Nucleon Spin Structure
30 Years of Experiment:
What have we learned?
M. Grosse Perdekamp, University of Illinois and RBRC
Overview
o Scientific Motivation and Early Beginnings
The Rabi School of Physics
The SLAC – Bielefeld -- Tsukuba – Yale Collaboration
Modern Experiments
o Nucleon Helicity Structure
Quark spin ΔΣ
Gluon spin ΔG
Orbital angular momentum Lz  GPDs !
o Transverse Spin
Transverse spin in hard scattering QCD
Transversity and Collins Quark Fragmentation
The Sivers Effect
June 6 th
Nucleon Spin Structure
2
Scientific Motivation: Proton Structure
Including Spin Degrees of Freedom
Constituents:
quarks = u, d, s and gluons

Quark
Spin : distributi on
q( x )Total
 quark
momentum


q(x)  q (x) - q (x)
  
x 1
q (x)

spin dependent quark distributi on
q ,q x 0
 Total Gluon Spin :
x
June 6 th
pquark
G(x)  G  (x) - G (x) x 1
spin dependent
distributi
G gluon
G
(x) on

x 0
p proton
Nucleon Spin Structure
3
Proton Spin Structure from Inclusive Deep
Inelastic Lepton-Nucleon Scattering
spin
Large Q2: measure photon-quark
absorption cross section double
spin asymmetry
spin
electron or
muon probe
q
ALL
 A1 
proton target
Extract spin dependent quark
distribution functions from the
spin structure function g1(x,Q2)
 q   q
 q   q
 g1 ( x, Q 2 )
g1 ( x, Q 2 )  q ( x)  q  ( x)  q  ( x)
1
     q ( x)dx
at Q 02
q ,q 0
June 6 th
Nucleon Spin Structure
4
The Rabi School of Physics
N. F. Ramsey, Eur. J. Phys. 11 (1990) 137
J. Rigden, Physics World, Nov. 1999
(I) Molecular beam laboratory at Columbia University
with strong emphasize on the development of new
experimental technology.
Rabi, Nobel Prize 1944
(II) Field new, precise instrumentation to study
fundamental questions of physics.
Example: Precision Measurements of “Hydrogen Spin Structure”
June 6 th
g-2 of the electron, P. Kusch
Lamb shift, W. E. Lamb
Nobel Prize 1955
Dirac Theory  QED
Tomonaga, Schwinger,
Feynman
Nobel Prize 1965
Nucleon Spin Structure
5
SLAC: Quark Structure of the Proton
New instrumental method & fundamental physics !
Experiment:
Deep inelastic electron
nucleon scattering
Quantum
Chromo Dynamics
Nucleon
Theory:
quark structure of
hadrons, QCD
June 6 th
Friedman,
Kendall, Taylor
Nobel Prize 1990
Nucleon Spin Structure
Gell Mann
Nobel Prize 1969
also Nakano, Nishijima
6
Polarized Deep Inelastic Scattering
a contribution from the Rabi School of Physics !
(I) Molecular beam technology as starting point
for the development of polarized electron
beams at Yale starting 1959.
(II) Physics:
(a) Proton spin structure
(b) Test the Bjorken sum rule as
fundamental QCD prediction
Experiments E80+E130 at SLAC
Bielefeld – CUNY – SLAC –
Nagoya – Tsukuba – Yale
(Coward, Kondo, Hughes)
EMC experiment at CERN
(Gabathuler, Sloan, Hughes)
June 6 th
Nucleon Spin Structure
Vernon W. Hughes
7
The Quark Spin Contribution ΔΣ
Quark Spin Contribution to the Proton Spin.
SLAC: 0.10 < xSLAC <0.7
CERN: 0.01 < xCERN <0.5
A1(x)
First Thesis on Nucleon Spin
Structure E80/Yale, 1977:
Noboru Sasao
0.1 < xSLAC < 0.7
SLAC CERN  0.07  0.05  0.1
EMC, Phys.Lett.B206:364,1988
1338 citations in SPIRES
0.01 < xCERN < 0.5
“Proton Spin Crisis”
x-Bjorken
June 6 th
Nucleon Spin Structure
8
Nucleon Spin Structure:
30 Years of Experiment
Quark Spin – Gluon Spin – Transverse Spin – GPDs – Lz
SLAC
2000
CERN
ongoing
E80-E155
EMC,SMC
FNAL
COMPASS
E704
1995
DESY
HERMES
2007
JLAB
Halls A, B, C
ongoing
RHIC
BRAHMS, PHENIX, STAR
ongoing
major experimental innovations
DIS
semi inclusive + exclusive processes, luminosity
polarized pp
polarized proton beams, polarized proton collider
June 6 th
Nucleon Spin Structure
9
A novel experimental method: Probing Proton Spin
Structure in High Energy Polarized Proton Collisions
Instrumentation
Absolute Polarimeter (H jet)
Siberian Snakes
RHIC pC Polarimeters
High current polarized proton source
BRAHMS & PP2PP
High energy
proton polarimetry
PHOBOS
Control of spin coherence
during
acceleration + storage
Siberian Snakes
RHIC Spin
Instrumentation
Spin sorted luminosity
measurements
Development
1995-2005
Spin Flipper
PHENIX
Physics
STAR
Spin Rotators
Helical Partial
Partial
Snakecharge
Probes directly sensitive to
color
Snake
Strong Snake
Polarized
Source
Utilize
Parity violation
in W-production
Large Q2  clean pQCD interpretation
US-Japanese collaboration at
LINAC
200 MeV Polarimeter
AGS
BOOSTER
Brookhaven National Laboratory
RIKEN Radiation Laboratory
RIKEN BNL Research Center
Rf Dipole
AGS pC Polarimeter
June 6 th
Nucleon Spin Structure
RHIC SPIN: Proton Structure with
Quark and Gluon Probes
at ultra-relativistic energies
the proton represents a jet
of quark and gluon probes
For example, direct photon production
~ probe gluon content with quark probes
quark
gluon
The related double spin asymmetry:

