1DIS - Madrid, April 2009 E.C. Aschenauer
The Quest for the spin of the proton !or
“You think you understand something?Now add spin…” - R. Jaffe
Nobel Prize, 1943: "for his contribution to the development of the molecular ray method and his discovery of the magnetic moment of the proton" mp = 2.5 nuclear magnetons, ± 10% (1933)
Otto Stern Proton spins are used to image the structure and function of the human body
using the technique of magnetic resonance imaging.
Paul C. Lauterbur
Sir Peter Mansfield
Nobel Prize, 2003: "for their discoveries concerning magnetic resonance imaging"
The Spin of the Proton
E.C. Aschenauer
2DIS - Madrid, April 2009
3DIS - Madrid, April 2009
How do the partons contribute
E.C. Aschenauer
SqDq
DG
Lg
SqLq
dq1Tf
SqDq
DG
Lg
SqLq dq1Tf
Is the proton looking like this?
“Helicity sum rule”
12h= P,12 |JQCD
z |P,12 = 12q
∑ Sqz+Sgz+ Lqzq∑ +Lgz
total u+d+squark spin
angular momentum
gluonspin Where do we stand
solving the “spin puzzle” ?
Dq & DG contributions to the proton spin
E.C. Aschenauer
4DIS - Madrid, April 2009
γ*
u,d,s,gpolarized DISSqDq, DG
γ*
u,d,s
p,K
polarized SIDISDqf
polarized pp scattering
Dqf, DG
u,d,s,g
u,d,s,gu,d,s,g
p,Kjet
Existing data from:
to extract polarized PDFs! a “global QCD analysis” is required !
all processes tied together: universality of pdfs & Q2 – evolution
each reaction provides insights into different aspects and kinematics
in NLO DSSV PRL101:072001,2008
Inclusive World data
5DIS - Madrid, April 2009 E.C. Aschenauer
new
: input to the old GRSV-analysis: input to the DIS & SIDIS – analysis by DNS
Inclusive DIS-Data:
Semi-Inclusive World Data
6DIS - Madrid, April 2009 E.C. Aschenauer
not in DNS Semi-inclusive DIS-Data:
7DIS - Madrid, April 2009 E.C. Aschenauer
includes all world data from DIS, SIDIS and pp Kretzer FF favor SU(3) symmetric sea, not so for KKP, DSS DS ~25-30% in all cases
D. De Florian et al. arXiv:0804.0422 NLO @ Q2=10 GeV2
NLO FIT to World Data
KretzerKKP
c2DIS c2
SIDIS Duv DuDdv Dd Ds Dg DS
206206
225231
0.940.70 -0.26
-0.340.087-0.049
-0.11-0.055
-0.045-0.051
0.310.28
DSSV 0.813 -0.458 0.036 -0.115 -0.057 0.242
Polarized Strangeness
8DIS - Madrid, April 2009 E.C. Aschenauer
Driven by SIDISK-AsymmetriesK-FFdominated by
Driven bySU(3); (3F-D)
New Results from
isoscaler method AK++K- & Aincl
“Purity” Method using FFInput : A1,d , A1,d
p +
, A1,dp−
, A1,dK+
, A1,dK−
Results are completely consistent with Hermessea quark polarizations ~ 0
9DIS - Madrid, April 2009 E.C. Aschenauer
More on Strangeness PDF Kaon multiplicities from Deuterium target
strange quark sea in proton and neutron identical fragmentation simplifies
Only assumptions used: isospin symmetry between proton and neutron charge-conjugation invariance in fragmentation
.( ) 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
DiseQ x D z dz S x D z dzdN x dx
dN x dx Q x S x- +
=+
Fit x-dependence of multiplicitiesusing PDFs from CTEQ-6
dotted:CTEQ-6L & fit ( )K
SD z dz( )K
QD z dzdashed:
solid:S(x)=Q(x): CTEQ-6L & DSS
1 2/ (1 )a x ax e x- - -
s(x) + sbar(x)
dashed-dotted:
€
D sK(z )dz
The Gluon Polarization
10DIS - Madrid, April 2009 E.C. Aschenauer
unpolarised cross sections nicely reproduced in NLO pQCD
in NLO
RHIC: many sub-processes with a dominant gluon contribution high-pT jet, pion, heavy quark, …
RHIC Data
11DIS - Madrid, April 2009 E.C. Aschenauer
STARGRSV curves with cone radius 0.7 and -0.7 < < 0.9
2005 jet data: PRL 100, 232003 (2008)
2005: PRD 76, 051106
2006: arXiv:0810.0694
p0 @ 200 GeV
The Gluon Polarization
12DIS - Madrid, April 2009 E.C. Aschenauer
x RHIC range0.05· x · 0.2
small-x0.001· x · 0.05
large-xx ¸ 0.2
Dg(x) very small at medium x best fit has a node at x ~ 0.1 huge uncertainties at small x
small-x behavior completely unconstrained
Dg(x) small !?Dg(x) dx
0.
