π
π0
u
ud
u
d
u
ptarget nucleon
incoming lepton
String Breaking
virtual photon
uu
u
uud
ud
ud
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2 1/ 2 3 / 21 2 2
1/ 2 3 /2
'2
2 ''
2( , )( , , ) ~
'( , )
( , )
( , )( , )
( , )
h hqh
hq
qh
q qh q
e q x QA x Q z C
e
D z Q
Dq x Q
q Qq Q xzx Q
σ −σ −σ −σ −====
∆∆∆∆σσσσσ + σσ + σσ + σσ + σ ∑∑∑∑ ∑∑∑∑
COMPASS: Valence PDFsCOMPASS: Valence PDFs
/( ) ( )
( ) ( )
h h h h
h h h h
A
→ → → →→ → → →→ → → →→ → → →⇐ ⇐⇐ ⇐⇐ ⇐⇐ ⇐ ⇒ ⇒⇒ ⇒⇒ ⇒⇒ ⇒
+ − + −+ − + −+ − + −+ − + −
→ → → →→ → → →→ → → →→ → → →⇐ ⇐⇐ ⇐⇐ ⇐⇐ ⇐ ⇒ ⇒⇒ ⇒⇒ ⇒⇒ ⇒
+ − + −+ − + −+ − + −+ − + −
+ −+ −+ −+ − σ − σ − σ − σσ − σ − σ − σσ − σ − σ − σσ − σ − σ − σ====
σ − σ + σ − σσ − σ + σ − σσ − σ + σ − σσ − σ + σ − σ
( ) ( )( )
( ) ( )K K v v
d dv v
u x d xA x A
u x d xπ ππ ππ ππ π+ − + −+ − + −+ − + −+ − + −− −− −− −− − ∆ + ∆∆ + ∆∆ + ∆∆ + ∆
= == == == =++++ x
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PRELIMINARY
Deuteron data 2002-2004
h+ - h-A
1 1( )N a aΓ = +Γ = +Γ = +Γ = +
For LO:For LO:
Assuming:Assuming:x
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From diff asymmetry d
1From Inclusive gDNS fit (prediction)
)vd∆+vu∆x(
COMPASS
PRELIMINARY
2=10 GeV2SIDIS+DIS, Q
x -210 -110 1
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s∆s=∆=d∆=u∆
d∆=-u∆
unm
easu
red
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0.006∫ 0.05±0.07±)dx=0.40vd∆+vu∆(
∫x
0.7)dxvd∆+vu∆(
COMPASSPRELIMINARY
2=10 GeV2SIDIS+DIS, Q
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1 0 8
1 1( )
9 4N a aΓ = +Γ = +Γ = +Γ = +
1
0( ( ) ( ))v v vu x d x dxΓ = ∆ + ∆Γ = ∆ + ∆Γ = ∆ + ∆Γ = ∆ + ∆∫∫∫∫
1 8
8
1 13
2 121
( ) ( )2
Nv
v
u d a
s s a
∆ + ∆ = Γ − Γ +∆ + ∆ = Γ − Γ +∆ + ∆ = Γ − Γ +∆ + ∆ = Γ − Γ +
= ∆ + ∆ + − Γ= ∆ + ∆ + − Γ= ∆ + ∆ + − Γ= ∆ + ∆ + − Γ x -210 -110 1
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s∆s=∆=d∆=u∆
d∆=-u∆
unm
easu
red
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0.006∫ 0.05±0.07±)dx=0.40vd∆+vu∆(
∫x
0.7)dxvd∆+vu∆(
COMPASSPRELIMINARY
2=10 GeV2SIDIS+DIS, Q
ΓΓΓΓΓΓΓΓvv is 2.5is 2.5σσσσσσσσstatstat away from flavor away from flavor symmetric sea scenariosymmetric sea scenario
Polarised quark distributionsPolarised quark distributions
Correlation between detected hadron and struck Correlation between detected hadron and struck qqff“Flavor “Flavor –– Separation”Separation”
Inclusive DIS:Inclusive DIS:
SemiSemi--inclusive DIS:inclusive DIS:
( )u d u d s s∆Σ = ∆ + ∆ + ∆ + ∆ + ∆ + ∆∆Σ = ∆ + ∆ + ∆ + ∆ + ∆ + ∆∆Σ = ∆ + ∆ + ∆ + ∆ + ∆ + ∆∆Σ = ∆ + ∆ + ∆ + ∆ + ∆ + ∆
( , , , , , )u d u d s s∆ ∆ ∆ ∆ ∆ ∆∆ ∆ ∆ ∆ ∆ ∆∆ ∆ ∆ ∆ ∆ ∆∆ ∆ ∆ ∆ ∆ ∆In LOIn LO--QCD:QCD:
2 2 2 2( , ) ( , ) ( , )hh h e q x Q D z Q q x Qσ −σ −σ −σ − ∆∆∆∆σσσσ
∑∑∑∑
scattered lepton
u_
d_
u_
u_
u_
ρ−
u_
π0
π0
π+−π
π0
u
ud
u
d
u
ptarget nucleon
incoming lepton
String Breaking
virtual photon
uu
u
uud
ud
ud
1919SFU, VanCouver, March 2007SFU, VanCouver, March 2007EE.C. Aschenauer.C. Aschenauer
A PQ====ur urur urur urur ur
Extract Extract ∆∆∆∆∆∆∆∆qq by solving:by solving:
1, 1, 1, 1, 1,( ( ), ( ), ( ), ( ), ( ))Kp p d d dA A x A x A x A x A xπ± π± ±π± π± ±π± π± ±π± π± ±====
urururur
( , , , , , )u d u d s s
Qu d su d s
∆ ∆ ∆ ∆ ∆ ∆∆ ∆ ∆ ∆ ∆ ∆∆ ∆ ∆ ∆ ∆ ∆∆ ∆ ∆ ∆ ∆ ∆====urururur
2 1/ 2 3 / 21 2 2
1/ 2 3 /2
'2
2 ''
2( , )( , , ) ~
'( , )
( , )
( , )( , )
( , )
h hqh
hq
qh
q qh q
e q x QA x Q z C
e
D z Q
Dq x Q
q Qq Q xzx Q
σ −σ −σ −σ −====
∆∆∆∆σσσσσ + σσ + σσ + σσ + σ ∑∑∑∑ ∑∑∑∑
2( , , )hqP x Q z MCMC
0.03 0.1
-0.1
0
0.1
0.2
0.3
0.4
0.5A1
A1,d A1,dAh+
SMC
A1,dAπ+ A1,dAK+
0.03 0.1 0.4
-0.1
0
0.1
0.2
0.3
0.4
0.5A1,dAh−
SMC
0.03 0.1 0.4
A1,dAπ−
0.03 0.1 0.4x
A1,dAK−
Measured AsymmetriesMeasured Asymmetries
0
0.2
0.4
0.6
0.8
0.03 0.1
A1
A1,p A1,pAh+
SMC
A1,pAπ+
0
0.2
0.4
0.6
0.8
0.03 0.1 0.4
A1,pAh−
SMC
0.03 0.1 0.4x
A1,pAπ−
ProtonProton
DeuteriumDeuterium
2020SFU, VanCouver, March 2007SFU, VanCouver, March 2007EE.C. Aschenauer.C. Aschenauer
0.03 0.1
-0.1
0
0.1
0.2
0.3
0.4
0.5A1
A1,d A1,dAh+
SMC
A1,dAπ+ A1,dAK+
0.03 0.1 0.4
-0.1
0
0.1
0.2
0.3
0.4
0.5A1,dAh−
SMC
0.03 0.1 0.4
A1,dAπ−
0.03 0.1 0.4x
A1,dAK−
0
0.2
0.4
0.6
0.8
0.03 0.1
A1
A1,p A1,pAh+
SMC
A1,pAπ+
0
0.2
0.4
0.6
0.8
0.03 0.1 0.4
A1,pAh−
SMC
0.03 0.1 0.4x
A1,pAπ−1 ~ 0 ( )KA K us
−−−− −−−− ====⇒⇒⇒⇒