photon
quark
ALL 

N  N
N   N 
G ( x1 )
 aLL (qg  q ) 
 A1 ( x2 )
G ( x1 )
pQCD
June 6 th
experimental double
spin asymmetry
Nucleon Spin Structure
?
DIS
11
Nucleon Helicity Structure
Quark spin ΔΣ , Δq(x)
Gluon spin ΔG(x), ∫ ΔG(x)dx
Orbital angular momentum
Lz  GPDs ?
Inclusive Measurements of g1p, g1d and g1n
S. Paul, X. Lu, H. Gao, INPC 2007
Proton
Neutron
HERMES
ΔƩ = 0.33 ± 0.011(th) ± 0.025 (exp) ± 0.028 (evo) at 5 GeV2
COMPASS
ΔƩ = 0.35 ± 0.03 (stat) ± 0.05 (syst) at 3 GeV2
Bjorken sum
June 6 th
0.1821 ∓ 0.0019 (NNNLO)
Nucleon Spin Structure
13
Semi-Inclusive DIS: e+p  e+ h +X
Quark & Anti-Quark Helicity Distributions
[HERMES, PRL92(2004), PRD71(2005)]
xΔu(x)
Future:
uPrecision
quarks large
polarization
DIS positive
at JLAB-12
and at a
electron
– ionpolarization
collider!
dpossible
quark have
negative
Howquarks
well do(u,
wed,know
hadron
sea
s ,s) compatible
with 0
fragmentation
functions
in
the measured
x-range?0.02 < x < 0.6.
xΔd(x)
 new analysis of e+e- data,
Hirai, Kumano, Nagai, Sudo
hep-ph/0612009, INPC 2007
u  -0.002  0.043

