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Nucleon spin structure results
(from the HERMES experiment)
Michael Düren
Universität Gießen
— XII Conference on Hadron Spectroscopy, Frascati, Oct. 10, 2007 —
EMC 1988: Only 12±17% spin of the
proton is explained by the spin of the
u p - a n d d o w n - q u a r k s
Helicity sum rule:
Sz
 12 (u  Δd  Δs)  ΔG
q  ΔL g
  ΔL



proton
valence and sea gluon orbital angular
spin
spin
projection
quark
spin
momentum




 12
 
MS
a0= 
(theory)
(exp)
(evol)
= 0.330 ± 0.011 ± 0.025 ± 0.028
Remember: 1/3 of the
proton spin comes the from
q u a r k
s p i n
The Experiment:
* 1995
 2007
*)
proposed in ~1988 to solve the spin crisis
) plenty of beautiful data are waiting for being analyzed
Novel techniques: longitudinally polarized high energy
electron/positron beam at HERA
for beam-spin and beam-charge asymmetries
HERA electron beam
27.5 GeV (e+/e-)
<Pb>~ 53±2.5 %
M. Düren, Univ. Giessen
4
Novel techniques: The longitudinally and transverse
polarized internal gas target for double spin asymmetries
Storage cell target:
high polarization, no dilution
1H→
<|Pt|> ~ 85 %
2H→ <|P |> ~ 84 %
t
1H
M. Düren, Univ. Giessen
<|Pt|> ~ 74 %
5
Novel techniques: Dual radiator RICH for strangeness
THE HERMES
SPECTROMETER
• resolution:
dp/p~2%, dq<1 mrad
• PID: leptons with
e~98%, contam. <1%
hadronsp, K,p 2<Eh<15 GeV
M. Düren, Univ. Giessen
6
Novel techniques: Recoil detector for exclusive physics
Silicon Detector
● Inside beam vacuum
● 16 double-sided sensors
● Momentum reconstruction & PID
Scintillating Fiber Detector
● 2 barrels
● 2x2 parallel and 2x2 stereo layers
● 10° stereo angle
● Momentum reconstruction & PID
1 Tesla superconducting solenoid
Photon Detector
● 3 layers of tungsten/scintillator
●M.PID
for
higher
Düren,
Univ.
Giessenmomenta
● detects
7
Hot topics in spin physics:
•Moments and QCD-fits of PDFs
•Strange sea polarisation; SU(3)f
•Gluon spin
•Transverse spin effects (do not appear
in the helicity sum rule)
•Orbital angular momentum of quarks;
„3-D views“ of the proton; GPDs
M. Düren, Univ. Giessen
Polarized structure function g1p,d(x)
proton
deuteron
M.set
Düren,
Univ.
Giessen and complete
HERMES data
most
precise
in valence/sea overlap region
9
[PRD 75 (2007)]
First moment 1d
Deuteron data alone give  !
deuteron
[Q2>1 GeV2 data only]
deuteron
x
a8 from hyperon beta decay
MS
 =
theory
ωD=0.05±0.05
M. Düren, Univ. Giessen
theory
10
First moment 1d and 
Deuteron data alone give  !
MS
a0= 
(theory)
(exp)
[Q2>1 GeV2 data only]
(evol)
= 0.330 ± 0.011 ± 0.025 ± 0.028
Most precise result;
Consistent with other experiments
deuteron
x
a8 from hyperon beta decay
MS
 =
theory
ωD=0.05±0.05
M. Düren, Univ. Giessen
theory
11
q and G from inclusive data
NLO
1
g
( x)  g
LO
1
s 1
2
2
2

e
[

q(x,
Q
)

C


G
(
x
,
Q
)  Cg ]

q
q q
2p 2
•Valence quarks are
well determined:
uv >0, dv <0
• Gluons and sea
quarks are weakly
constrained by data
M. Düren, Univ. Giessen
SU(3)f flavor symmetry
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implicitly assumed!
Important remark on SU(3)f
and the polarization of strange quarks
 The violation of the Ellis-Jaffe sum rule means:
– either the strange quark polarization s is negative
– or SU(3)f flavor symmetry is broken
– or low-x region different than assumed in parameterizations
 Most analyses assume explicitly or implicitly SU(3)f flavor
symmetry (e.g. in parameterizations of the PDFs)
 Only semi-inclusive data can measure directly s
Kaon asymmetries
on deuterium
allow for the most direct
determination of s !
Final analysis is
in progress.
M. Düren, Univ. Giessen
13
Flavor separation
from semi-inclusive data
HERMES: Only direct 5-flavor
separation of polarized PDFs
Results (in short):
u
 u(x) is large and positive
 d(x) is smaller and negative
 s(x) is approx. zero
d
[PRL92(2004), PRD71(2005)]
strange
M. Düren, Univ. Giessen
14
How does spin flavor separation qf(x) work?
Principles:
Keep beam spin constant
and flip proton spin