statistics sufficient for statistics sufficient for 5 parameter fit5 parameter fit
( , , , , , 0)u d u d s s
Qu d su d s
∆ ∆ ∆ ∆ ∆ ∆∆ ∆ ∆ ∆ ∆ ∆∆ ∆ ∆ ∆ ∆ ∆∆ ∆ ∆ ∆ ∆ ∆= == == == =urururur
good agreement with NLOgood agreement with NLO--QCDQCDPolarised opposite to proton spinPolarised opposite to proton spin
Polarized Quark DensitiesPolarized Quark Densities
∆∆∆∆u(x) > 0
First complete separation of First complete separation of pol. PDFs without assumption on pol. PDFs without assumption on sea polarizationsea polarization
Polarised parallel to proton spinPolarised parallel to proton spin
∆∆∆∆d(x) < 0
∆∆∆∆u(x), ∆∆∆∆d(x) ~ 0~ 0
No indication forNo indication for ∆∆∆∆s(x) << 00
0
0.2
x⋅∆u
-0.2
0x⋅∆d
-0.1
0
GRSV 2000LO val
BB 01 LOx⋅∆u
–
Q2=2.5GeV2
-0.1
0
x⋅∆d–
-0.1
0
x⋅∆s
0.03 0.1 0.6
x
2121SFU, VanCouver, March 2007SFU, VanCouver, March 2007EE.C. Aschenauer.C. Aschenauer
No indication forNo indication for ∆∆∆∆s(x) << 00
In measured range (0.023 In measured range (0.023 –– 0.6)0.6)
0.002 0.043u∆ = − ±∆ = − ±∆ = − ±∆ = − ±∫∫∫∫0.054 0.035d∆ = − ±∆ = − ±∆ = − ±∆ = − ±∫∫∫∫
0.028 0.034s∆ = + ±∆ = + ±∆ = + ±∆ = + ±∫∫∫∫
0
0.2
x⋅∆u
-0.2
0x⋅∆d
-0.1
0
GRSV 2000LO val
BB 01 LOx⋅∆u
–
Q2=2.5GeV2
-0.1
0
x⋅∆d–
-0.1
0
x⋅∆s
0.03 0.1 0.6
x
-0.2
0
0.2
0.4
-0.2
0
0.2
0.4
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
10-2
10-2
x(∆u+∆u–)
x(∆d+∆d–)
x∆uv
x∆dv
x∆g–
x∆u–
xBj
x∆d–
xBj
x∆s–
xBj
KRE (NLO)KKP (NLO)unpolarizedKRE χ2KRE χmin+1KRE χ2KRE χmin+2%
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
10-2
D. De Florian et al. hepD. De Florian et al. hep--ph/0504155ph/0504155NLO @ Q2=10 GeV2
KretzerKretzer
KKPKKP
χ2DIS χ2
SIDIS ∆uv ∆u∆dv ∆d ∆s ∆g ∆Σ
206206206206206206206206
225225225225231231231231
0.940.940.940.940.700.700.700.70 −−−−0.260.260.260.26
−−−−0.340.340.340.340.0870.0870.0870.087
−−−−−−−−0.0490.0490.0490.0490.0490.0490.0490.049−−−−0.110.110.110.11
−−−−−−−−0.0550.0550.0550.0550.0550.0550.0550.055−−−−0.0450.0450.0450.045−−−−−−−−0.0510.0510.0510.0510.0510.0510.0510.051
0.570.570.570.570.680.680.680.68
0.310.310.310.310.280.280.280.28
NLO FIT to DIS & SIDIS DataNLO FIT to DIS & SIDIS Data
2222SFU, VanCouver, March 2007SFU, VanCouver, March 2007EE.C. Aschenauer.C. Aschenauer
-0.2
0
0.2
0.4
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
10-2
10-2
x(∆u+∆u–)
x(∆d+∆d–)
x∆uv
x∆dv
x∆g–
x∆u–
xBj
x∆d–
xBj
x∆s–
xBj
KRE (NLO)KKP (NLO)unpolarizedKRE χ2KRE χmin+1KRE χ2KRE χmin+2%
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
10-2
SIDIS data improves description of allSIDIS data improves description of all ∆∆∆∆∆∆∆∆qq, especially light sea, especially light seaKretzer FF favor SU(3) symmetric sea, not so for KKPKretzer FF favor SU(3) symmetric sea, not so for KKP∆Σ ∆Σ ∆Σ ∆Σ ∆Σ ∆Σ ∆Σ ∆Σ ~30%~30% in all casesin all cases
The Gluon PolarizationThe Gluon Polarization
Naïve parton modelNaïve parton model
43∆ =∆ =∆ =∆ =vu 1
3∆ = −∆ = −∆ = −∆ = −vd Unpolarised structure fct.Unpolarised structure fct.
2323SFU, VanCouver, March 2007SFU, VanCouver, March 2007EE.C. Aschenauer.C. Aschenauer
1 1( )
2 2 v svu q Gd∆∆∆∆ ∆∆∆∆+ ++ ++ ++ +∆∆∆∆ ++++ ∆∆∆∆====
43∆ =∆ =∆ =∆ =vu 1
3∆ = −∆ = −∆ = −∆ = −vdBUTBUT
1989 EMC measured1989 EMC measuredΣΣΣΣΣΣΣΣ = 0.120 0.094 0.138= 0.120 0.094 0.138± ±
Spin PuzzleSpin Puzzle
Unpolarised structure fct.Unpolarised structure fct.
Gluons are important !Gluons are important !
Sea quarksSea quarks ∆∆∆∆∆∆∆∆qq ss
∆∆∆∆∆∆∆∆GG
1 1( )
2 2 v v su qd= += += += + ∆∆∆∆++++∆∆∆∆∆∆∆∆
( )∆ + ∆ + ∆ + ∆ + ∆ + ∆∆ + ∆ + ∆ + ∆ + ∆ + ∆∆ + ∆ + ∆ + ∆ + ∆ + ∆∆ + ∆ + ∆ + ∆ + ∆ + ∆s su d u d s s
Unpolarized Gluon Distribution Unpolarized Gluon Distribution 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-5x=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
15
20
15
20xg 2 = 20 GeV2Q
2 = 200 GeV2Q15
20 ZEUS-JETS (prel.) 94-00
H1 PDF 2000
total uncert.
exp. uncert.
total uncert.
H1+ZEUS
big Qbig Q22--x lever armx lever armvery accurate G(x)very accurate G(x)
2424SFU, VanCouver, March 2007SFU, VanCouver, March 2007EE.C. Aschenauer.C. Aschenauer
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-5x=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=0.650
5
10
15
-410 -310 -210 -110 10
5
10
15
x
2 = 5 GeV2Q
0
5
10
15 total uncert.