Possible Improvements
 d  -0.054  0.035
 s   0.028  0.034
xΔu(x)
 include e-p, p-p and e+e- in fragmentation
function analysis  done!
De Florian, Sassot, Stratmann
hep-ph/0703242
xΔd(x)
xΔs(x)
June 6
th
 “add data” from b-factories e+e-  hadrons
x
Nucleon Spin Structure
14
Possible Impact on the Knowledge of
Hadron FFs from Analysis of b-Factory Data
Compilation of data
available for the charged hadron FF
FF
Belle MC: Charged h+/-, pions, kaons, protons
FF
Belle MC
Input for precision
measurements of quark
helicity distributions in
SIDIS, with JLab-12 and
a possible future electronpolarized proton collider.
<1% of data sample
work in progress
June 6 th
Eh
z
s /2




h+,pions
kaons
protons
precision
at high z!
z
Nucleon Spin Structure
15
Another Alternative:
W-production at RHIC
Hermes – 243 pb-1
SIDIS:
large x-coverage
uncertainties from
knowing fragmentation
functions
PHENIX – 800 pb-1
Ws in polarized p-p:
limited x-coverage
high Q2  theoretically
clean
no FF-info needed
June 6 th
Nucleon Spin Structure
16
Gluon Spin Contribution ΔG(x)
gP1(x,Q2)
from scaling violation of world g1(x,Q2):
Hirai, Kumano, Saito
Phys.Rev.D74:014015,2006
ΔG=∫ΔG(x) dx = 0.47 ∓ 1.08 , Q2=1GeV2
June 6 th
Nucleon Spin Structure
17
Gluon Polarization from
Photon Gluon Fusion in DIS
S. Paul, X. Lu
INPC 2007
“direct” measurements
• golden channel: charm production
• hadron production at high PT
Photon-Gluon Fusion
(PGF)
Favors small ΔG(x≈0.1)
June 6 th
Nucleon Spin Structure
18
Gluon Polarization from Inclusive
Hadrons and Jets in Polarized pp
K.Aoki,
R. Fatemi,
B. Surrow
INPC 2007
2005 data
ALL also for p , p , J/Y
June 6 th
Nucleon Spin Structure
19
Gluon Polarization from Inclusive
Hadrons and Jets in Polarized pp
 2006: 7.5 pb-1 @ 60% polarisation
projections
June 6 th
Nucleon Spin Structure
20
NLO QCD Analysis of DIS A1 + ALL(π0)
Hirai, Kumano, Saito
Phys.Rev.D74:014015,2006
DIS A1 + ALL(π0)
ACC03
 G ( x )dx

DIS A1  ALL (p 0 )
0.31  0.32
0.27  0.07
DIS A1
0.47  1.08
0.25  0.10
AAC03
0.5  1.27
0.21  0.14
x
DIS +DIS
pp ∫ΔG(x) dx = 0.31
Only
0.47 ∓ 0.32
1.08 , Q2=1GeV2
June 6 th
Nucleon Spin Structure
21
PHENIX π0 ALL vs GSA-LO and GSC-NLO
ALL
PHENIX-2005
GSA-LO: ΔG = ∫ΔG(x)dx = 1.7
GSA-LO and GSC-NLO
courtesy Marco Stratmann
and Werner Vogelsang
GSC-NLO: ΔG = ∫ΔG(x)dx = 1.0
GSA-LO
GSC-NLO
Large uncertainties resulting
from the functional form used
for ΔG(x) in the QCD analysis!
pT[GeV]
June 6 th
Nucleon Spin Structure
22
ΔG(x) A, B and C from Gehrmann Stirling
Much of the first moment
ΔG = ∫ΔG(x)dx might
emerge from low x!
present
x-range
Some theoretical
guidance:
ΔG(x) ≤ x G(x)
but G(X) diverges faster
than x-1 !
NEED TO EXTEND
MEASUREMENTS TO
LOW x !!
June 6 th
Nucleon Spin Structure
23
Next Steps for ΔG(x) at RHIC
Increase integrated luminosity by factor 10
(2008)
Extend measurements to low x
 Di-hadron Production extends
measurements to x  0.01
(2008)
NLO treatment available:
Marco Stratmann -- INPC 2007
(EMC forward calorimeters available
in STAR and PHENIX!)
Forward detector upgrades for direct
photons and heavy flavor + electron cooling
(2011)
reach x  0.001
Polarized Electron Ion Collider
measure ΔG(x) through scaling violations
June 6 th
Nucleon Spin Structure
24
Generalized Parton Distributions
vs Orbital Angular Momentum ?
GPDs Hu, Hd, Eu, Ed provide access to total quark
contribution to proton angular momentum in exclusive
processes l + N  l’ + N + γ
½ = ½ (u+d+s) + Lq + Jg
Proton spin sum
Jq
J
q

