Recent Results in Spin Physics at and

Anselm VossenCenter 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

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

Millenium

Prize

4

RHIC: The QCD Machine

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

Versatility:• Polarized p+p Sqrt(s) collisions at 62.4 GeV, 200 GeV and 500 GeVRecent 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)

ANDY/ BRAHMS

STAR

PHENIX

AGS

LINACBOOSTERPol. H- Source

Spin Rotators(longitudinal polarization)

Siberian Snakes

200 MeV Polarimeter

RHIC pC PolarimetersAbsolute Polarimeter (H jet)

AGS pC PolarimeterStrong AGS Snake

Helical Partial Siberian Snake

Spin Rotators(longitudinal polarization)

Siberian Snakes

E-Lens and Spin Flipper

EBIS

STAR6

7Time Projection Chamber (TPC)Charged Particle Tracking |η|<1.3

Barrel Electromagnetic Calorimeter (BEMC):|η|<1

Endcap Electromagnetic Calorimeter:1<η<2

h = - ln(tan( /q 2))

The STAR Detector in 2010

Forward EMC2<η<4

Full azimuth spanned with nearly contiguous electromagnetic calorimetry from -1<h<4

approaching full acceptance detector

PID (Barrel) with dE/dx, in the future: ToF pi/K separation up to 1.9 GeV 8

Central Region (-1<h<1)• Identified Pions, h• Jets

Endcap (1<eta<2)• Pi0, eta, (some) jets

FMS (2<eta<4)• Pi0, eta

9

at ultra-relativistic energiesthe proton represents a beamof quark and gluon probes

Jet production provides direct probe of gluon content

Proton Spin Structure with Quark and Gluon Probes

Hard Scattering Process

2P

2 2x P

1P

1 1x P

jet

Dominates at RHIC:

10

20

30 pT(GeV)

10

~ probe gluon content in jet production

)...(

)()(

)()( 21

1

1

gggga

xAxG

xGqgqga

NN

NNA

LL

LL

jetjet

jetjetLL

The related double spin asymmetry:

Gluon Polarization Measurement

experimental doublespin asymmetry

pQCD DIS?DG2 DGDq Dq2

Hard Scattering Process

2P

2 2x P

1P

1 1x P

Dominates at RHIC

LGS pz ΔΔΣ2

1

2

1

Polarized DIS: ~ 0.3 Poorly

constrained

Jets: Proven Capabilities in p+p, pQCD regime

Jets well understood in STAR, experimentally and theoretically

B.I. Abelev et al. (STAR Coll.), Phys.Rev.Lett. 97, 252001, 2006

SPIN-2010: Matt Walker/Tai Sakuma, for the collaboration

12

Improved precision from 2006 to 2009

Substantially larger figure of merit (P4 x L) than in all previous runs combined

STAR

13

New global analysis with 2009 RHIC data

DSSV++ is a new, preliminary global analysis from the DSSV group that includes 2009 ALL measurements from PHENIX and STAR

First experimental evidence of non-zero gluon polarization in the RHIC range (0.05 < x < 0.2)

2.0

05.0

06.007.0

22 10.0)GeV10,( dxQxg

Special thanks to the DSSV group!

14

Probing sea quark polarization through Ws

Weak interaction process Only left-handed quarks Only right-handed anti-quarks

Perfect spin separation

Parity violating single helicity asymmetry AL

lWdu

lWdu

ALW

u(x1)d (x2)d (x1)u(x2)

ALW d(x1)u (x2)u (x1)d(x2)

• Complementary to SIDIS measurements– High Q2 ~ MW

2

– No fragmentation function effects

15

High precision W asymmetry era

First preliminary results from 2012 already provide substantial sensitivity Future results will provide a dramatic reduction in the uncertainties

Δu

Δd

PHENIX and STAR

through 2013 run

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) )

Xpp π+

π-

π0

LR

N

LR

PA

1 :Observable

GeV 20s

Experiment (E704, Fermi National Laboratory):

4q 10,20,3m example, N

qN AGeVsMeV

s

mA

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) )

Xpp

LR

N

LR

PA

1 :Observable

Experiment (STAR, Brookhaven National Laboratory):

4q 10,20,3m example, N

qN AGeVsMeV

s

mA

Effect persists at high energies (pQCD valid)

Possible AN Explanations: Transverse Momentum Dep. Distributions

18

SPkT,p

p

p

SP

p

p

Sq kT,π

Sivers Effect:Introduce transverse momentum of parton relative to proton.

