Recent Results in Spin Physics at
and
Anselm Vossen
Center for Exploration of Energy
and Matter
(Re)Stating the Obvious: Motivation for Studying
QCD
 QCD successful in describing high energy reactions
 BUT No consistent description of hadronic sector
 Many phenomena that are not understood
 No consistent description of fundamental bound state of the theory
 Compare to QED:
 Bound state: QED: atom
 Stringent tests of QED from study of spin structure of hydrogen




g-2 of the electron
Lamb shift (Nobel prize 1955)
Vacuum effects: Polarization, Casimir
Atomic physics
 QCD:
 Phenomena fundamentally richer
 Fundamental bound state proton
 QCD binding energy : most of the visible energy in the universe
 Nucleon Sea, Theta vacua transitions related to EW Baryogenesis
 Use transverse spin to study QCD on amplitude level with interference
 Tools: Light source p-p Collider
(Re)Stating the Obvious: Motivation for Studying
QCD
Millenium
Prize
 QCD successful in describing high energy reactions
 BUT No consistent description of hadronic sector
 Many phenomena that are not understood
 No consistent description of fundamental bound state of the theory
 Compare to QED:
 Bound state: QED: atom
 Stringent tests of QED from study of spin structure of hydrogen




g-2 of the electron
Lamb shift (Nobel prize 1955)
Vacuum effects: Polarization, Casimir
Atomic physics
 QCD:
 Phenomena fundamentally richer
 Fundamental bound state proton
 QCD binding energy : most of the visible energy in the universe
 Nucleon Sea, Theta vacua transitions related to EW Baryogenesis
 Use transverse spin to study QCD on amplitude level with interference
 Tools: Light source p-p Collider
RHIC: The QCD Machine
4
Outline
•
RHIC and the STAR detector
•
Highlights of the longitudinal Spin Program at STAR
• Gluon Polarization
• Sea Quark Polarization
•
Transverse polarization of quarks in the proton
•
Measuring Spin Dependent Fragmentation Functions in
e+e- at Belle
RHIC: The QCD Machine
Absolute Polarimeter (H jet)
RHIC pC Polarimeters
ANDY/ BRAHMS
E-Lens and
Spin
Siberian Snakes
Flipper
Siberian Snakes
PHENIX
STAR
Spin Rotators
(longitudinal polarization)
Pol. H Source
LINAC
BOOSTER
EBIS
Spin Rotators
(longitudinal polarization)
AGS
200 MeV Polarimeter
Helical Partial Siberian Snake
AGS pC Polarimeter
Strong AGS Snake
Versatility:
• Polarized p+p Sqrt(s) collisions at 62.4 GeV, 200 GeV and 500 GeV
Recent Spin Runs:
• 2011 500 GeV, longitudinal at Phenix, transverse at STAR ~30 pb-1 sampled
• 2012 200 GeV, Phenix and STAR, transverse ~20 pb-1 sampled (STAR: ~x10 statistics)
STAR
6
The STAR Detector in 2010
Time
Projection
Chamber (TPC)
Charged
Particle
Tracking
|η|<1.3
7
Endcap
Electromagnetic
Calorimeter:
1<η<2
Forward EMC
2<η<4
Barrel
Electromagnetic
Calorimeter (BEMC):
|η|<1
h = - ln(tan(q/2))
 Central Region (-1<h<1)
•
•
Identified Pions, h
Jets
 Endcap (1<eta<2)
•
Pi0, eta, (some) jets
 FMS (2<eta<4)
•
Pi0, eta
Full azimuth spanned with nearly contiguous
electromagnetic calorimetry from -1<h<4
 approaching full acceptance detector
8
PID (Barrel) with dE/dx, in the future: ToF pi/K separation up to 1.9 GeV
Proton Spin Structure with Quark and Gluon Probe
at ultra-relativistic energies
the proton represents a beam
of quark and gluon probes
Hard Scattering
Process
P1
jet
x 1 P1
x 2 P2
P2
9
10
20
Dominates at RHIC:
Jet production provides direct probe of gluon content
30
pT(GeV)
Gluon Polarization Measurement
Polarized DIS: ~ 0.3
Poorly constrained
Hard Scattering
Process
P1
The related double spin asymmetry:
x 1 P1
x 2 P2
A LL 
P2
10
G2
Gq
q2
Dominates at RHIC
~ probe gluon content in jet production
N