1
xdx [H q( x , x , 0 )  E q( x , x , 0 )]

2
1
1
X. Ji, Phy.Rev.Lett.78,610(1997)
June 6 th
Nucleon Spin Structure
25
First Model Dependent Constraint of Ju vs Jd
E. Burtin, P. Bertin, X. Lu, INPC 2007
June 6 th
Nucleon Spin Structure
26
Transverse Spin
Transverse spin in hard scattering QCD
Transversity and Collins Quark Fragmentation
The Sivers Effect
Transverse Spin Phenomena in
Hard Scattering QCD
QCD: Asymmetries for transverse spin are small at
high energies (Kane, Pumplin, Repko, PRL 41, 1689–1692 (1978) )
Experiment
AN 
mq
4
example, mq  3MeV , s  20GeV
,
A

10
N
+
(E704, Fermi National Laboratory):
s
π
QCD
pp  
p Test
X !
π0
s  20 GeV
1  R  L
Observable : AN 
P R L
π-
Is QCD the correct theory
of the strong interaction?
June 6 th
Nucleon Spin Structure
28
Single Transverse Spin Asymmetries AN
M. Chiu
at √=62.4 GeV and 200 GeV
INPC 2007
√s=200 GeV STAR
√s=62.4 PHENIX and BRAHMS
AN
AN
STAR
xF
Large single spin asymmetries persist
at higher √s=62.4 and 200 GeV
June 6 th
Nucleon Spin Structure
xF
29
Inspect Factorized Expression for Cross Section

s p1
qi ( x1 )
Proton
Structure
q j ( x2 )
P2

p
fragmentation
process
x1P1
ij
a LL
x2 P2
hard scattering
reaction

Jet
Can initial and/or final state effects
generate large transverse spin
asymmetries? (ALL ~10-1)
pQCD
Proton Structure
3 
d
ˆ (qi q j  qk ql )
d 3  pp   p  X

 qi ( x1 , kq ,T )  q j ( x2 ) 
 FFqk .l ( z, ph,T )
dx1dx2 dz
dx1dx2
small spin
dependence
(aLL~10-4)
June 6 th
Nucleon Spin Structure
fragmentation
function
30
Transverse Spin in QCD: Two Solutions
(I) “Transversity” quark-distributions
and Collins fragmentation
Correlation between proton- und quark-spin
and spin dependent fragmentation
AN
π+
 q( x)  H1 ( z2 , k 2 )
Quark transverse
spin distribution
π0
Collins FF
π-
(II) Sivers quark-distribution
Correlation between proton-spin and
transverse quark momentum
q
1T
f
( x, k )  D ( z)
2

h
q
xF
Sivers distribution
June 6 th
Nucleon Spin Structure
31
Collins Effect in the Quarkfragmentation into the Final State

ss
q
π
q
Collins q
Effect
sq

pp 
h, p h
q

k
π
NL : pions to the left
q
Collins Effect:
Fragmentation of a
transversely polarized NL
AN =
quark q into spin-less
hadron h carries an NL
azimuthal dependence:


NR : pions to the right
- NR
+ NR

pp 

ph 
=0

 

 k  ph   s q
 sin 
June 6 th
Nucleon Spin Structure
32
Artru Model for Collins Fragmentation
A simple model to illustrate that spin-orbital angular
momentum coupling can lead to left right asymmetries
in spin-dependent fragmentation:
Proton spin
is pointing up!
String breaks and
a dd-pair with spin
1 is inserted.
L = -1
u-quark absorbs
photon/gluon and
flips it’s Spin.
June 6 th
π+ picks up L=-1 to
compensate for the
pair S=1 and is emitted
up.
Nucleon Spin Structure
33
Measurements of Quark Transversity Distributions
and Collins Fragmentation Functions (I) SIDIS
New HERMES results for Collins Asymmetries
Diefenthaler, DIS 2007, Lu INPC 2007
Collins Asymmetries in semiinclusive deep inelastic scattering
e+p  e + π + X
~ Transversity (x) x Collins(z)
AUT sin(s)
June 6 th
Nucleon Spin Structure
34
Measurements of Quark Transversity Distributions
and Collins Fragmentation Functions (II) e+eNew Belle Collins Asymmetries
Seidl, DIS 2007
PRELIMINARY
Collins Asymmetries in e+eannihilation into hadrons
e++e-  π+ + π- + X
~ Collins(z1) x Collins (z2)
j2p
Q

Ph 2
e-

Ph1
e+
A12 cos(12)
June 6 th
Nucleon Spin Structure
35
j1
First Extraction of Quark Transversity Distributions
and Collins Fragmentation Functions SIDIS + e+eFit includes:
HERMES SIDIS
+ COMPASS SIDIS
+ Belle e+e transversity dist.
+ Collins FF
Anselmino, Boglione, D’Alesio,
Kotzinian, Murgia, Prokudin, Turk
Phys. Rev. D75:05032,2007
June 6 th
Nucleon Spin Structure
36
The Sivers Effect
Sivers:
Correlation between the transverse spin of the
proton and the transverse momentum kT of
quarks and gluons in the proton (link to orbital
angular momentum?)
Sivers function:
proton
D. Sivers 1990
Sp
Observed asymmetry:
June 6 th
Sp
proton