Collins Effect:Introduce transverse momentum of fragmenting hadron relative to parton.

Correlation between Proton spin (Sp) and quark spin (Sq) + spin dep. frag. function

Correlation between Proton spin (Sp) and parton transverse momentum kT,p

Number ofCitations:

Intrinsic transverse momentum challenges Current QCD framework

Possible AN Explanations: Transverse Momentum Dep. Distributions

19

SPkT,p

p

p

SP

p

p

Sq kT,π

Sivers Effect:Introduce transverse momentum of parton relative to proton.

Collins Effect:Introduce transverse momentum of fragmenting hadron relative to parton.

Correlation between Proton spin (Sp) and quark spin (Sq) + spin dep. frag. function

Correlation between Proton spin (Sp) and parton transverse momentum kT,p

Talk about this next time;-)

Number ofCitations:

Intrinsic transverse momentum challenges Current QCD framework

Nex

t Tim

e

20

The three leading order, collinear PDFs

Parton Distribution Functions

q(x)f1

q (x)

q(x) g1

q(x)

Tq(x)

h1q(x)

chiral odd, poorly knownCannot be measured inclusively

unpolarized PDFquark with momentum x=pquark/pproton in a nucleon well known – unpolarized DIS

helicity PDFquark with spin parallel to the nucleon spin in a longitudinally polarized nucleon known – polarized DIS

transversity PDFquark with spin parallel to the nucleon spin in a transversely polarized nucleonHelicity – transversity: direct measurement of the nonzero angular momentum components in the protons wavefunction

21

Probability to Find Polarized Quark

γ*

u,d,s

e-

Optical Theorem:

s=-Im(Aforward scattering)

+

+ +

+

22

Transversity is Chiral Odd

_

+1h

_

+↑

↑ ↑

↑ ↓

↑ ↑

↓ =_

• Helicity base: chiral odd• Needs chiral odd partnerFragmentation Function• Does not couple to gluons adifferent QCD evolution than

g1(x)• Valence dominateda Tensor charge gT comparable to

Lattice calculations

Difference in densities for ↑, ↓ quarks in ↑ nucleon

• Transversity base:

23

Chiral odd FFs

+

_

+

1h

_

* *

+

_1H

Collins effect

q

N

1H : Collins FF

24

Chiral odd FFs

+

_

+ _

* *

+ q

N

_

Lz-1Lz

1H

Interference Fragmentation Function ( )

1h

25

J.C. Collins, Nucl. Phys. B396, 161(1993)

q

momentum hadron relative : 2

z

momentum hadron e transvers:

momentum hadron :

spinquark :

momentumquark :

h

sE

EE

p

p

s

k

h

qh

h

h

q

qs

k

hph

,

Collins Effect:Fragmentation with of a quark q with spin sq into a spinless hadron h carries anazimuthal dependence:

hp

sin

qh spk

Collins effect in quark fragmentation

26

Mid-Rapidity Collins Asymmetry Analysis at STAR

Aexp 2 N sin(C )dc

PBeam N

Φh

–pbeam

pbeamS⊥

pπ

PJET

jT

ΦS STAR provides the full mid-rapidity jet reconstruction and charged pion identification

Look for spin dependent azimuthal distributions of charged pions inside the jets! First proposed by F. Yuan in Phys.Rev.Lett.100:032003.

Measure average weighted yield:

d dUU 1 AN sin(h s)

Run 12 Projections

Mid-rapidity Collins analysis

28

Interference FF in Quark Fragmentation

q

qs

R

Interference Fragmentation Function:Fragmentation of a transversely polarizedquark q into two spin-less hadron h1, h2 carries anazimuthal dependence:

R

sin

T qk R s

1h

2h

𝑘𝑠𝑞

𝑅𝑅𝑇

𝑧𝑝𝑎𝑖𝑟

=2 𝐸𝑝𝑎𝑖𝑟 / √ 𝑠𝑚

: quark   momentum:quark  spin  : momentum   difference𝑝h 1 −𝑝h 2

transverse   hadron   momentum  difference ¿𝐸𝑝𝑎𝑖𝑟 /𝐸𝑞

: relative   hadron   pair   momentum:hadron   pair   invariant   mass

Di-Hadron Correlations

291 2

1 2

1 2

p+p c.m.s. = lab frame

, : momenta of protons

, : momenta of hadrons

( ) / 2

: proton spin orientation

A B

h h

C h h

C h h

B

P P

P P

P P P

R P P

S

::::::::::::::::::::::::::::

