Transverse Single Spin Asymmetries in PHENIX(♯)

K. Oleg Eyser

29th Workshop onNuclear Dynamics

Squaw Valley, CA, Feb. 3-10, 2013

2 2

The Proton Spin Structure

What is the connection to orbital angular momentum?Transversity ↔ tensor charge from lattice QCD

momentummomentum

Eur. Phys. J. A39, 89 (2009)

3 3

Transverse Spin Asymmetries

𝑃 𝑡=𝑁↑−𝑁↓

𝑁↑+𝑁↓

𝐴𝑁=𝑑𝜎 𝐿−𝑑𝜎𝑅

𝑑𝜎 𝐿+𝑑𝜎𝑅

Sp0

x

y

S P

Beam Polarization

Azimuthal Modulation of Cross Section

𝐴𝑁= 1𝑃 𝑡

×𝑁 𝐿−𝑁𝑅

𝑁 𝐿+𝑁𝑅

Reaction plane

4 4

Transverse Spin Asymmetries

𝑥𝐹=2𝑝𝑙

√ 𝑠

In pQCD (collinear) AN suppressed by𝑚𝑞𝛼𝑠/𝑃⊥

What is the origin of these asymmetries?

Do they persist at higher energies?

5 5

Proton-Proton Collisions

Initial State

pQCD

Final State

fa

fb

σFFq

How valid is factorization for hadronic collisions?

Are the separate contributions universal?

)(),( 21 zDkxf h

qq

T

Sivers Effect Phys. Rev. D 41, 83 (1990)

Correlation between proton spin & transverse parton momentum

),()( 221

kzHxq

Collins Fragmentation Nucl. Phys. B396, 161 (1993)

correlation between proton spin & quark spin

+ spin dependant fragmentation function

6 6

Higher TwistX. Ji, J.-W. Qiu, W. Vogelsang, F. YuanPRL 97, 082002 (2006)

TMD parton distribution functionsvs. collinear QCD factorization

twist-three quark-gluon correlation functions

soft pT breaks factorization 1 / pT shape not yet observed

𝑔𝑇 𝑞 ,𝐹 (𝑥 ,𝑥 )=∫𝑑2𝑘⊥|𝑘⊥|

2

𝑀 𝑓 1𝑇⊥𝑞 (𝑥 ,𝑘⊥2 )

7 7

Transverse Asymmetries

Sivers effect

Collins

effect

Twist-3

TransverseAsymmetries e+p

p+p

e++e-

Inclusive hadrons Direct photons Jets Jet correlations/structure Hadron Correlations Interference fragmentation Drell-Yan W-bosons

8 8

@ RHIC

AGSLINACBOOSTER

Polarized Source

Spin Rotators

200 MeV Polarimeter

Absolute Polarimeter (H jet)

PHENIX

AnDY

STARSiberian Snakes

Siberian Snakes

Spin Flipper

RHIC pC Polarimeters

Rf Dipole AGS Internal Polarimeter

AGS pC Polarimeter

Strong SnakePartial Snake

Helical Partial Snake

9 9

@ RHIC

Year(GeV)

Pol.(%)

STAR PHENIXL (pb-1) P2L (pb-1) L (pb-1) P2L (pb-1)

2006 62 48 n/a 0.02 0.0052006 200 57

(51)6.8 2.1 2.7 0.7

2008 200 46 7.8 1.7 5.2 1.12011 500 46 25.0 5.3 n/a2012 200 58 23.0 7.7 9.2* 3.1

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Mid-rapidity Asymmetries

p0 @ s = 200 GeV

Partonic contributions change with pT

Compare Phys. Rev. D 74, 094011

11 11

Forward Asymmetries

No strong dependence on s from 19.4 ~ 200 GeV Slight differences in pseudo-rapidity and/or pT

p0 processs contributionGuzey et al, PLB 603,173 (2004)

12 12

Isospin Dependence

Tran

sver

sity

√s = 62.4 GeV

Siv

ers

𝝅+¿(𝒖𝒅 )¿

𝝅−(𝒖𝒅)

𝝅𝟎(𝒖𝒖+𝒅𝒅)

u u

d d

fragmentation u/d

1:0

2:1

1:1

13 13

Projection for 2012/13

pT Dependence

Expected 1/pT fall-off √s = 500 GeV

PHENIX-MPCtower size 2.252 cm2

220 cm from vertex

decay photon

p0

direct photon

14 14

Forward AN( )

STAR sees large asymmetry at high xF (arXiv 1205.6826) Difference in fragmentation

mass, strangeness, isospin

STAR√s = 200 GeV

15 15

Heavy Flavor Highly dominated by gluon fusion No transversity/Collins Clean gluon Sivers

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Collins Asymmetries Azimuthal asymmetry of hadrons in jets

F. Yuan, PRL 100, 032003 (2008)

𝐴≡2∙ ⟨𝑠𝑖𝑛 (𝜑𝑆−𝜑h ) ⟩compare PRD 86, 039905 (2012)

17 17

Interference Fragmentation Di-hadron correlation

A. Bacchetta, M. Radici, PRD 70, 094032 (2004)

Factorization is preserved: compare PRL 107, 072004 (2011)

18 18

Direct Photons

MPC-EX upgradearxiv:1301.1096Ready in 2014

p0 identification up to 80 GeV

19 19

Sivers Asymmetries

SIDIS

Drell-Yan A. Prokudin, Z.-B. Kang

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The Path ForwardSivers/transversity Drell-Yan

Transversity IFF

Collins Hadrons in jet

Sivers Jets

Sivers Direct photon

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So… where we at? Non-vanishing transverse single spin asymmetries have

been measured over a wide range of energies Details of mechanism not finally understood

Isospin dependence Flavor dependence

Transversity (high-x) andfundamental (p)QCD tests

Is factorization valid for TMDs?Are TMDs universal? How do they evolve?How do they relate to orbital angular momentum?

22 22

Know thyself!

�⃗� �⃗� ′𝜑 𝑠

𝜑𝑝h

�⃗�⊥

�⃗�

DIS 𝑥 ,𝑄2

semi−inclusive 𝑧 ,𝑘𝑇polarization𝜑

𝑄2=−𝑞2=− (𝑘𝜇−𝑘𝜇′ )2 𝑄2=2𝐸𝑒𝐸𝑒

′ (1− cos𝜃𝑒)

𝑦=𝑝𝑞𝑝𝑘=1−

𝐸𝑒′

𝐸𝑒cos2

𝜃𝑒

2𝑥=

𝑄2

2𝑝𝑞=𝑄2

𝑠𝑦

23 23

Intrinsic Parton Motion

√s = 20~100 GeV L ≈ 1033-34 cm-2s-1

P ≈ 70%

24 24

Nucleon Tomography

arxiv: 1212.1701

BACKUP

26 26

Heavy Flavor

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Jets AnDY run 2012

Trigger on EMCal introduces bias (high-z pion)√s = 500 GeV