1
∫ = −0.084@10GeV 2
d g = Δg(x,10GeV 2 ) dx0.05
0.2
∫
13DIS - Madrid, April 2009 E.C. Aschenauer
Compass & Hermes: The golden channels for Dg
Idea: Direct measurement of DGIsolate the photon gluon fusion process
detection of hadronic final states charmed mesons high pT pairs of hadrons
single high pT hadronsh±h±
h±
2 1Q 2 0.1Q
2 0.1Q 2 0.1Q
less sub-processes contributing more sub-processes contributing
higher statistics
less sub-processes contributing more sub-processes contributing
higher statistics + + + ..
|||| ||| |( ) ;B SigSig
gmeas i it i i
i tB
tog f AA p f A ff A
s= = + =
s
|| ||ˆ]1 [ meas
Sig
BgBgf
GA
aAG
f-
D=
Several possible contributions to the measured asymmetryMC needed to determine R and aLL
q
g
q
g qg
Important at Q2<0.1
h±h± vs. h±: h± more inclusive → pQCD NLO calculations (easier) possible
Dg from electro production
14DIS - Madrid, April 2009 E.C. Aschenauer
DSSV gluon agrees well with model-dependent “LO” extractions of Dg/g
not in global fit[NLO not available]
a future global NLO fit will use measured ALL not derived Dg/gneed first to check unpolarized cross section
15DIS - Madrid, April 2009
Beyond form factors and quark distributions
E.C. Aschenauer
Generalized Parton Distributions
Proton form factors, transverse charge & current densities
Structure functions,quark longitudinalmomentum & helicity distributions
X. Ji, D. Mueller, A. Radyushkin (1994-1997)
Correlated quark momentum and helicity distributions in transverse space - GPDs
How to access GPDs?quantum number of final state selects different GPDs: theoretically very clean DVCS (g): H, E, H, E VM (r, w, f): H E info on quark flavors PS mesons (p, ): H E ~
~ ~
~
ρ0 2u+d, 9g/4ω 2u-d, 3g/4f s, g
ρ+ u-d
J/ψ g
p0 2Du+Dd 2Du-Dd
Jq
z =12
xdx H q + E q( )−1
1
⎛⎝
⎞⎠t→ 0
J q
z =12
Dqq∑ + Lq
z
q∑
12=Jq
z + Jgz =
12
Dqq∑ + Lq
z
q∑ + Jg
z
E.C. Aschenauer
16DIS - Madrid, April 2009
W & t dependences: probe transition from soft hard regime
VM production @ small x
r f J/YU
s ~ Wd
steep energy dependence of s in presence of the hard scale
s ~ e-b|t|
universality of b-slope parameter: point-like configurations dominate
E.C. Aschenauer
17DIS - Madrid, April 2009
18DIS - Madrid, April 2009 E.C. Aschenauer
HERMES / JLAB kinematics: BH >> DVCS
Deeply Virtual Compton Scattering DVCS
two experimentally undistinguishable processes:
DVCS Bethe-Heitler (BH)
p + D
( )* 2 2*~ | | | |BH DVCS DVC BS HB DVCSHd t t + t ts + t + t
isolate BH-DVCS interference term non-zero azimuthal asymmetries
€
ds / dpe dΩe dΩg(pb / GeV sr2 )
H, %H, E, %Emost clean channel for interpretation in terms of GPDs
can measure DVCS – cross section and I
19DIS - Madrid, April 2009 E.C. Aschenauer