::::::::::::::::::::::::::::

::::::::::::::::::::::::::::::::::::::::::

::::::::::::::::::::::::::::::::::::::::::

::::::::::::::

1hP::::::::::::::

2hP::::::::::::::

100 GeVAP::::::::::::::

100 GeVBP::::::::::::::

CP::::::::::::::

BS::::::::::::::

pp hhX

1 2hadron plane: ,

scattering plane: ,

h h

C B

P P

P P

::::::::::::::::::::::::::::

:::::::::::::::::::::::::::: : from scattering plane

to hadron planeR : from polarization vector

to scattering plane S

2 CR::::::::::::::

Bacchetta and Radici, PRD70, 094032 (2004)

( ) sin( )S R UT S RA

1 1UTA h H

: Angle between polarisation vector and event plane

30

b

X

1f p

a

X

1hSp,

Interference Fragmentation Function in p-p

c

0 /

H

D0 /

( ) sin( )S R UT S RA

1 1UTA h H

fS

fR-fS

: Angle between polarisation vector and event plane

NEW: STAR shows significant Signal!

Additional precision data from last years run+ increased kinematic reachExplore p0/p+-channels

p+/p-

p+/p-

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

33

o Asymmetry is 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-jet events!

Spin Dependent FF in e+e- : NeedCorrelation between Hemispheres !

1 1UTA h H

34

( )

q1

quark-1 spin

Spin dependence in e+e-

quark fragmentation will lead to (azimuthal)asymmetries incorrelation measurements!

Experimental requirements:

Small asymmetries very large data sample!

Good particle ID to high momenta.

Hermetic detector

Measuring spin dependent FFsin e+e- Annihilation into Quarks

electron

positron

q2

quark-2 spin

z1,2 relative pion pair momenta

z2 z1

( )

21221111 m,zHm,zHA cos

Here for di-hadron correlations:

Anselm Vossen 3535

Belle detectorKEKB

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●Integrated Luminosity: > 1000 fb-1

●Continuum production: 10.52 GeV●e+e-(u, d, s, c)●>70 fb-1 => continuum

36Collins Asymmetries in Belle 36Large acceptance, good tracking and particle identification!

He/C2H6

Measuring Light Quark Fragmentation Functions on the ϒ(4S) Resonance37

ii

ii

p

npTThrust

ˆ

:

• small B contribution (<1%) in high thrust sample• >75% of X-section continuum under ϒ(4S) resonance• ~100 fb-1 ~1000 fb-1

9.44 9.46

e+e- Center-of-Mass Energy (GeV)

0

5

10

15

20

25

(e+

e-

had

ron

s)(n

b)

(1S)10.0010.02

0

5

10

15

20

25

(2S)10.34 10.37

0

5

10

15

20

25

(3S)10.54 10.58 10.62

0

5

10

15

20

25

(4S)9.44 9.46

e+e- Center-of-Mass Energy (GeV)

0

5

10

15

20

25

(e+

e-

had

ron

s)(n

b)

(1S)10.0010.02

0

5

10

15

20

25

(2S)10.34 10.37

0

5

10

15

20

25

5

10

15

20

25

(2S)10.34 10.37

0

5

10

15

20

25

(3S)10.54 10.58 10.62

0

5

10

15

20

(3S)10.54 10.58 10.62

0

5

10

15

20

25

(4S)

BB00 BB

e+e-qq, q uds∈

e+e-cc

0.5 0.8 1.0

4s“off”

Interference Fragmentation – thrust method

38

e+e- (p+p-)jet1(p+p-)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)]

21221111 m,zHm,zHA cos

j2-p

-p j1

1hP

2hP

2h1h PP

Model predictions by:

•Jaffe et al. [PRL 80,(1998)]

•Radici et al. [PRD 65,(2002)]