How to measure How to measure ∆∆∆∆∆∆∆∆GG
Indirect from scaling violationIndirect from scaling violation
fixed target experimentsfixed target experimentssmall Qsmall Q22--x lever armx lever armeven sign of even sign of ∆∆∆∆∆∆∆∆G unknownG unknown
0
1
2
3
4
5
6
7
8
9
10
E143
HERMES
E155
COMPASS
SMC
g1d(x,Q2) + C(x)
1 10 100Q2 (GeV2)
0
0.1
0.2
0.3AAC06
GRSV
BB
LSS
x∆Σ∆Σ∆Σ∆Σ(x)
2525SFU, VanCouver, March 2007SFU, VanCouver, March 2007EE.C. Aschenauer.C. Aschenauer
0
1
2
3
4
5
6
7
8
9
10
E143
HERMES
E155
COMPASS
SMC
g1d(x,Q2) + C(x)
1 10 100Q2 (GeV2)
-0.10.001 0.01 0.1 1
-0.6-0.4-0.2
00.20.40.60.8
11.21.4
0.001 0.01 0.1 1
x
x∆∆∆∆g(x)
Q2 = 1 GeV2
hephep--ph/0603213ph/0603213
Several more fitsSeveral more fits
using mainly only inclusive data or a combination of inclusive and using mainly only inclusive data or a combination of inclusive and some semisome semi--inclusive datainclusive dataResults for Results for ∆∆∆∆∆∆∆∆G still completely all over the placeG still completely all over the placeNeed a consistent approach for fit and uncertainty determinationNeed a consistent approach for fit and uncertainty determinationwith all world data taken into accountwith all world data taken into account
∆∆∆∆G>0G>0G>0G>0
2626SFU, VanCouver, March 2007SFU, VanCouver, March 2007EE.C. Aschenauer.C. Aschenauer
∆G<0 ∆G<0
∆∆∆∆G>0G>0G>0G>0Lets measure Lets measure ∆∆∆∆∆∆∆∆G more directlyG more directly
The golden channelsThe golden channelsIdea: Direct measurementIdea: Direct measurement ofof ∆∆∆∆∆∆∆∆GG
Isolate the photon gluon fusion process (PGF)Isolate the photon gluon fusion process (PGF)Open Charm productionOpen Charm production
Reaction:Reaction: * 0 0p D D Xγγγγ → + +→ + +→ + +→ + +⇒⇒⇒⇒ * 0reconstruct Dc ,Dcˆ ˆ( , )
ˆ ˆ( , )
PGF
gPGF
N PGF
g
ds G x sA
ds G x sγγγγ
σσσσ
σσσσ
∆ ∆∆ ∆∆ ∆∆ ∆==== ∫∫∫∫∫∫∫∫
PGF
LLa
G
G
∆∆∆∆≈≈≈≈
) 0N(D 604± 14577
Mass 2 1.1 MeV/c± 2.9
Sigma 2 1.2 MeV/c± 26.6
2N
/ 20
MeV
/c
100
310×
candidates in 2002-20040D
=1051 +- 18effS
candidates in 2002-20040D
2727SFU, VanCouver, March 2007SFU, VanCouver, March 2007EE.C. Aschenauer.C. Aschenauer
Sigma 2 1.2 MeV/c± 26.6
]2)[MeV/clit
0)-m(D0m(D-400 -200 0 200 400
N /
20 M
eV/c
20
40
60
80
COMPASS preliminary
) 0N(D 104± 3869
Mass 2 0.8 MeV/c± 4.9 Sigma 2 0.9 MeV/c± 28.6
]2)[MeV/clit
0)-m(D0m(D-400 -200 0 200 400
2N
/ 20
MeV
/c
200
400
600
800
1000
1200
1400
1600
1800
2000
2200
D* candidates in 2002-2004
) 0N(D 104± 3869
Mass 2 0.8 MeV/c± 4.9 Sigma 2 0.9 MeV/c± 28.6
=1966 +/- 51effS
COMPASS preliminary
]2)[MeV/clit
0)-m(D0m(D-400 -200 0 200 400
2N
/ 20
MeV
/c
200
400
600
800
1000
1200
1400
1600
1800
2000
2200
D* candidates in 2002-2004
2002 2003 2004 02-04 0D*+D2002 2003 2004 02-04 0D*+D
G/G
∆
-4
-3
-2
-1
0
1
G/G∆COMPASS Data 2002-2004
preliminaryD*
0D0 D* + D
G/G∆COMPASS Data 2002-2004
(stat.)0.57 0.41 0.17G
G∆∆∆∆ = − ± ±= − ± ±= − ± ±= − ± ±
2 20.15 13Gx µµµµ ====���� GeV
LOLO--MC: AromaMC: Aroma
The golden channelsThe golden channelsIdea: Direct measurement ofIdea: Direct measurement of ∆∆∆∆∆∆∆∆GG
Isolate the photon gluon fusion processIsolate the photon gluon fusion processdetection of hadronic final states with high pdetection of hadronic final states with high pTT
high phigh pTT pairs of hadronspairs of hadronssingle high psingle high pTT hadronshadrons
hh±±hh±±2 1Q >>>>2 0.1Q <<<<
less subless sub--processes contributing processes contributing ☺☺☺☺☺☺☺☺
more submore sub--processes contributing processes contributing ��������higher statistics higher statistics ☺☺☺☺☺☺☺☺
Several possible contributions to the measured asymmetrySeveral possible contributions to the measured asymmetry
MC needed to determine R and aMC needed to determine R and aLLLL
2828SFU, VanCouver, March 2007SFU, VanCouver, March 2007EE.C. Aschenauer.C. Aschenauer
hh±±2 0.1Q >>>>2 0.1Q <<<<
higher statistics higher statistics ☺☺☺☺☺☺☺☺
less subless sub--processes contributing processes contributing ☺☺☺☺☺☺☺☺
more submore sub--processes contributing processes contributing ��������higher statistics higher statistics ☺☺☺☺☺☺☺☺
+ + + ..
|||| ||| |( ) ;B SigSig
gmeas i it i i
i tB
tog f AA p f A ff A
σσσσ= = + == = + == = + == = + =σσσσ∑∑∑∑
|| ||ˆ]
1[ meas
Sig
BgBgf
GA
aA
Gf
−−−−∆∆∆∆ ====
q
g
q
g qg
Important Important at Q2<0.1at Q2<0.1
The golden channelsThe golden channelsIdea: Direct measurement ofIdea: Direct measurement of ∆∆∆∆∆∆∆∆GG
Isolate the photon gluon fusion processIsolate the photon gluon fusion processdetection of hadronic final states with high pdetection of hadronic final states with high pTT
high phigh pTT pairs of hadronspairs of hadronssingle high psingle high pTT hadronshadrons
hh±±hh±±2 1Q >>>>2 0.1Q <<<<
less subless sub--processes contributing processes contributing ☺☺☺☺☺☺☺☺
more submore sub--processes contributing processes contributing ��������higher statistics higher statistics ☺☺☺☺☺☺☺☺
Several possible contributions to the measured asymmetrySeveral possible contributions to the measured asymmetry
MC needed to determine R and aMC needed to determine R and aLLLL
2929SFU, VanCouver, March 2007SFU, VanCouver, March 2007EE.C. Aschenauer.C. Aschenauer
hh±±2 0.1Q >>>>2 0.1Q <<<<
higher statistics higher statistics ☺☺☺☺☺☺☺☺
less subless sub--processes contributing processes contributing ☺☺☺☺☺☺☺☺
more submore sub--processes contributing processes contributing ��������higher statistics higher statistics ☺☺☺☺☺☺☺☺
+ + + ..
|||| ||| |( ) ;B SigSig
gmeas i it i i
i tB
tog f AA p f A ff A
σσσσ= = + == = + == = + == = + =σσσσ∑∑∑∑
|| ||ˆ]
1[ meas
Sig
BgBgf
GA
aA
Gf
−−−−∆∆∆∆ ====
q
g
q
g qg
Important Important at Q2<0.1at Q2<0.1
hh±±hh±± vs. hvs. h±±::hh±± more inclusive more inclusive → → pQCD NLO calculations (easier) possiblepQCD NLO calculations (easier) possible
COMPASS ResultsCOMPASS Results
1 2, 0.7T Tp p GeV>>>> 2 2 2,1 ,2 2.5T Tp p GeV+ >+ >+ >+ >
Channel:Channel:hh±±hh±±
xxFF > 0.1 z > 0.1> 0.1 z > 0.1m(hm(h11,h,h22) > 1.5 GeV) > 1.5 GeV
10% ofstatistics
RRPGFPGF = 0.34 +/= 0.34 +/-- 0.070.07
µµµµµµµµ22((scale) ~ 3 GeVscale) ~ 3 GeV22 <x<xGG> > ~~ 0.130.13
|| 0.015 0.080( ) 0.013( )A
stat systD
= − ± ±= − ± ±= − ± ±= − ± ±
0.06 0.31( ) 0.06( )stg
gat syst==== ±±±±
∆∆∆∆ ±±±±
QQ22 > 1 GeV> 1 GeV22Cuts:Cuts:
QQ22 < 1 GeV< 1 GeV22
3030SFU, VanCouver, March 2007SFU, VanCouver, March 2007EE.C. Aschenauer.C. Aschenauer
used for used for ∆∆∆∆∆∆∆∆g/g extractiong/g extraction
&&
∆∆∆∆∆∆∆∆g/g=g/g=0.0160.016±±0.058(stat.)0.058(stat.)±±0.055(syst.)0.055(syst.)0.070.0350.085gx ++++
−−−−==== µµµµµµµµ22=3.0GeV=3.0GeV22
HERMES ResultsHERMES ResultsChannels:Channels: hh±±hh±±, h, h±±
Subprocess AsymmetriesSubprocess Asymmetries
Subprocess FractionsSubprocess Fractions
3131SFU, VanCouver, March 2007SFU, VanCouver, March 2007EE.C. Aschenauer.C. Aschenauer
Subprocess AsymmetriesSubprocess Asymmetries(using GRSV std.)(using GRSV std.)