Helicity conservation in polarized DIS: select specific quark spin orientation

Hadron tagging: select specific quark flavor

Matrix inversion brings you back from hadron asymmetries to quark spin
flavor distributions qf (purity formalism)
M. Düren, Univ. Giessen
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How does a direct gluon spin extraction work?
Principle:
 Large pT hadron pairs
come from photon gluon
fusion processes
 They carry information
of the gluon spin
However, other sub-processes make life hard:
+
+
M. Düren, Univ. Giessen
+ .. qg
q
q
g
g
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Measurement of gluon polarisation
HERMES: first measurement of gluon polarisation
[PRL 84 (2000)] TOPCITE 50+
Further analysis going on:
•Measurement of high pT pairs
•Separation of the subprocesses
•Two different methods
•Significant reduction of g uncertainty
•Still sign ambiguity at low x
For more details see talk
by Riccardo FABBRI
g/g=0.071 ± 0.034 ± 0.010 -0.105
M. Düren, Univ. Giessen
17
Transverse spin effects
There are two three leading-twist structure functions:
Quark density
Helicity distribution
Transversity
Interesting properties of transversity:
 QCD-evolution independent of gluon distribution
(to be tested by experiment)
 1st moment of dq is tensor charge (pure valence
object); value predicted by lattice QCD

M. Düren, Univ. Giessen
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Transversity is chiral odd (i.e.does
not contribute to inclusive DIS cross section!)
Transverse spin distribution of quarks
 The azimuthal angular distributions of hadrons from a
transversely polarized target show two effects:
– Collins asymmetry in sin(+s)
Target spin
– Sivers asymmetry in sin(-s)
M. Düren, Univ. Giessen
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Transverse spin distribution of quarks
 The azimuthal angular distributions of hadrons from a
transversely polarized target show two effects:
– Collins asymmetry in sin(+s)
Product of the chiral-odd
transversity distribution h1(x)
and the chiral-odd
fragmentation function H1(z)
 related to the transverse
spin distribution of quarks
First
results
from Belle
Target spin
– Sivers asymmetry in sin(-s)
M. Düren, Univ. Giessen
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Transverse spin distribution of quarks
 The azimuthal angular distributions of hadrons from a
transversely polarized target show two effects:
– Collins asymmetry in sin(+s)
Product of the chiral-odd
transversity distribution h1(x)
and the chiral-odd
fragmentation function H1(z)
 related to the transverse
spin distribution of quarks
First
results
from Belle
Target spin
– Sivers-Asymmetrie in sin(-s)
Product of the T-odd
distribution function f1T(x)
and the ordinary
fragmentation function D1(z)
 related to the orbital
angular momentum of quarks
M. Düren, Univ. Giessen
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Sivers function is related to
orbital angular momentum of quarks
quarks
photon
attractive final
state interaction
Side view
proton
photon

Proton with spin
out of this plane
right
left
photon
some go
left
photon
Right-left symmetric
M. Düren, Univ. Giessen
(M. Burkardt)
many go
right

Right-left SSA
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SSA for pions [PRL94(2005)]
Collins
Asiv (  S )  f1T ( x) D1 ( z )
Acoll (  S )  d q( x) H1 ( z )
•Significant non zero asymmetries
•Ap+>0, Ap-<0
•Evidence of

1,disf
H

1,fav
 H
Sivers
First measurement of naïve T-odd
distr. fkt. in DIS

M. Düren, Univ. Giessen
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π : Asinφ

0

L

0
UT
q
SSA for pions and kaons
Collins
Sivers
Acoll (  S )  d q( x) H1 ( z )
For more details see talk
by Luciano PAPPALARDO
Asiv (  S )  f1T ( x) D1 ( z )
Asiv(K+) > Asiv(p+)
Sea
M. Düren, Univ. Giessen
quarks may provide important
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contribution to Sivers function
General Parton Distributions
Quantum phase-space „tomography“ of the nucleon

Wigner introduced the first phase-space distribution in
quantum mechanics (1932)
The Wigner function contains the
most complete (one-body) info
about a quantum system.