HERMES: combined analysis of charge & polarization dependent data separation of interference term + DVCS2
DVCS
Beam Charge Asymmetry
~ Ac(n=0)cosΦ
~ Re[F1H]
higher twist
higher twist
s LU (Φ, Pl ,el ) = σ UU (Φ){1 + Pl ALUDVCS (Φ) + el Pl ALU
I + el AC (Φ)}
snI sin(nΦ)
n=1
2
∑ cnI cos(nΦ)
n=1
3
∑Beam Spin Asymmetry
~ Im[F1H]
DVCS
DVCS from &
20DIS - Madrid, April 2009 E.C. Aschenauer
Archiv: 0812.2517
only some appetizers on existing data lets see what theory says
Hermes BCA CLAS BSA
Hall A Hall A
different GPD parametrisations
Results from Theory
21DIS - Madrid, April 2009 E.C. Aschenauer
cont
ribu
tion
to
nucl
eon
spin
mp2 GeV2
LHPC Collab. hep-lat/0705.4295
Lattice:K. Kumericki & D. MuellerarXiv: 0904.0458
t=0
t=-0.3
First hints for a small Jq Lq
More insights to the proton - TMDs
22DIS - Madrid, April 2009 E.C. Aschenauer
Unpolarized distribution function q(x), G(x)
Helicity distribution function Dq(x), DG(x)
Transversity distribution function dq(x)
kr⊥q
Correlation between and rs⊥q
kr⊥q
Correlation between and rS⊥
N
Correlation between and rs⊥q
rS⊥
N
Sivers distribution functionf1T⊥
Boer-Mulders distribution functionh1⊥
Single Spin Asymmetries
Explore spin orbit correlations
peculiarities of f1T
chiral even naïve T-odd DFrelated to parton orbital
angular momentumviolates naïve universality of
PDFsQCD-prediction: f1T,DY = -f1T,DIS
Transverse Polarization Effects @ RHIC
23DIS - Madrid, April 2009 E.C. Aschenauer
Left-Right
Naive pQCD (in a collinear picture) predicts AN ~ mq/sqrt(s) ~ 0
However, large AN observed in forward pions / Kaons.
Proposed mechanisms - Sivers - Collins - twist-3 process - ...need correlations between particles (g-jet)to disentangle underlying process
Boer-Mulders
24DIS - Madrid, April 2009 E.C. Aschenauer
dsdxdydzdΦdP⊥
2 =2p a2
xyQ2y2
2(1−e)(1+ g2
2x)[ΦUU,T + 2e(1+e)cosΦΦUU
cosΦ +e cos(2Φ)Φuucos(2Φ)]Unpol. SIDIS cross section:
Boer-Mulders x Collins FF
remember Collins FF:H1fav⊥ (z)=−H1unfav
⊥ (z)
Boer-Mulders fct. for u and d quark seem to have same sign consistent with Fermi-lab DY-experiments E605++
h1,u⊥ =1d
⊥
K+ > 0 K- ~ 0 K+ > p+
importance of sea quarks? Deuterium ~ 0
u and d quark cancel
25DIS - Madrid, April 2009 E.C. Aschenauer
HERMES & COMPASS Measurements
ASivers ∝ f1T (x)D1(z)
Proton
Proton: Sivers moment:
p+ > 0 p- ~ 0
hep-ex/0802.2160Deuterium
Fit M. Anselmino et al. arXiv:0805.2677
Sivers function and OAM
26DIS - Madrid, April 2009 E.C. Aschenauer
Anselmino et al. arXiv:0809.2677
Model dependent statement:
(1−x)f1T⊥q(x)=−3
2MCΦasEq(x,0,0)
dx0
1
(1−x)f1T⊥q(x)=−32MCΦasκ q
anomalous magnetic moment:κu = 1.67κd = -2.03
x
Sivers fct. from fit to M. Burkardt et al.