World Data on World Data on ∆∆∆∆∆∆∆∆G/GG/G
3232SFU, VanCouver, March 2007SFU, VanCouver, March 2007EE.C. Aschenauer.C. Aschenauer
Long way to go till Long way to go till ∆∆∆∆∆∆∆∆g(x)g(x)
xx
RHIC SPINRHIC SPIN
hadronic final stateshadronic final states
JetsJets
Reaction mechanism:Reaction mechanism:
3333SFU, VanCouver, March 2007SFU, VanCouver, March 2007EE.C. Aschenauer.C. Aschenauer
Hard sub processes:Hard sub processes:
ππππππππ0 0 ProductionProductionunpolarized cross section:unpolarized cross section: sub processes:sub processes:
3434SFU, VanCouver, March 2007SFU, VanCouver, March 2007EE.C. Aschenauer.C. Aschenauer
good agreement with NLO pQCDgood agreement with NLO pQCD
Jet ProductionJet Production
STARSTARunpolarized cross section:unpolarized cross section: Asymmetry:Asymmetry:
3535SFU, VanCouver, March 2007SFU, VanCouver, March 2007EE.C. Aschenauer.C. Aschenauer
good agreement with NLO pQCDgood agreement with NLO pQCD ∆∆∆∆∆∆∆∆G seems smallG seems small
RHIC RESULTSRHIC RESULTS
3636SFU, VanCouver, March 2007SFU, VanCouver, March 2007EE.C. Aschenauer.C. Aschenauer
maybe the way is a bit shorter till maybe the way is a bit shorter till ∆∆∆∆∆∆∆∆g(x)g(x)
Quark Orbital Angular MomentumQuark Orbital Angular Momentum
Naïve parton modelNaïve parton model
43∆ =∆ =∆ =∆ =vu 1
3∆ = −∆ = −∆ = −∆ = −vd Unpolarised structure fct.Unpolarised structure fct.
3737SFU, VanCouver, March 2007SFU, VanCouver, March 2007EE.C. Aschenauer.C. Aschenauer
1 1( )
2 2 v gsv qLd LGqu= + + + += + + + += + + + += + + + +∆∆∆∆∆∆∆∆ ++++∆∆∆∆∆∆∆∆
∆Σ∆Σ∆Σ∆Σ
1 1( )
2 2 v svu q Gd∆∆∆∆ ∆∆∆∆+ ++ ++ ++ +∆∆∆∆ ++++ ∆∆∆∆====
( )∆ + ∆ + ∆ + ∆ + ∆ + ∆∆ + ∆ + ∆ + ∆ + ∆ + ∆∆ + ∆ + ∆ + ∆ + ∆ + ∆∆ + ∆ + ∆ + ∆ + ∆ + ∆s su d u d s s
43∆ =∆ =∆ =∆ =vu 1
3∆ = −∆ = −∆ = −∆ = −vdBUTBUT
1989 EMC measured1989 EMC measuredΣΣΣΣΣΣΣΣ = 0.120 0.094 0.138= 0.120 0.094 0.138± ±
Spin PuzzleSpin Puzzle
Unpolarised structure fct.Unpolarised structure fct.
Gluons are important !Gluons are important !
Sea quarksSea quarks ∆∆∆∆∆∆∆∆qq ss
∆∆∆∆∆∆∆∆GG Full description of JFull description of Jqq and Jand Jggneedsneeds
orbital angular momentumorbital angular momentum
The Hunt for LThe Hunt for Lqq
Study of hard Study of hard exclusive processesexclusive processes leads toleads toa new class of PDFsa new class of PDFs
GGeneralized eneralized PParton arton DDistributionsistributions
, , ,q qq qH H EE % %% %% %% %
possible access topossible access toorbital angular momentumorbital angular momentum
3838SFU, VanCouver, March 2007SFU, VanCouver, March 2007EE.C. Aschenauer.C. Aschenauer
orbital angular momentumorbital angular momentum
(((( ))))(((( ))))1
1 0
12
q
tHJ Exdx
−−−− →→→→++++==== ∫∫∫∫
12q qLJ ∆∆∆∆ ++++ΣΣΣΣ====
exclusive:exclusive: all products of the reaction are detectedall products of the reaction are detectedmissing energymissing energy ((∆∆∆∆∆∆∆∆E) and missing Mass (ME) and missing Mass (Mxx) = 0) = 0
from DIS:from DIS:HERMES ~0.3HERMES ~0.3
GPDs IntroductionGPDs Introduction
What does GPDs charaterize?What does GPDs charaterize?
unpolarized unpolarized polarizedpolarized
(((( )))), ,qH x tξξξξ (((( )))), ,qH x tξξξξ%%%%
(((( )))), ,qE x tξξξξ%%%%(((( )))), ,qE x tξξξξ
conserve nucleon helicityconserve nucleon helicity����( ,0,0) , ( ,0,0)
qqH x q H x q= = ∆= = ∆= = ∆= = ∆flip nucleon helicityflip nucleon helicitynot accessible in DISnot accessible in DIS
quantum numbers of final state select different GPDquantum numbers of final state select different GPD
3939SFU, VanCouver, March 2007SFU, VanCouver, March 2007EE.C. Aschenauer.C. Aschenauer
DDVVCCSS
∆2
P +∆P -2
x - ξ ξx +
γ∗ γ
GPD
0+
P - ∆2
P + ∆2
π , π
x - ξ ξx +
γ∗
GPD
q 0ρ , Φ , ωq
P + ∆2
P - ∆2
x - ξ ξx +
GPD
γ∗
,q qH E% %% %% %% %pseudopseudo --scaler mesonsscaler mesons
,q qH Evector mesonsvector mesons
AACC,A,A LULU,, AAUTUT, A, AULUL
qE%%%%qH%%%%qEqHAAUTUT,,σσσσσσσσππππππππ++ AAUTUT,,σσσσσσσσρ,Φ,ωρ,Φ,ωρ,Φ,ωρ,Φ,ωρ,Φ,ωρ,Φ,ωρ,Φ,ωρ,Φ,ω
ee++/e/e--
27.5 GeV27.5 GeV
PPbb=55%=55%
Exclusivity @ HERMESExclusivity @ HERMES
4040SFU, VanCouver, March 2007SFU, VanCouver, March 2007EE.C. Aschenauer.C. Aschenauer
�� missing mass (energy) missing mass (energy) techniquetechnique�������� background estimated by MCbackground estimated by MC
(detected)(detected)MC
associated BH
Bethe-Heitler
+ data
no recoil detectionno recoil detection
HERMES / JLAB HERMES / JLAB kinematics: BH >> DVCSkinematics: BH >> DVCS
DVCSDVCStwo experimentally undistinguishable processes:two experimentally undistinguishable processes:
e’e
γ
p + ∆
γ∗
p
ee’
γγ∗
p ∆p +
DVCSDVCS BetheBethe--Heitler (BH)Heitler (BH)
p + p + ∆∆∆∆∆∆∆∆
(((( ))))* 2 2*~ | | | |d τ τ + τ ττ τ + τ ττ τ + τ ττ τ + τ τσ + τ + τσ + τ + τσ + τ + τσ + τ + τ
4141SFU, VanCouver, March 2007SFU, VanCouver, March 2007EE.C. Aschenauer.C. Aschenauer
(((( ))))* 2 2*~ | | | |BH DVCS DVC BS HB DVCSHd τ τ + τ ττ τ + τ ττ τ + τ ττ τ + τ τσ + τ + τσ + τ + τσ + τ + τσ + τ + τ
isolate isolate BHBH--DVCS interferenceDVCS interference term nonterm non--zero azimuthal asymmetrieszero azimuthal asymmetries
∆σ∆σ∆σ∆σC ~ cosφφφφ ·Re{ H + ξH +… }~
�polarization observables:polarization observables:
� different charges: edifferent charges: e++ ee-- (only @HERA!):(only @HERA!):
H
DVCS ASYMMETRIESDVCS ASYMMETRIES
(((( ))))* 2 2*~ | | | |BH DVCS DVC BS HB DVCSHd τ τ + τ ττ τ + τ ττ τ + τ ττ τ + τ τσ + τ + τσ + τ + τσ + τ + τσ + τ + τ