A Wigner operator can be defined that describes quarks
in the nucleon; The reduced Wigner distribution is
related to GPDs
GPDs contain a
more complete info than
form factors or parton distributions
M. Düren, Univ. Giessen
25
Quarks in quantum mechanical phase-space
 Elastic form factors  charge distribution (space coordinates)
 Parton distributions  momentum distribution of quark
(momentum space)
 Generalized parton distributions (GPDs) are reduced Wigner
functions  correlation in phase-space  e.g. the orbital
momentum of quarks:
L  r p
 Angular momentum of quarks can be extracted from GPDs:
Ji sum rule:
Jq 
1
1
2 1


xdx H q ( x,  ,0)  Eq ( x,  ,0)

 GPDs provide a unified theoretical framework for many
experimental processes
M. Düren, Univ. Giessen
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M. Düren, Univ. Giessen
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Exclusive processes: The handbag diagram
Q2 large, t small
Q2
• high Q2  hard regime
• high luminosity  s~1/Q4, 1/Q6
• high resolution  exclusivity
t
Quantum number of final state selects different GPDs:
Vector mesons (r, w, ): H E
~ ~
Pseudoscalar mesons (p, h): H E
~ ~
DVCS (g) depends on H, E, H, E
 polarization provides new observables sensitive
to different (combinations of) GPDs
Deeply Virtual Compton Scattering (DVCS)

e p  e' p' γ
 /-
Beam Spin Asymmetry
s  sin  
e p  e' p' γ
Beam Charge Asymmetry
[PRL87(2001)] +100 top cite
M. Düren, Univ. Giessen
s  cos  
[PRD 75 (2007)]
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Hard exclusive meson production
e p  e’ n p+
[hep-ex/0405078,
arXiv 07070222 PLB submitted]
GPDs predictions:
Vanderhaeghen, Guichon &
Guidal [PRD 60 (1999)]
(LO and LO+ power corrections)
•
•
Model calculation:
Regge formalism, Laget
[PRD 70 (2004)]
• LO predictions + power correction to space like pion form factor
in agreement with magnitude of data
• Regge formalism for long. and transv. part of the cross section
provides good description of dependence of data
M. Düren, Univ. Giessen
 Information on pion form factor at high
Q2 and
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on polarised GPDs
Quark total angular momentum
AUT most sensitive observable to access Jq via GPDs
HERMES data 2002-04:
0709.0450[nucl-ex]
•U: unpolarized beam
•T: transv. pol. Target
• ~50% of total stat.
 Im[F2 Η  F1E]
GPD model by:
arXiv:0705.4295[hep-lat]
[Goeke et al. (2001)]
[Ellinghaus et al. (2005)]
hep-ex/0606061
first model dependent extraction of Ju & Jd possible
Düren, Univ. Giessen
VGG-Code: GPD-model:M.LO/Regge/D-term=0
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The HERMES recoil detector (2006-07)
 Installed Dec 05, commissioned
and successfully operated
 Dedicated to exclusive processes:
– Recoil proton detection
– High luminosity:
semi-incl.
2006: 7 M DIS events e20 M DIS events e+
2007: 20 M DIS events e+
exclusive
PID (first data)
missing mass
(from MC)
M. Düren, Univ. Giessen
For more details see 32
talk
by Tibor KERI
Conclusions
 1/3 of the proton spin comes from quark spin
 Direct measurements of the strange quark sea could not verify a
negative strange polarization. This indicates a SU(3)f flavor
symmetry breaking or large contributions from low x.
 Analysis of gluon spin from inclusive DIS is difficult and ongoing
 Transversity and Sivers functions are non-zero. Sivers
asymmetry for kaon data indicates an orbital angular momentum
contribution from sea quarks.
 DVCS beam charge and beam spin asymmetries
have been measured. First data of orbital angular
momentum (OAM) fits to GPD functions indicate
non-zero OAM of up-quarks
 HERMES has the potential of further discoveries
in spin physics with the new abundant recoil data!
M. Düren, Univ. Giessen
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