Transcript Document
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
Gq
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
ud 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 partnerFragmentation 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/BelleSuperKEKB,
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
JqJ g
2
1
Σ Lq
2
G58 Lg