4242SFU, VanCouver, March 2007SFU, VanCouver, March 2007EE.C. Aschenauer.C. Aschenauer
∆σ∆σ∆σ∆σUT ~ sinφφφφ·Im{k(H - E) + … }
∆σ∆σ∆σ∆σLU ~ sinφφφφ·Im{H + ξH + kE}~
∆σ∆σ∆σ∆σUL ~ sinφφφφ·Im{H + ξH + …}~
�polarization observables:polarization observables:
∆σUT
beam target
kinematically suppressedkinematically suppressed
H
H
H, E
~
ξ = xB/(2-xB ),k = t/4M2
CLAS: DVCS CLAS: DVCS -- BSABSA
<-t> = 0.18 GeV2 <-t> = 0.30 GeV2 <-t> = 0.49 GeV2 <-t> = 0.76 GeV2
4343SFU, VanCouver, March 2007SFU, VanCouver, March 2007EE.C. Aschenauer.C. Aschenauer
Integrated over tIntegrated over t
Accurate data in a Accurate data in a large kinematical large kinematical domaindomain
AA way to E and Jway to E and Juu--JJdd
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0 0.5
-0.2
-0.4
-0.6
0
0.2
-0.2
-0.4
-0.6
0
0.2
0 0.25 0.5
-t (GeV2)
AU
Tsi
n(φ-
φ s)cos
(φ) HERMES
PRELIMINARY(in HERMES acceptance)
0 0.2 0.4
e+ p ⇑ → e+ γ X(Mx < 1.7 GeV)
0 0.1 0.2 0.3
xB
0 5 10
Ju=0.2Ju=0.4
Ju=0
(hep-ph/0506264)
0 2.5 5 7.5 10
Q2 (GeV2)
2 1Im( )F H F E−−−−
sin( )cos( ) ~sUTA φ−φ φφ−φ φφ−φ φφ−φ φ
Hermes DVCSHermes DVCS--TTSA:TTSA:
4444SFU, VanCouver, March 2007SFU, VanCouver, March 2007EE.C. Aschenauer.C. Aschenauer
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0 0.5
-0.2
-0.4
-0.6
0
0.2
-0.2
-0.4
-0.6
0
0.2
0 0.25 0.5
-t (GeV2)
AU
Tsi
n(φ-
φ s)cos
(φ) HERMES
PRELIMINARY(in HERMES acceptance)
0 0.2 0.4
e+ p ⇑ → e+ γ X(Mx < 1.7 GeV)
0 0.1 0.2 0.3
xB
0 5 10
Ju=0.2Ju=0.4
Ju=0
(hep-ph/0506264)
0 2.5 5 7.5 10
Q2 (GeV2)
Hall A nDVCSHall A nDVCS--BSA:BSA:
x=0.36 and Qx=0.36 and Q22=1.9GeV=1.9GeV22
Neutron obtained combining Neutron obtained combining deuterium and protondeuterium and proton
FF11 small u & d cancel in small u & d cancel in H%%%%1 1 2 22~ ( )
4LU
tF H x F F H F E
MA + + −+ + −+ + −+ + −%%%%
Can we constrain (JCan we constrain (Juu -- JJdd))
4545SFU, VanCouver, March 2007SFU, VanCouver, March 2007EE.C. Aschenauer.C. Aschenauer
first model dependent extraction of first model dependent extraction of JJuu -- JJdd possiblepossibleVGGVGG--Code: GPDCode: GPD--model: LO/Regge/Dmodel: LO/Regge/D--term=0term=0
The end of polarized targets at HERMESThe end of polarized targets at HERMESDVCS exclusivity by missing mass MDVCS exclusivity by missing mass Mxx
Improve ExclusivityImprove ExclusivityDetect recoiling protonDetect recoiling proton
modify target regionmodify target region
4646SFU, VanCouver, March 2007SFU, VanCouver, March 2007EE.C. Aschenauer.C. Aschenauer
The HERMES Recoil Detector The HERMES Recoil Detector
detection of the recoiling protondetection of the recoiling protonp; 135 p; 135 --1200 MeV/c1200 MeV/c76% 76% φφφφφφφφ acceptanceacceptanceππππππππ/p PID via dE/dx/p PID via dE/dx
improved timproved t--resolutionresolutionstudy kinematical study kinematical dependencesdependences
−−−−background suppressionbackground suppression
SciFiSciFi
4747SFU, VanCouver, March 2007SFU, VanCouver, March 2007EE.C. Aschenauer.C. Aschenauer
Build by DESY, Erlangen, Ferrara, Frascati,Build by DESY, Erlangen, Ferrara, Frascati,Gent, Giessen and GlasgowGent, Giessen and Glasgow
~pp t−−−−~ xt M−−−−
background suppressionbackground suppressionsemisemi--incl.: 5% incl.: 5% ֏ ֏ <<1%<<1%associated: 11% associated: 11% ֏ ֏ ~1%~1%
SiliconSilicon
Access to LAccess to Lqq in semiin semi--inclusive scatteringinclusive scatteringNew structure function accessible with SSANew structure function accessible with SSA
2
11
φ φφ φφ φφ φ−−−−
⊥⊥⊥ ⊥
⊥⊥⊥ ⊥⋅⋅⋅⋅= −= −= −= −
sin( )
,( , , )h s
T
T
UU T h
h pF x z P f D
M
$
C�
std. FFstd. FFSivers DFFSivers DFFSide viewSide view Front viewFront viewleftleftleft
quarks
4848SFU, VanCouver, March 2007SFU, VanCouver, March 2007EE.C. Aschenauer.C. Aschenauer
right
photon
NOTE: QCD tells us that the FSI has to be attractive, since NOTE: QCD tells us that the FSI has to be attractive, since quark and remnants form a color antisymmetric statequark and remnants form a color antisymmetric state
right
photon
rightproton
��������
A distortion in the distribution of quarks in transverse A distortion in the distribution of quarks in transverse space can give rise to a nonzero Sivers functionspace can give rise to a nonzero Sivers function
The presence of spin can distort the distribution of quarks in The presence of spin can distort the distribution of quarks in transverse space (orbital angular momentum of quarks is required)transverse space (orbital angular momentum of quarks is required)
HERMES & COMPASS MeasurementsHERMES & COMPASS Measurements
0
0.05
0.1
0.15
0.2
0.25
2 ⟨s
in(φ
-φS)⟩
h U
T
K+
π+
-0.15
-0.1
-0.05
0
0.05
0.1
0.15
0.1 0.2 0.3
2 ⟨s
in(φ
-φS)⟩
h U
T
K-
π-
x0.2 0.3 0.4 0.5 0.6
z0.2 0.4 0.6 0.8 1
Ph⊥ [GeV]
IIIHERMES PRELIMINARY 2002-2005lepton beam asymmetry, Sivers amplitudes8.1% scale uncertainty
Proton:Proton:Sivers moment:Sivers moment:ππππππππ++ > 0 > 0 ππππππππ-- ~ 0~ 0
KK+ + > 0 K> 0 K-- ~ 0~ 0KK++ >> ππππππππ++
sea quarks importantsea quarks importantDeuterium ~ 0 Deuterium ~ 0
4949SFU, VanCouver, March 2007SFU, VanCouver, March 2007EE.C. Aschenauer.C. Aschenauer
0
0.05
0.1
0.15
0.2
0.25
2 ⟨s
in(φ
-φS)⟩
h U
T
K+
π+
-0.15
-0.1
-0.05
0
0.05
0.1
0.15
0.1 0.2 0.3
2 ⟨s
in(φ
-φS)⟩
h U
T
K-
π-
x0.2 0.3 0.4 0.5 0.6
z0.2 0.4 0.6 0.8 1
Ph⊥ [GeV]