Lattice: P. Haegler et al.lowest moment of distribution of unpol. q in transverse pol. protonand of transverse pol. quarks in unpol. proton
Conclusions
27DIS - Madrid, April 2009 E.C. Aschenauer
many avenues for further important measurements and theoretical developments
we have just explored the tip of the iceberg
you are here
Lq,g
DsDg
Dutot, Ddtot
Du, Dd
spin sum ruleThank you for your attention &to everybody, who helped preparing the talk, especially Werner and Marco
28DIS - Madrid, April 2009 E.C. Aschenauer
BACKUP SLIDES
29DIS - Madrid, April 2009 E.C. Aschenauer
good agreement with NLO-QCDPolarised opposite to proton spin
Polarized Quark Densities
Du(x) > 0
First complete separation of pol. PDFs without assumption on sea polarization
Polarised parallel to proton spinDd(x) < 0
Du(x), Dd(x) ~ 0 No indication for Ds(x) < 0 In measured range (0.023 – 0.6)
0.002 0.043uD =- 0.054 0.035dD =- 0.028 0.034sD =+
DSS: good global fit of all e+e-, ep, and pp hadron data
30DIS - Madrid, April 2009 E.C. Aschenauer
de Florian, Sassot, MSmain results:• results for p, K±, chg. hadrons• full flavor separation for Di
H(z) and DgH
• uncertainties (L.M.) well under control• fits all LEP, HERMES, SMC, RHIC, … data • supersede old fits based only on e+e- data
apart from cross-over trajectory (x=x) GPDs not directly
accessible: deconvolution needed ! (model dependent)
but only x and t accessible experimentally ),,( txH x
x is mute variable (integrated over):
GPD moments cannot be directly revealed,
extrapolations t 0 are model dependent +
++
-
1
1
),,(~ dxixtxHT DVCSex
x+
-
+-
1
1
),,(),,(~ tHidxx
txHP xxpxxe.g.
cross sections & beam-charge asymmetry ~ Re(T
DVCS )
beam or target-spin asymmetries ~ Im(T DVCS )
accessing GPDs: some caveats
t=0 q(x)x=0 q(x)
E.C. Aschenauer
31DIS - Madrid, April 2009
detour: DSS kaon FF’s DiK(z)
32DIS - Madrid, April 2009 E.C. Aschenauer
RHIC pp data (BRAHMS,STAR) explain different Dg
smaller u & larger s-frag. required by SIDIS
note: some issues with K- data (slope!)await eagerly final HERMES data
33DIS - Madrid, April 2009 E.C. Aschenauer
DsUT ~ sinf∙Im{k(H - E) + … }
DsC ~ cosf ∙Re{ H + xH +… }~
DsLU ~ sinf∙Im{H + xH + kE}~
DsUL ~ sinf∙Im{H + xH + …}~
polarization observables:
DsUT
beam target
kinematically suppressed
H
H
H, E
~
different charges: e+ e- (only @HERA!):
H
DVCS ASYMMETRIES
x = xB/(2-xB ),k = t/4M2
( )* 2 2*~ | | | |BH DVCS DVC BS HB DVCSHd t t + t ts + t + t
34DIS - Madrid, April 2009 E.C. Aschenauer
[M. Burkardt, M. Diehl 2002]FT (GPD) : momentum space impact parameter space:
probing partons with specified long. momentum @transverse position b
T
polarized nucleon:
[x=0]
from lattice
What does theory tell
d-quarku-quark
35DIS - Madrid, April 2009 E.C. Aschenauer
Hermes: Charge and Beam Spin Asymmetry Heavy Targets
Beam Charge Asymmetry
Beam Spin Asymmetry
Why nuclear DVCS: constrain nuclear GPDs constrain models attempting
to describe nuclear matter neutron and proton matter distribution in nuclei
Beam: 27.5 GeV e±; <50>% polarizationTarget: (un)-polarized gas targets; <85%> polarizationLumi: pol: 5x1031 cm-2/s-1; unpol: 3x1032-33 cm-2/s-1
Data taking finished June 2007
36
The contemporary experiments
E.C. Aschenauer
DIS - Madrid, April 2009
SM1
SM2
6LiD Target
160 GeV μ
RICH
ECal & HCalμ Filter
Trigger-hodoscopes
SiliconMicromegas
SciFi
Gems
Drift chambers
StrawsMWPC
50 m
Beam: 160 GeV m: 80% polarizationTarget: 6LiD: 50% polarization (2002-2006) NH3: 80% polarisation (2007)Lumi: 5x1032 cm-2s-1
STAR Detector
Beams: √s=200 GeV pp; 50% polarizationLumi: 50 pb-1