jet
N

jet
N

jet
N

jet
experimental double
spin asymmetry
 a LL ( qg  qg ) 
pQCD
 a LL ( gg  gg )...
 G ( x1 )
G ( x1 )
?
 A1 ( x 2 )
DIS
Jets: Proven Capabilities in p+p, pQCD regime
B.I. Abelev et al. (STAR Coll.), Phys.Rev.Lett. 97, 252001, 2006
SPIN-2010: Matt Walker/Tai Sakuma, for the collaboration
Jets well understood in STAR, experimentally and theoretically
Improved precision from 2006 to 2009
12
STAR
 Substantially larger figure of merit (P4 x L)
than in all previous runs combined
New global analysis with 2009 RHIC data
Special thanks to the DSSV group!
13
 DSSV++ is a new, preliminary global analysis from the DSSV
group that includes 2009 ALL measurements from PHENIX and
STAR
0 .2

0 . 05
 0 . 06
 g ( x , Q  10 GeV ) dx  0 . 10  0 .07
2
2
 First experimental evidence of non-zero gluon polarization in
the RHIC range (0.05 < x < 0.2)
Probing sea quark polarization through Ws
14
ud W

 l 

u d W

 l 

 Weak interaction process


Only left-handed quarks
Only right-handed anti-quarks
 Perfect spin separation
Parity violating single helicity asymmetry AL
A
W
L
  d ( x 1 ) u ( x 2 )   u ( x 1 ) d ( x 2 )
A
W
L

 u( x1 )d ( x 2 )  d ( x1 )u( x 2 )
• Complementary to SIDIS
measurements
– High Q2 ~ MW2

– No fragmentation function effects
High precision W asymmetry era
Δu
15
PHENIX and
STAR
through 2013 run
Δd
 First preliminary results from 2012 already provide substantial sensitivity
 Future results will provide a dramatic reduction in the uncertainties
Discovery of Large Asymmetries in p+p
Test of QCD: Asymmetries for transverse spin are small at
high energies (Kane, Pumplin, Repko, PRL 41, 1689–1692 (1978) )
AN 
mq
example,
s
m q  3 MeV ,
s  20 GeV , A N  10
Experiment
(E704, Fermi National Laboratory):
pp

  X
π+
π0
s  20 GeV
Observable
: AN 
1 
R

πL
P R L
4
Discovery of Large Asymmetries in p+p
Test of QCD: Asymmetries for transverse spin are small at
high energies (Kane, Pumplin, Repko, PRL 41, 1689–1692 (1978) )
AN 
mq
example,
s
m q  3 MeV ,
s  20 GeV , A N  10
Experiment
(STAR, Brookhaven National Laboratory):
pp
Observable

  X
: AN 
1 
R

L
P R L
Effect persists at high energies (pQCD valid)
4
Possible AN Explanations: Transverse
Momentum Dep. Distributions
Sivers Effect:
Collins Effect:
Introduce transverse momentum of parton Introduce transverse momentum of
relative to proton.
fragmenting hadron relative to parton.
SP
SP
kT,p
p
p
p
p
Sq
Correlation between Proton spin (Sp)
and parton transverse momentum kT,p
Number of
Citations:
kT,π
Correlation between Proton spin (Sp) and
quark spin (Sq) + spin dep. frag. function
Intrinsic transverse momentum challenges
Current QCD framework
18
Possible AN Explanations: Transverse
Momentum Dep. Distributions
Sivers Effect:
Collins Effect:
Introduce transverse momentum of parton Introduce transverse momentum of
relative to proton.
fragmenting hadron relative to parton.
SP
SP
kT,p
p
p
Talk about this next time;-)
p
p
Sq
Correlation between Proton spin (Sp)
and parton transverse momentum kT,p
Number of
Citations:
kT,π
Correlation between Proton spin (Sp) and
quark spin (Sq) + spin dep. frag. function
Intrinsic transverse momentum challenges
Current QCD framework
19
Parton Distribution Functions
The three leading order, collinear PDFs
q(x)
f1q (x)
q(x)
g1q(x)
unpolarized PDF
quark with momentum x=pquark/pproton in a
nucleon
well known – unpolarized DIS
helicity PDF
quark with spin parallel to the nucleon spin in
a longitudinally polarized nucleon
known – polarized DIS
transversity PDF
Tq(x)
h1q(x)
quark with spin parallel to the nucleon spin in
a transversely polarized nucleon
Helicity – transversity: direct measurement of
the nonzero angular momentum components
in the protons wavefunction
chiral odd, poorly known
Cannot be measured inclusively
20
Probability to Find Polarized Quark
21
e-
γ*
u,d,s

Optical Theorem:
=-Im(Aforward scattering)
+
+
+
+

Transversity is Chiral Odd
• Transversity base:

↑
↑
↑

_
↑

↓
↑
↓
↑



+
+
_
h1

_
Difference in densities for ↑, ↓ quarks
in ↑ nucleon
• Helicity base: chiral odd
• Needs chiral odd partnerFragmentation Function
• Does not couple to gluons adifferent QCD evolution than g1(x)
𝟏
• Valence dominateda Tensor charge gT = −𝟏 𝒉𝟏 𝒙 𝒅𝒙
comparable to Lattice calculations
22
Chiral odd FFs
23
Collins effect
*
H
+
+
+
: Collins FF
_
_
q
N

1
h1
_
*
Chiral odd FFs
24
Interference Fragmentation Function

*
Lz
H
+
+

1
_
_
q
N
+
Lz-1
h1
_


(  )
*
Collins effect in quark fragmentation
J.C. Collins, Nucl. Phys. B396, 161(1993)

sq
q

k

sq

ph

ph

h, ph

k

ph
: quark momentum
: quark spin
: hadron momentum
: transvers e hadron momentum
zh  Eh Eq
 2 Eh
s : relative

hadron momentum
25
Collins Effect:
Fragmentation with of a
quark q with spin sq
into a spinless
hadron h carries an
azimuthal dependence:
 

 (k  p h    s q
 sin 
Mid-Rapidity Collins Asymmetry Analysis
at STAR
S⊥
 STAR provides the full mid-rapidity
jet reconstruction and charged pion
identification
pπ
 Look for spin dependent azimuthal
distributions of charged pions inside
the jets! First proposed by F. Yuan in
Phys.Rev.Lett.100:032003.
jT
Φh
–pbeam
 Measure average weighted yield:
A exp 
2
 N sin(
C )d c
PBeam N
ΦS
pbeam
PJET
d  d
26
UU
1 
A N sin(  h   s ) 
Mid-rapidity Collins analysis
Run 12 Projections
Interference FF in Quark Fragmentation

sq
q
𝑘
𝑠𝑞
𝑅
𝑅𝑇
𝑧𝑝𝑎𝑖𝑟
=2𝐸𝑝𝑎𝑖𝑟 / 𝑠
𝑚
h1

R
R
h2
: quark momentum
:quark spin
: momentum difference 𝑝ℎ1 − 𝑝ℎ2
transverse hadron momentum difference
= 𝐸𝑝𝑎𝑖𝑟 /𝐸𝑞
: relative hadron pair momentum
: hadron pair invariant mass
28
Interference Fragmentation
Function:
Fragmentation of a
transversely polarized
quark q into two spin-less
hadron h1, h2 carries an
azimuthal dependence:
(

 k  RT  s q
 sin 
Di-Hadron Correlations
p+ p c.m .s. = lab fram e
SB
P A , P B : m om enta of protons
P h1
P B 1 0 0 G eV
29
2RC
P h 1 , P h 2 : m om enta of hadrons
P C  P h1  P h 2
P A 1 0 0 G eV
R C  ( P h1  P h 2 ) / 2
S B : proton spin orientation
PC

pp  hhX
hadron plane: P h 1 , P h 2
scattering plane: P C , P B




 
 
P h2
 R : from scattering plane
 S : from polarization vector
to hadron plane
to scattering plane
( S   R )  AU T sin( S   R )
AU T  h1  H 1
: Angle between polarisation vector and event plane
Bacchetta and Radici, PRD70, 094032 (2004)
Interference Fragmentation Function in p-p
R-S
 /
0
X
c
h1
p, S

 /
0




 
 
a
ˆ
b
H

f1
p
X
D
( S   R )  AU T sin( S   R )
AU T  h1  H 1
S : Angle between polarisation vector and event plane
30

NEW: STAR shows significant Signal!
 Strong Rapidity
Dependence
 STAR upgrades will cover
h<2 in the near future
 <xBj>0.25 (current)0.45:
Not probed in SIDIS yet!
 Proposed Forward upgrade:
h<4
+/-
+/-
Additional precision data from last years run
+ increased kinematic reach
0

Spin Dependent FF in e+e- : Need
Correlation between Hemispheres !
o Asymmetry is AU T  h1  H 1
o Need fragmentation function
o Quark spin direction unknown: measurement of
Interference Fragmentation function in one hemisphere is not possible
sin φ modulation will average out.
o Correlation between two hemispheres with
sin φRi single spin asymmetries results in
cos(φR1+φR2) modulation of the observed di-hadron
yield.
Measurement of azimuthal correlations for di-pion pairs
around the jet axis in two-jet33events!
Measuring spin dependent FFs
in e+e- Annihilation into Quarks
electron