IIIHERMES PRELIMINARY 2002-2005lepton beam asymmetry, Sivers amplitudes8.1% scale uncertainty
DeuteriumDeuteriumProtonProton
sea quarks importantsea quarks importantDeuterium ~ 0 Deuterium ~ 0
u and d quark cancelu and d quark cancel
Results from theoryResults from theoryLattice QCD: SiversLattice QCD: Sivers
negative negative for up quarksfor up quarks
Pheno. analysis from data:Pheno. analysis from data:
5050SFU, VanCouver, March 2007SFU, VanCouver, March 2007EE.C. Aschenauer.C. Aschenauer
QCDSF/UKQCD Collab. (hepQCDSF/UKQCD Collab. (hep--ph/05110032) ph/05110032)
positive positive for down quarksfor down quarks
Anselmino et al., hepAnselmino et al., hep--ph/0511017ph/0511017
[20] Anselmino et al., PRD72 (05)[20] Anselmino et al., PRD72 (05)
[21] Vogelsang, Yuan, PRD72 (05)[21] Vogelsang, Yuan, PRD72 (05)
[23] Collins et al., hep[23] Collins et al., hep--ph/0510342ph/0510342
SummarySummary
∆∆∆∆∆∆∆∆GGLLqq
∆∆∆∆∆∆∆∆qq δδδδδδδδqq1Tf⊥⊥⊥ ⊥
0
0.2
x⋅∆u
-0.2
0x⋅∆d
-0.1
0
GRSV 2000LO val
BB 01 LOx⋅∆u
–
Q2=2.5GeV2
-0.1
0
x⋅∆d–
-0.1
0
x⋅∆s
0.03 0.1 0.6
x
5151SFU, VanCouver, March 2007SFU, VanCouver, March 2007EE.C. Aschenauer.C. Aschenauer
LLggδδδδδδδδqq1Tf⊥⊥⊥ ⊥
∆∆∆∆∆∆∆∆GGLLgg
LLqq
Spin is fascinatingSpin is fascinating
W. PauliN.Bohr
5252SFU, VanCouver, March 2007SFU, VanCouver, March 2007EE.C. Aschenauer.C. Aschenauer
Thank you for your attentionThank you for your attention
BACKUP SLIDESBACKUP SLIDES
5353SFU, VanCouver, March 2007SFU, VanCouver, March 2007EE.C. Aschenauer.C. Aschenauer
Results for Results for ∆∆∆∆∆∆∆∆Q and Q and ∆∆∆∆∆∆∆∆SS
-0.05
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
x
A1d
Inclusive Asym
metry
Inclusive Asym
metry
Kaon A
symm
etryK
aon Asym
metry
xbj
A1K(x
)
HERMES PRELIMINARY
e + d → K± + X→ →
-0.2
0
0.2
0.4
0.6
0.8
1
10-1
'e d e K X±±±±+ →+ →+ →+ →r urr urr urr ur
Need a longitudinal polarized deuterium targetNeed a longitudinal polarized deuterium targetstrange quark sea in proton and neutron identicalstrange quark sea in proton and neutron identicalfragmentation simplifiesfragmentation simplifies
All needed information can be extracted from HERMES data aloneAll needed information can be extracted from HERMES data aloneinclusive Ainclusive A1,d1,d(x,Q(x,Q22)and kaon A)and kaon AKK
1,d1,d (x,Q(x,Q22) double spin asym.) double spin asym.Kaon multiplicitiesKaon multiplicities
5454SFU, VanCouver, March 2007SFU, VanCouver, March 2007EE.C. Aschenauer.C. Aschenauer
-0.110
-1
x
A1d
xbj
A1K(x
)
HERMES PRELIMINARY
e + d → K± + X→ →
-0.2
0
0.2
0.4
0.6
0.8
1
10-1
.( ) 4 ( ) ( )K K K K Kds un trD z dz D z dz D z dz
+ − + −+ − + −+ − + −+ − + −+ ++ ++ ++ +−−−− = += += += +∫ ∫ ∫∫ ∫ ∫∫ ∫ ∫∫ ∫ ∫
( ) 2 ( )strangK K K
seD z dz D z dz+ −+ −+ −+ −++++====∫ ∫∫ ∫∫ ∫∫ ∫
.( ) ( ) ( ) ( )( ) /( ) / 5 ( ) 2 ( )
nK
str strangKK
Dis
eQ x D z dz S x D z dzdN x dxdN x dx Q x S x
−−−− ++++====
++++∫ ∫∫ ∫∫ ∫∫ ∫
Fit xFit x--dependence of multiplicitiesdependence of multiplicitiesusing PDFs from CTEQusing PDFs from CTEQ--66
x
(dN
K(x
)/dx
)/(d
ND
IS(x
)/dx
)
0.5
HERMES PRELIMINARY (Evolved to Q 2=2.5 GeV2)
Q(x)∫DQ(z)dz+S(x) ∫DS(z)dz
5Q(x)+2S(x)
Non Strange contribution
Strange contribution
10-2
10-1
1
10-1
( )trgKsD z dz∫∫∫∫
( )KnstrgD z dz∫∫∫∫
This Work Kretzer KKPThis Work Kretzer KKP
0.410.41±±0.02 1.103 1.1110.02 1.103 1.111
1.411.41±±0.29 0.783 0.2960.29 0.783 0.296
Only assumptions used:Only assumptions used:isospin symmetry between proton and neutronisospin symmetry between proton and neutronchargecharge--conjugation invariance in fragmentationconjugation invariance in fragmentation
Results for Results for ∆∆∆∆∆∆∆∆Q and Q and ∆∆∆∆∆∆∆∆SS-2
-1
0
10-1
XBj
XBj
x.∆S
(x)
HERMES PRELIMINARY
-0.1
0
0.1
10-1
0
0.1
10-1
XBj
XBj
x.∆Q
(x)
HERMES PRELIMINARY
0
0.1
0.2
10-1
( ) ( ) ( ) ( ) ( )Q x u x u x d x d x= + + += + + += + + += + + + ( ) ( ) ( )S x s x s x= += += += +
1
0.020.286 0.026 0.011Q∆ = ± ±∆ = ± ±∆ = ± ±∆ = ± ±∫∫∫∫
1
0.020.006 0.029 0.007S∆ = ± ±∆ = ± ±∆ = ± ±∆ = ± ±∫∫∫∫
5555SFU, VanCouver, March 2007SFU, VanCouver, March 2007EE.C. Aschenauer.C. Aschenauer
Earlier HERMES conclusions of Earlier HERMES conclusions of unpolarized strange sea confirmedunpolarized strange sea confirmed
factor 2 smaller error barsfactor 2 smaller error barsErrors very sensitive to FF inputErrors very sensitive to FF input
The golden channelsThe golden channelsIdea: Direct measurement ofIdea: Direct measurement of ∆∆∆∆∆∆∆∆GG
Isolate the photon gluon fusion processIsolate the photon gluon fusion processdetection of hadronic final states with high pdetection of hadronic final states with high pTT
high phigh pTT pairs of hadronspairs of hadronssingle high psingle high pTT hadronshadrons
COMPASSCOMPASS HERMESHERMES
------
5656SFU, VanCouver, March 2007SFU, VanCouver, March 2007EE.C. Aschenauer.C. Aschenauer
hh±±hh±± vs. hvs. h±±::
hh±±hh±± ------
hh±± ------
2 1Q >>>>2 1Q <<<< 2 0.1Q <<<<
2 0.1Q >>>>2 0.1Q <<<<
less subless sub--processes contributing processes contributing ☺☺☺☺☺☺☺☺
more submore sub--processes contributing processes contributing ��������higher statistics higher statistics ☺☺☺☺☺☺☺☺
less subless sub--processes contributing processes contributing ☺☺☺☺☺☺☺☺
more submore sub--processes contributing processes contributing ��������higher statistics higher statistics ☺☺☺☺☺☺☺☺
------