( Pˆ  kT )  S P
q
2
AN  q( x1 )  f1T ( x2 , k  ) 
M
Nucleon Spin Structure
37
Sivers Asymmetries at HERMES
and COMPASS
implies non-zero Lq
p/
K/
June 6 th
Nucleon Spin Structure
38
Sivers Effect and Orbital Angular Momentum
M. Burkardt
>
June 6 th
Nucleon Spin Structure
39
The Sivers Effect : Needs Final
State Soft Gluon Exchange
M. Burkardt
June 6 th
Nucleon Spin Structure
40
What have we learned from this?
The Sivers effect arises from soft gluon interactions in the
final state (SIDIS) or initial state (Drell Yan).
Need to modify naïve concepts of factorization which
reduce hard scattering to partonic processes and neglect soft
gluon interactions in the initial or final state: hard scattering
matrix elements are modified with gauge link integrals that
account for initial and final state soft gluon exchange.
A modified concept of universality has been obtained which shows
how the presence of initial or final state interactions can impact
transverse momentum dependent distribution; eg. the Sivers
function changes sign between SIDS and Drell Yan!
There may be exciting applications elsewhere, eg. other transverse
momentum dependent effects or the understanding nuclear effects
in hard scattering.
June 6 th
Nucleon Spin Structure
41
Goals for the Future
Quantitative understanding of transverse spin phenomena in QCD
Do Sivers and Collins mechanisms reconcile QCD with
transverse spin phenomena?
Precision measurements of transversity distributions and Collins
fragmentation function measurements.
This will complete the experimental survey of the nucleon at leading
twist. Determine sum of first moments (tensor charge) which can be
compared to lattice calculations.
Survey Sivers and Boer Mulders effects in SIDIS and pp
Fundamental understanding of factorization and universality in hard
scattering.
Relation to orbital angular momentum ?!
Future results expected from COMPASS, RHIC, JLAB, Belle, JLAB-12-GEV,
JPARC FAIR and EIC. This includes high precision measurements in e-p, e-e
and p-p  possibly first systematic study of factorization + universality
June 6 th
Nucleon Spin Structure
42
Transversity, Sivers and Boer Mulders
in the Proton Wavefunction
Transversity : correlation between transverse
proton spin and quark spin
q( x2 )
Sp– Sq – coupling ?
Sivers
:
correlation between transverse proton
spin and quark transverse momentum
f1Tq ( x2 , k 2 )
Sp- Lq– coupling ??
Boer/Mulders:
correlation between transverse quark
spin and quark transverse momentum
h1q ( x1 , k 2 )
Sq- Lq– coupling ??
June 6 th
Nucleon Spin Structure
43
Summary
Bjorken sum rule holds
Integral quark spin contributions are well known
Δq(x), Δq(x) only well known for up-quarks only
Hints that ΔG(x) is small at x~0.1. ∫ΔG(x)dx remains
largely unconstraint  RHIC luminosity, low-x
Possible route to OAM through
Exp. Observation of Sivers and Collins asymmetries
Theoretical advance in understanding TMD
+ concepts of factorization and universality
Plenty of work for theory + existing and future experimental tools!
June 6 th
Nucleon Spin Structure
44
Sivers in SIDIS and Drell Yan vs
Factorization and Universality
June 6 th
Nucleon Spin Structure
45
Transverse Spin Drell Yan at RHIC
vs
π-Sivers Asymmetry in Deep Inelastic Scattering
• Important test at RHIC of the fundamental
QCD prediction of the non-universality of
the Sivers effect!
• requires very high luminosity (~ 250pb-1)
June 6 th
Nucleon Spin Structure
46
Non-universality of Sivers Asymmetries:
Unique Prediction of Gauge Theory !
Simple QED
example:
DIS: attractive
Drell-Yan: repulsive
Same in QCD:
As a result:
June 6 th
Nucleon Spin Structure
47
Experiment SIDIS vs Drell Yan: Sivers|DIS= − Sivers|DY
*** Test QCD Prediction of Non-Universality ***
Sivers Amplitude
HERMES Sivers Results
RHIC II Drell Yan Projections
0
0
Markus Diefenthaler
DIS Workshop
Műnchen, April 2007
0.1
June 6 th
0.2
0.3 x
Nucleon Spin Structure
48
Is pQCD applicable at RHIC?
2
I) Can one extract G(x,Q ) from pp?
II) NLO pQCD vs RHIC data
June 6 th
Nucleon Spin Structure
49
Global QCD Analysis for G(x,Q2) and q(x,Q2):
J. Pumplin et.al JEHP 0207:012 (2002)
CTEQ6: use DGLAP Q -evolution of
2
quark and gluon distributions to extract q(x,Q2)
and G(x,Q2) from global fit to data sets at different
scales Q2.
u at Q  3.16GeV
error on G(x,Q2)
+/- 10%
Quark and Gluon Distributions
H1 + Zeus F2
CTEQ6M
up-quarks
gluon
CDF + D0 Jets
CTEQ5M1
10-410-3 10-2
error for
u(x,Q2)
down
d -1at Q  3.16GeV
10
0.5
error for
d(x,Q2)
anti-down
+/- 5%
10-410-3 10-2
June 6 th
10-1
0.5
+/- 5%
x
Nucleon Spin Structure
50
x
G(x,Q2) and q(x,Q2) + pQCD beautifully
agree Tevatron + HERA!
D0 Jet Cross Section
June 6 th
Nucleon Spin Structure
J. Pumplin et.al JEHP 0207:012 (2002)
ZEUS F2
51
and at RHIC ?
q(x,Q2), G(x,Q2) and D(z,Q2) + pQCD
are nicely consistent with experiment!
PHENIX π0 cross section a |η|<0.35
Phys.Rev.Lett.91:241803,2003
STAR π0 cross section a 3.4<η<4.0
Phys.Rev.Lett.92:171801,2004
gluon fragmentation !?
o Good agreement between NLO pQCD
calculations and experiment
 can use a NLO pQCD analysis to extract
spin dependent quark and gluon distributions
from RHIC data!
June 6 th
Nucleon Spin Structure
52
Direct Photons: NLO pQCD vs RHIC data
•
NLO-pQCD calculation
–
–
–
–
Private communication with W.Vogelsang
CTEQ6M PDF.
direct photon + fragmentation photon
Set Renormalization scale
and factorization scale pT/2,pT,2pT
Theory calculation show good
agreement with the experimental
cross section.
June 6 th
Nucleon Spin Structure
53
W Production in Polarized pp Collisions
Single Spin Asymmetry in the naive Quark Parton Model
W
L
A
u( x1 , M )