(  )
z2

(  )

Spin dependence in e+equark fragmentation
will lead to (azimuthal)
asymmetries in
correlation measurements!
q1
Experimental requirements:
q2
quark-2
spin
z1,2 relative pion pair
momenta
z1
quark-1
spin
 Small asymmetries 
very large data sample!
 Good particle ID to high
momenta.
 Hermetic detector
positron
Here for di-hadron
correlations:
34
Measurement of Fragmentation Functions @
KEKB: L>2.11 x 1034cm-2s-1
●Asymmetric collider:
+
●8GeV e + 3.5 GeV e
●√s=10.58 GeV ( (4S))
+ ●e e
(4S) BB
-1
●Integrated Luminosity: > 1000 fb
●Continuum production: 10.52 GeV
+ - (u, d, s, c)
●e e
-1 => continuum
●>70 fb
●
35
Anselm Vossen
Belle detector
KEKB
35
He/C2H6
Large acceptance, good tracking
and particle identification!
36
36
Collins Asymmetries in Belle
Measuring Light Quark Fragmentation Functions
on the ϒ(4S) Resonance
37
e+e-qq̅, q∈uds
4s
“off”
e+e-cc̅
0.5
0.8
1.0
• small B contribution (<1%) in high thrust sample
• >75% of X-section continuum under
ϒ (4S) resonance
• ~100 fb-1  ~1000 fb-1
Interference Fragmentation –
thrust method
 e+e- (+-)jet1()jet2X
 Find pion pairs in opposite
hemispheres
 Observe angles j1+j2 between the
event-plane (beam, jet-axis) and
the two two-pion planes.
 Theoretical guidance by papers of
Boer,Jakob,Radici[PRD 67,(2003)]
and
Artru,Collins[ZPhysC69(1996)]
 Early work by Collins,
Heppelmann, Ladinsky
[NPB420(1994)]
j2

Ph 1

Ph 2


Ph 1  Ph 2
j1
Model predictions by:
•Jaffe et al. [PRL 80,(1998)]
•Radici et al. [PRD 65,(2002)]
A  H 1 (z 1 , m 1 H 1 (z 2 , m 2 cos (j 1  j 2 


38
Transverse Spin Dependent FFs: Cuts and Binning
39
 Full off-resonance and on-resonance data







(7-55): ~73 fb-1 + 588 fb-1
Visible energy >7GeV
PID: Purities in for pion pairs > 90%
Opposite hemisphere between pairs pions
All hadrons in barrel region: -0.6 < cos (q) <0.9
Thrust axis in central area:
cosine of thrust axis around
beam <0.75
Thrust > 0.8 to remove B-events  < 1% B events in sample
Zhad1 >0.2
Asymmetry extraction
 Build normalized
yields:
N ( 1   2 )
,
N
 Fit with:
a 12 cos(  1   2 )  b12
or
a12 cos( 1   2 )  b12 
c12 cos 2 (1   2 )  d 12 sin( 1   2 )
Amplitude a12 directly
measures ( IFF ) x ( -IFF )
(no double ratios)
(z1x m1) Binning
arXiv:1104.2425
AV et. al, PRL 107, 072004(2011)
41
(m1x z1) Binning
arXiv:1104.2425
AV et. al, PRL 107, 072004(2011)
42
Comparison to theory predictions
Red line: theory prediction + uncertainties
Blue points: data
• Mass dependence : Magnitude at low masses comparable, high masses
significantly larger (some contribution possibly from charm )
• Z dependence : Rising behavior steeper
43
Subprocess contributions (MC)
44
8x8 m1 m2 binning
tau contribution (only significant at high z)
charged B(<5%, mostly at higher mass)
Neutral B (<2%)
charm( 20-60%, mostly at lower z)
uds (main contribution)
Measurement at Belle leads to first point by
point extraction of Transversity
M. Radici at FF workshop,
RIKEN, 11/2012
See also: Courtoy: Phys.
Rev. Lett.
107:012001,2011
Is Soffer Bound violated?
h(x)<|f(x)+g(x)|/2
Handedness Correlations


Thrust direction
L
R

𝑘+ × 𝑘− ⋅ 𝑡
Handedness:
∣ 𝑘+ ∣∣ 𝑘− ∣
?
= sinΦ > 0
𝑁𝑅𝐿 + 𝑁𝐿𝑅 − 𝑁𝑅𝑅 − 𝑁𝐿𝐿
C:
𝑁𝑅𝐿 + 𝑁𝐿𝑅 + 𝑁𝑅𝑅 + 𝑁𝐿𝐿