hh±± more inclusive more inclusive → → pQCD NLO calculations (easier) possiblepQCD NLO calculations (easier) possible
The Model in PYTHIAThe Model in PYTHIA--66
VMD VMD directdirect anomalous photonanomalous photon
„Soft“ VMD:„Soft“ VMD: QCDQCD-- Splitting of Splitting of
p a) p b) p )Model:Model: Mix processes with different photon characteristicsMix processes with different photon characteristics
5757SFU, VanCouver, March 2007SFU, VanCouver, March 2007EE.C. Aschenauer.C. Aschenauer
„Soft“ VMD:„Soft“ VMD:Elastic, diffractive, Elastic, diffractive, nonnon--diffractive diffractive („minimum bias“,(„minimum bias“,„low„low--pp TT““ ) ) processesprocessesHard VMD:Hard VMD:QCD 2QCD 2→→2 2 processesprocesses
QCDQCD--ComptonComptonPGFPGFLO DIS LO DIS (virtual (virtual photonsphotons))
Splitting of Splitting of γγγγγγγγ→→qqqqQCD 2QCD 2→→2 2 processesprocesses
Small QSmall Q 22: VMD+anomalous (=„resolved“) photon dominate: VMD+anomalous (=„resolved“) photon dominateLarge QLarge Q 22: LO DIS dominates: LO DIS dominatesChoice of hard process according to hardest scale i nvolved:Choice of hard process according to hardest scale i nvolved:If all scales are too small: „soft“ VMD (diffractiv e or „lowIf all scales are too small: „soft“ VMD (diffractiv e or „low--pT“)pT“)The „resolved“ part is modeled to match the world d ata on The „resolved“ part is modeled to match the world d ata on σσσσσσσσ((γγγγγγγγp) p)
k⊥⊥⊥ ⊥
p⊥⊥⊥ ⊥
Q
The MethodThe Method
Measured asymmetry is an incoherent superposition of Measured asymmetry is an incoherent superposition of different subdifferent sub--process asymmetries:process asymmetries:
Signal: Gluon of the nucleon in the initial stateSignal: Gluon of the nucleon in the initial state
|||| ||| |( ) ;B SigSig
gmeas i it i i
i tB
tog f AA p f A ff A
σσσσ= = + == = + == = + == = + =σσσσ∑∑∑∑
Asymmetry of the Asymmetry of the hard subhard sub--processprocess|| ˆ ˆ( ) ; :Sig
t Sig Sig
GA p a a
∆∆∆∆====
5858SFU, VanCouver, March 2007SFU, VanCouver, March 2007EE.C. Aschenauer.C. Aschenauer
Background: all other subBackground: all other sub--processesprocesses
The gluon polarization is then:The gluon polarization is then:
hard subhard sub--processprocess|| ˆ ˆ( ) ; :t Sig SigA p a aG
====
|| ||ˆ]
1[ meas
Sig
BgBgf
GA
aA
Gf
−−−−∆∆∆∆ ====
HERMES ResultsHERMES Results
1 2, 0.5T Tp p GeV>>>> 2 2 2,1 ,2 2.0T Tp p GeV+ >+ >+ >+ >
Channels:Channels:
hh±±hh±± with Qwith Q22<<0.1GeV0.1GeV22;;hh±± with Qwith Q22>>0.1GeV0.1GeV22; P; PTT>1GeV>1GeVhh±± with Qwith Q22<<0.1GeV0.1GeV22; ; ppTT>1GeV>1GeV
-0.1
0
0.1
0.2
0.3
MC, ∆G/G= 0MC, ∆G/G= -1
MC, ∆G/G= +1
ep→h+XHERMES Preliminary
A||
Hermes Data (e± not in acc.)
ep→h-X
-0.1
0
0.1
0.2
0.3
0 1 2
ed→h+X
0 1 2
ed→h-X
pT(beam)(GeV)
Considered subConsidered sub--processes:processes:LOLO--MC: PYTHIA 6.2MC: PYTHIA 6.2
0
0.2
0.4
0.6
0.8
1
0 0.25 0.5 0.75 1 1.25 1.5 1.75 2 2.25
low pTQCD 2→2(q)
ela./diff. VMDLO DISQCDC
PGFQCD 2→2(g)
pT(beam) (GeV)
Sub
proc
ess
Fra
ctio
ns-0.4-0.2
00.20.40.60.8
11.21.4
1.2 1.4 1.6 1.8 2
h+ antitagged (e± not in acc.)h- antitagged (e± not in acc.)
Proton
<∆g/
g>
1.2 1.4 1.6 1.8 2
h+ taggedh- taggedpairs
Deuteron
HERMES Preliminary
pT (GeV)
5959SFU, VanCouver, March 2007SFU, VanCouver, March 2007EE.C. Aschenauer.C. Aschenauer
-0.1
0
0.1
0.2
0.3
MC, ∆G/G= 0MC, ∆G/G= -1
MC, ∆G/G= +1
ep→h+XHERMES Preliminary
A||
Hermes Data (e± not in acc.)
ep→h-X
-0.1
0
0.1
0.2
0.3
0 1 2
ed→h+X
0 1 2
ed→h-X
pT(beam)(GeV)
0
0.2
0.4
0.6
0.8
1
0 0.25 0.5 0.75 1 1.25 1.5 1.75 2 2.25
low pTQCD 2→2(q)
ela./diff. VMDLO DISQCDC
PGFQCD 2→2(g)
pT(beam) (GeV)
Sub
proc
ess
Fra
ctio
ns-0.4-0.2
00.20.40.60.8
11.21.4
1.2 1.4 1.6 1.8 2
h+ antitagged (e± not in acc.)h- antitagged (e± not in acc.)
Proton
<∆g/
g>
1.2 1.4 1.6 1.8 2
h+ taggedh- taggedpairs
Deuteron
HERMES Preliminary
pT (GeV)
COMPASS ResultsCOMPASS Results
1 2, 0.7T Tp p GeV>>>> 2 2 2,1 ,2 2.5T Tp p GeV+ >+ >+ >+ >
Channel:Channel:Cuts:Cuts:
hh±±hh±± with Qwith Q22<<1GeV1GeV22
Considered subConsidered sub--processes:processes:LOLO--MC: PYTHIA 6.2MC: PYTHIA 6.2
0
0.1
0.2
0.3
6060SFU, VanCouver, March 2007SFU, VanCouver, March 2007EE.C. Aschenauer.C. Aschenauer
(PGF)qq→g*γqg→q*γ
q→q*γ
qq’→qq’qg→qggg→gg
Tlow p
(PGF)qq→g*γqg→q*γ
q→q*γ
qq’→qq’qg→qggg→gg
Tlow p
0
0.1
0.2
0.3
used for used for ∆∆∆∆∆∆∆∆g/g extractiong/g extraction
∆∆∆∆∆∆∆∆g/g=0.016g/g=0.016±±0.058(stat.)0.058(stat.)±±0.055(syst.)0.055(syst.)0.070.0350.085gx ++++
−−−−==== µµµµµµµµ22=3.0GeV=3.0GeV22
10-510-410-310-210-11
ed→h+Xdσh /d
p T (
µb/G
eV)
HERMES Preliminary
PYTHIADeuteron Data, e± not in acc.
ed→h-X
0.20.40.60.8
11.2
0 0.5 1 1.5 2
LO MC
σMC/σ
Dat
a
0 0.5 1 1.5 2
pT(beam) (GeV)
10-510-410-310-210-11
ed→h+Xdσh /d
p T (
µb/G
eV)
HERMES Preliminary
PYTHIADeuteron Data, e± not in acc.
ed→h-X
0.20.40.60.8
11.2
0 0.5 1 1.5 2
LO MC
LO MC×k-Factor
σMC/σ
Dat
a
0 0.5 1 1.5 2
pT(beam) (GeV)
Cross Section DataCross Section Data--MCMCHERMES cross section:HERMES cross section:kkTT, p, pT T standard values:standard values:
, 0.40pTk GeVγγγγ ==== 0.40frag
Tp GeV====M.Anselmino et al. Phys. Rev. D71,074006M.Anselmino et al. Phys. Rev. D71,074006
2 20.25 20%tk GeV= ±= ±= ±= ± 2 20.20 20%tp GeV= ±= ±= ±= ±
6161SFU, VanCouver, March 2007SFU, VanCouver, March 2007EE.C. Aschenauer.C. Aschenauer
10-510-410-310-210-11
ed→h+Xdσh /d
p T (
µb/G
eV)
HERMES Preliminary
PYTHIADeuteron Data, e± not in acc.