39

Transverse Spin Dependent FFs: Cuts and Binning

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 pionsAll hadrons in barrel region: -0.6 < cos (q) <0.9Thrust axis in central area: cosine of thrust axis

around beam <0.75Thrust > 0.8 to remove B-events < 1% B events

in sampleZhad1 >0.2

Asymmetry extraction

Build normalized yields:

Fit with:

or

,)( 21

N

N

)sin()(2cos

)cos(

21122112

122112

dc

ba

122112 )cos( ba

Amplitude a12 directly measures ( IFF ) x ( -IFF ) (no double ratios)

41

(z1x m1) Binning

arXiv:1104.2425AV et. al, PRL 107, 072004(2011)

(m1x z1) Binning

arXiv:1104.2425AV et. al, PRL 107, 072004(2011)

42

43

Comparison to theory predictions

• Mass dependence : Magnitude at low masses comparable, high masses significantly larger (some contribution possibly from charm )• Z dependence : Rising behavior steeper

Red line: theory prediction + uncertaintiesBlue points: data

Subprocess contributions (MC)448x8 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)

M. Radici at FF workshop, RIKEN, 11/2012See also: Courtoy: Phys. Rev. Lett. 107:012001,2011

Measurement at Belle leads to first point by point extraction of Transversity

Is Soffer Bound violated?h(x)<|f(x)+g(x)|/2

46

Handedness Correlations

Thrust direction

Handedness :¿¿

L R

L/RJet   handedness:

𝑁𝑅 − 𝑁 𝐿

𝑁𝑅+𝑁 𝐿

C:𝑁𝑅𝐿+𝑁 𝐿𝑅− 𝑁𝑅𝑅−𝑁 𝐿𝐿

𝑁𝑅𝐿+𝑁 𝐿𝑅+𝑁𝑅𝑅+𝑁 𝐿𝐿

QCD Vacuum Transitions carry Chirality QN

The QCD Vacuum

Difference in winding number:Net chirality carried byInstanton/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

Kharzeev, McLerran and Warringa, arXiv:0711.0950,Fukushima, Kharzeev and Warringa, arXiv:0808.3382

arXiv:0909.1717v2 [

49

Handedness Correlations

Expect negative correlation for local p-odd effect

Thrust direction

Handedness :¿¿

L R

L/RJet   handedness:

𝑁𝑅 − 𝑁 𝐿

𝑁𝑅+𝑁 𝐿

C:𝑁𝑅𝐿+𝑁 𝐿𝑅− 𝑁𝑅𝑅−𝑁 𝐿𝐿

𝑁𝑅𝐿+𝑁 𝐿𝑅+𝑁𝑅𝑅+𝑁 𝐿𝐿

Q=1

Unpolarized Fragmentation Functions

Precise knowledge of upol. FFs necessary for virtually all SIDIS measurements

First FF extraction including uncertainties (e+e-): Hirai, Kumano, Nagai, Sudoh (KEK)Phys. Rev. D 75, 094009 (2007)

q

qγ*e-

e+

h

hqD

51

KEKB/BelleSuperKEKB, Upgrade

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

Charged pions and kaons Vector mesons and di-hadrons

Polarized fragmentation functions in correlation between hemispheres 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

57

Jet ReconstructionD

etec

tor

GE

AN

TP

YT

HIA

etcp

e

,,

,

gq,

Par

ticl

e

Data Jets MC Jets Midpoint Cone Algorithm:• Adapted from Tevatron II (hep-exp/0005012• Cone radius = √(Δη2+Δφ2) = 0.7• Split / Merge fraction = 0.5

Anti-KT Algorithm:• Radius = 0.6• Less sensitive to underlying event affectsSTAR Detector has:• Full azimuthal coverage • Charged particle tracking from TPC for |η| < 1.3• E/BEMC provide electromagnetic energy reconstruction for -1 < η < 2.0STAR well suited for jet measurements

58

Spin Decomposition of the Proton

v v s

1 1Δu Δd Δq

2 2Σ 1 ???

Naïve quark model – 3 valence quark

CERN, SLAC, DESY, JLAB:DS ~ 0.30

…and orbital angular momentum…

1

2 q gJ J 1

Σ2

G

q

g

L

L

QCD:..additional contributions from gluons and gluon splitting, sea quarks…

GΣ21

21 D+D=

ΔG, Δ/Σ= ?