, x1  x2
u( x1 , M )
2
W
2
W
Parity violation of the weak
interaction in combination with
control over the proton spin
orientation gives access to the
flavor spin structure in the proton!
Experimental Requirements:
W dominates for
pT  20 GeV
 tracking at high pT
June 6 th
W
event selection for muons
difficult due to hadron decays
and beam backgrounds
Z
 control of all backgrounds
Nucleon Spin Structure
54
Extraction of quark polarizations at LO
 Machine and detector requirements:
– ∫Ldt=800pb-1, P=0.7 at √s=500 GeV
– trigger upgrade
– Control of backgrounds
 contributions both from
FVTX and NCC!
2009 to 2012 running at √s=500 GeV
is projected to yield ∫Ldt ~950pb-1
June 6 th
Nucleon Spin Structure
55
Run 5 ALL(p0): First constraints for ∆G(x)
PANIC, October 2005
PHENIX
Asymmetries are consistent
with gluon spin contributions
from ʃ∆G(x)dx ~ 0 to 0.5
curves: comparison with ALL
obtained with ∆G from deep
Inelastic lepton nucleon
scattering
∆G =0
(M. Glück, E. Reya, M. Stratmann,
und W. Vogelsang, Phys. Rev. D 53
(1996) 4775).
¨
June 6 th
Nucleon Spin Structure
56
EMC-RICH Trigger
(RBRC/UIUC, UCR, Tokyo)
Physics (p-p, d-Au) :
p0
p0
d
for p 0 ,  , J /
dpT
EMC Trigger Efficiency
ALL , AN ,
Information from EMC (172 elements with
4 energy thresholds) and RICH (256 elements with one threshold) is used to tag
high energy electrons and photons:
June 6 th
Nucleon Spin Structure
57
∆G Measurements by 2012
see Spin report to DOE http://spin.riken.bnl.gov/rsc/
s=200 GeV incl. p0 prod’n
s=500 GeV incl. jet prod’n
 Final results on ∆G will come from combined NLO analysis
of RHIC and DIS
 RHIC measurements will span broad range in x with good precision.
Multiple channels with independent theo. and exp. uncertainties.
June 6 th
Nucleon Spin Structure
58
Sivers Function in PHENIX:
The Muon Piston Calorimeter (MPC)
Measure the Sivers function through the asymmetry
AN in hadron-hadron correlationen, for neutral pions
(Boer and Vogelsang Phys.Rev.D69:094025,2004)
AN
p0
Jets
Hadron Paare
∫Ldt = 0.35pb-1 (Run 3)
p0
June 6 th
Nucleon Spin Structure
59
First attempt at lower x: ALL(2π0)
from Les Bland (for STAR FMS)
Measure ALL for neutral
pion pairs: one in the central
arm the second in the MPC
 0.1 > x  0.001 !
MPC
June 6 th
Nucleon Spin Structure
60
ΔG(x) – x-range with Detector Upgrades
NCC direct photons
June 6 th
Nucleon Spin Structure
61
Gluon Polarization from Inclusive
Hadrons and Jets in Polarized pp
June 6 th
Nucleon Spin Structure
K.Aoki,
R. Fatemi,
B. Surrow
INPC 2007
62