ed→h-X
0.20.40.60.8
11.2
0 0.5 1 1.5 2
LO MC
σMC/σ
Dat
a
0 0.5 1 1.5 2
pT(beam) (GeV)
10-510-410-310-210-11
ed→h+Xdσh /d
p T (
µb/G
eV)
HERMES Preliminary
PYTHIADeuteron Data, e± not in acc.
ed→h-X
0.20.40.60.8
11.2
0 0.5 1 1.5 2
LO MC
LO MC×k-Factor
σMC/σ
Dat
a
0 0.5 1 1.5 2
pT(beam) (GeV)hephep--ph/0505157ph/0505157
2000
4000
COMPASS standard values:COMPASS standard values:
0.50Tk GeVγγγγ ====
0.36fragTp GeV====
1.00pTk GeV====
Cross Section Data Cross Section Data -- MCMC
6262SFU, VanCouver, March 2007SFU, VanCouver, March 2007EE.C. Aschenauer.C. Aschenauer
2000
[GeV/c]T
p0 1 2 3
1
2
hephep--ph/0505157ph/0505157
=q1h −=q
1g −=q1f
{ } +++=Φ nxhxgxfx T1
5151L1Tw2Corr Sγγ)(γ)(S)(
2
1)(
The 3The 3rdrd TwistTwist--2 structure function 2 structure function
6363SFU, VanCouver, March 2007SFU, VanCouver, March 2007EE.C. Aschenauer.C. Aschenauer
longitudinally polarizedlongitudinally polarizedquarks and nucleonsquarks and nucleons
∆∆∆∆∆∆∆∆q(x): helicity differenceq(x): helicity difference
�������� axial chargeaxial charge
knownknown
unpolarised quarksunpolarised quarksand nucleonsand nucleons
q(x): spin averagedq(x): spin averaged
�� vector chargevector charge
well knownwell known
transversely polarizedtransversely polarizedquarks and nucleonsquarks and nucleons
δδδδδδδδq(x): q(x): helicity fliphelicity flip
�������� tensor chargetensor charge
measuring!measuring!
=q1h −
{ } +++=Φ nxhxgxfx T1
5151L1Tw2Corr Sγγ)(γ)(S)(
2
1)(
Peculiarities of transversityPeculiarities of transversity
chiral odd chiral odd FFFF
relativistic nature of quarkrelativistic nature of quark : : in absence of relativistic effects hin absence of relativistic effects h 11(x)=g(x)=g11(x)(x)
QQ22 ––evolutionevolution : unlike for g: unlike for g 11pp(x), (x),
the gluon doesn’t mix with quark inhthe gluon doesn’t mix with quark inh 11pp(x)(x)
6464SFU, VanCouver, March 2007SFU, VanCouver, March 2007EE.C. Aschenauer.C. Aschenauer
transversely polarizedtransversely polarizedquarks and nucleonsquarks and nucleons
δδδδδδδδq(x): q(x): helicity flip helicity flip
�������� tensor chargetensor charge
measuring !measuring !single helicity
flip
CHIRAL ODD CHIRAL ODD NOT ALLOWED IN NOT ALLOWED IN
E.M. E.M. INTERACTIONSINTERACTIONS
doubledoublehelicity fliphelicity flip
the gluon doesn’t mix with quark inhthe gluon doesn’t mix with quark inh 11 (x)(x)(no gluon analog for spin(no gluon analog for spin--½ nucleon)½ nucleon)
sensitive to the sensitive to the valence quark polarisationvalence quark polarisationq and q have opposite sign.q and q have opposite sign.
_
tensor charge:tensor charge: first moment of hfirst moment of h 11(large from lattice QCD)(large from lattice QCD)
first data for Collins FF first data for Collins FF available from Belleavailable from Belle
extraction of hextraction of h 11 fromfrom
1 ( )H z⊥
Collins momentsCollins moments
Collins moment:Collins moment:ππππππππ++ > 0 > 0 ππππππππ-- < 0< 0
ππππππππ-- unexpected largeunexpected largerole of unfavoured FFrole of unfavoured FF
[PRL94(2005),012002; hep-ex0507013]
-0.02
0
0.02
0.04
0.06
0.08
0.1
2 ⟨s
in(φ
+φS)⟩
π U
T
π+
-0.12
-0.1
-0.08
-0.06
-0.04
-0.02
0
0.02
0.1 0.2 0.3
2 ⟨s
in(φ
+φS)⟩
π U
T
π-
x0.2 0.3 0.4 0.5 0.6
z0.2 0.4 0.6 0.8 1
Ph⊥ [GeV]
IIIIIIHERMES PRELIMINARY 2002-2004virtual photon asymmetry amplitudes6.6% scale uncertainty
-0.1
0
0.1
0.2
0.3
0.4
2 ⟨s
in(φ
+φS)⟩
h U
T
K+
-0.4
-0.2
0
0.2
0.4
0.6
0.1 0.2 0.3
2 ⟨s
in(φ
+φS)⟩
h U
T
K-
x0.2 0.3 0.4 0.5 0.6
z0.2 0.4 0.6 0.8 1
Ph⊥ [GeV]
IIIIIIHERMES PRELIMINARY 2002-2004virtual photon asymmetry amplitudes6.6% scale uncertainty
6565SFU, VanCouver, March 2007SFU, VanCouver, March 2007EE.C. Aschenauer.C. Aschenauer
extraction of hextraction of h 11 fromfromHermes asymmetriesHermes asymmetries
2005 data:2005 data:2 dimensional binning2 dimensional binning
disentangle x (PDF) and disentangle x (PDF) and zz (FF) dependence(FF) dependence
-0.02
0
0.02
0.04
0.06
0.08
0.1
2 ⟨s
in(φ
+φS)⟩
π U
T
π+
-0.12
-0.1
-0.08
-0.06
-0.04
-0.02
0
0.02
0.1 0.2 0.3
2 ⟨s
in(φ
+φS)⟩
π U
T
π-
x0.2 0.3 0.4 0.5 0.6
z0.2 0.4 0.6 0.8 1
Ph⊥ [GeV]
IIIIIIHERMES PRELIMINARY 2002-2004virtual photon asymmetry amplitudes6.6% scale uncertainty
-0.1
0
0.1
0.2
0.3
0.4
2 ⟨s
in(φ
+φS)⟩
h U
T
K+
-0.4
-0.2
0
0.2
0.4
0.6
0.1 0.2 0.3
2 ⟨s
in(φ
+φS)⟩
h U
T
K-
x0.2 0.3 0.4 0.5 0.6
z0.2 0.4 0.6 0.8 1
Ph⊥ [GeV]
IIIIIIHERMES PRELIMINARY 2002-2004virtual photon asymmetry amplitudes6.6% scale uncertainty
KK++ > 0 K> 0 K-- > 0> 0KK++ in agreement with in agreement with ππππππππ++
)( Sφφ− angle of hadron relative to angle of hadron relative to initialinitial quark spin (Sivers)quark spin (Sivers)
)( Sφφ+ angle of hadron relative to angle of hadron relative to finalfinal quark spin (Collins)quark spin (Collins)
⊥⊗ 11 Hh (Collins)(Collins)
Azimuthal angles and asymmetriesAzimuthal angles and asymmetries
6666SFU, VanCouver, March 2007SFU, VanCouver, March 2007EE.C. Aschenauer.C. Aschenauer
)( Sφφ− initialinitial quark spin (Sivers)quark spin (Sivers)
1T1 Df ⊗⊥(Sivers)(Sivers) chiralchiral--even naïve Teven naïve T--odd DFodd DF
related to parton orbital related to parton orbital momentummomentum
violates naïve universality of PDFviolates naïve universality of PDF
peculiarity of fpeculiarity of f ⊥⊥⊥ ⊥⊥ ⊥⊥ ⊥1T1T
different sign of fdifferent sign of f ⊥⊥⊥ ⊥⊥ ⊥⊥ ⊥1T1T in DYin DY