Transverse Single Spin Asymmetries in PHENIX (♯)
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Transcript of Transverse Single Spin Asymmetries in PHENIX (♯)
Transverse Single Spin Asymmetries in PHENIX(♯)
K. Oleg Eyser
29th Workshop onNuclear Dynamics
Squaw Valley, CA, Feb. 3-10, 2013
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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)
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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
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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?
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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
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
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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⊥|
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𝑀 𝑓 1𝑇⊥𝑞 (𝑥 ,𝑘⊥2 )
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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
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@ 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
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@ 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
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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)
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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
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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
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Forward AN( )
STAR sees large asymmetry at high xF (arXiv 1205.6826) Difference in fragmentation
mass, strangeness, isospin
STAR√s = 200 GeV
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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)
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Interference Fragmentation Di-hadron correlation
A. Bacchetta, M. Radici, PRD 70, 094032 (2004)
Factorization is preserved: compare PRL 107, 072004 (2011)
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Direct Photons
MPC-EX upgradearxiv:1301.1096Ready in 2014
p0 identification up to 80 GeV
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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?
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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
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Intrinsic Parton Motion
√s = 20~100 GeV L ≈ 1033-34 cm-2s-1
P ≈ 70%
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Nucleon Tomography
arxiv: 1212.1701
BACKUP
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Heavy Flavor
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Jets AnDY run 2012
Trigger on EMCal introduces bias (high-z pion)√s = 500 GeV