L/R
Jet
handedness:
46
𝑁𝑅 − 𝑁𝐿
𝑁𝑅 + 𝑁𝐿
QCD Vacuum Transitions carry Chirality QN
The QCD Vacuum
Difference in winding number:
Net chirality carried by
Instanton/Sphaleron
–
Vacuum states are characterized by “winding number”
–
Transition amplitudes: Gluon configurations, carry net chirality
–
e.g. quarks: net spin momentum alignment
–
Similar mechanism to EW baryogenesis
QCD Vacuum Transitions carry Chirality QN
arXiv:0909.1717v2 [
Kharzeev, McLerran and Warringa, arXiv:0711.0950,
Fukushima, Kharzeev and Warringa, arXiv:0808.3382
Handedness Correlations


Thrust direction
L
R
Q=1

𝑘+ × 𝑘− ⋅ 𝑡
Handedness:
∣ 𝑘+ ∣∣ 𝑘− ∣
?
= sinΦ > 0
𝑁𝑅𝐿 + 𝑁𝐿𝑅 − 𝑁𝑅𝑅 − 𝑁𝐿𝐿
C:
𝑁𝑅𝐿 + 𝑁𝐿𝑅 + 𝑁𝑅𝑅 + 𝑁𝐿𝐿

L/R
Jet
handedness:
𝑁𝑅 − 𝑁𝐿
𝑁𝑅 + 𝑁𝐿
Expect negative correlation for local p-odd effect
49
Unpolarized Fragmentation Functions
 Precise knowledge of
upol. FFs necessary
for virtually all SIDIS
measurements
e-
q
γ*
e+
q
h
Dq
First FF extraction including
uncertainties (e+e-):
Hirai, Kumano, Nagai, Sudoh (KEK)
Phys. Rev. D 75, 094009 (2007)
h
KEKB/BelleSuperKEKB,
Upgrade
51
 Aim: super-high luminosity ~1036 cm-2s-1 (~40x KEK/Belle)
 Upgrades of Accelerator (Microbeams + Higher Currents) and Detector
(Vtx,PID, higher rates, modern DAQ)
 Significant US contribution
http://belle2.kek.jp
First data in 2016
52
Highlights for FF Measurements
 Kaon efficiency > 95% over
relevant kinematics, fake
rate < 5%
 Vertex resolution improved
by order of magnitude
 Obviously more statistics
Belle II Status
Summary and Outlook
 RHIC is ideal machine to study gluonic properties of the nucleon




First result indicating non-zero Gluon polarization in the proton
Sea-quark polarization
Investigation in surprising transverse spin effects
Transversity in di-hadron Correlations and from Collins effect




Investigate high x, high Q2 region
Contribution to AN
Evolution of kT dependent Collins FF
Soffer bound, tensor charge
 Belle is the ideal machine to study quark fragmentation

Unpolarized Fragmentation functions



Polarized fragmentation functions in correlation between hemispheres








Charged pions and kaons
Vector mesons and di-hadrons
IFF in charged pion pairs
IFF with neutral pions
Collins in charged pion pairs
Collins in charged kaons, 0, h, vector mesons
Theory of transverse single spin asymmetries is developing rapidly
Tests will come from upgrades at STAR/PHENIX and Belle II
STAR and Belle are in the middle of major upgrades
Far Future: eSTAR at eRHIC
Backup
Jet Reconstruction
 , p , etc
q, g
GEANT
e ,   
MC Jets Midpoint Cone Algorithm:
• Adapted from Tevatron II (hepexp/0005012
• Cone radius = √(Δη2+Δφ2) = 0.7
• Split / Merge fraction = 0.5
PYTHIA
Particle
Detector
Data Jets
Anti-KT Algorithm:
• Radius = 0.6
• Less sensitive to underlying event
affects
STAR Detector has:
• Full azimuthal coverage
• Charged particle tracking from TPC
for |η| < 1.3
• E/BEMC provide electromagnetic
energy reconstruction for -1 < η < 2.0
STAR well suited for jet
57measurements
Spin Decomposition of the Proton
Naïve quark model –
3 valence quark
1 1
 ( Δu v  Δd v  Δqs 
2 2
Σ  1 ???
CERN, SLAC, DESY, JLAB:
S ~ 0.30
QCD:
..additional
contributions from
gluons and gluon
splitting, sea quarks…
1 1
 Σ  G
2 2
ΔG, Δ/Σ= ?
…and orbital
angular
momentum…
1
 JqJ g
2
1
 Σ  Lq
2
 G58 Lg