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Transcript
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
12
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
15
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
16
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
18
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
19
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
20
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
21
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
22
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
23
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
24
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
26
M. Düren, Univ. Giessen
27
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)]
29
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
30
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
31
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
33