From Polarized Targets to Polarized Ion Beams EIC Accelerator Collaboration Meeting 2019 Opportunities and challenges for EIC spin physics Whitney R. Armstrong October 11, 2019 Argonne National Laboratory
1 Polarized DIS with Longitudinal and Transverse nuclear polarization Recent results from JLab 2 Overview of Fixed Target Technology 3 Comparing polarized fixed targets with polarized ion colliders 4 Polarized Heavy Ions W.R. Armstrong October 11, 2019 1 / 13
Introduction Polarized Deep Inelastic Scattering Measured Asymmetries � � σ 0 = 4 α 2 E ′ 2 M F 1 sin 2 ( θ/ 2) + 1 2 ν F 2 cos 2 ( θ/ 2) = σ ⇑↓ − σ ⇑↑ q 4 A raw � σ ⇑↓ + σ ⇑↑ � � E + E ′ cos θ E ′ 2 σ 0 A � = − 4 α 2 g 1 − Q 2 = σ ⇐↓ − σ ⇐↑ Mν 2 g 2 A raw Q 2 E Mν ⊥ σ ⇐↓ + σ ⇐↑ � � 2 σ 0 A ⊥ = − 4 α 2 E ′ 2 Mν g 1 + 2 E 1 k ′ E sin θ cos φ Mν 2 g 2 k MQ 2 A raw � , ⊥ Need � and ⊥ polarizations q A � , ⊥ = fP b P t X P W.R. Armstrong October 11, 2019 2 / 13
SANE results for x 2 g p 1 and x 2 g p 2 p p 2 2 x g x g 1 2 0.08 0.15 〈 〉 〈 〉 2 2 2 2 SLAC E143 Q =1.6 GeV Q =1.6 GeV Stat 2015 SLAC E143 Stat 2015 SLAC E155 BB 〈 〉 BB 〈 〉 2 2 SLAC E155 2 2 Q =2.9 GeV Q =2.9 GeV EMC 0.06 LSS2006 LSS2006 SLAC E155x 0.1 〈 2 〉 2 〈 2 〉 2 Q =4.1 GeV Q =4.1 GeV SMC DSSV DSSV SMC HERMES 〈 2 〉 2 〈 2 〉 2 Q =6.1 GeV Q =6.1 GeV HERMES COMPASS 0.04 CLAS 0.05 0.02 0 0 − 0.05 − 0.02 − 0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 x x W.R. Armstrong October 11, 2019 3 / 13
The dynamical twist-3 matrix element: d 2 An average color Lorentz force � 1 n − 1 g 2 } = 1 n dxx n − 1 { g 1 + 2 d n − 1 E n 2 ( Q 2 , g ) Interpretations of d 2 0 For n = 3 • Color Polarizabilities (X.Ji 95, E. Stein et � 1 x 2 { 2 g 1 + 3 g 2 } dx = d 2 al. 95) 0 • Average Color Lorentz force (M.Burkardt) M. Burkardt Phys.Rev.D 88,114502 (2013) and Nucl.Phys.A 735,185 (2004). 1 q (0) gG + y (0) γ + q (0) | P, S � d 2 = 2 MP + 2 S x � P, S | ¯ but with � v = − c ˆ z √ 2 G + y = − E y + B x = − ( � v × � B ) y E + � d 2 ⇒ average color Lorentz force acting on quark moving backwards (since we are in inf. mom. frame) the instant after being struck by the virtual photon. � F y � = − 2 M 2 d 2 W.R. Armstrong October 11, 2019 4 / 13
Quark-gluon Correlations : g 2 ( x, Q 2 ) = g WW ( x, Q 2 ) + ¯ g 2 ( x, Q 2 ) 2 W.R. Armstrong October 11, 2019 5 / 13
Quark-gluon Correlations : g 2 ( x, Q 2 ) = g WW ( x, Q 2 ) + ¯ g 2 ( x, Q 2 ) 2 Twist-2 (Wandzura, Wilczek, 1977) 1 � g W W ( x, Q 2 ) = − g LT ( x, Q 2 ) + g LT ( y, Q 2 )d y/y 2 1 1 x ≡ g tw 2 ( x, Q 2 ) 2 Twist-3 (Cortes, Pire, Ralston, 1992) � m q � dy 1 � ∂ g 2 ( x, Q 2 ) = − ¯ M h T ( y, Q 2 ) + ξ ( y, Q 2 ) ∂y y x ≡ g tw 3 ( x, Q 2 ) 2 � 1 d 2 ( Q 2 ) = 3 x 2 ¯ g 2 ( x, Q 2 ) dx As Q 2 decreases, 0 when do higher twists begin to matter? 1 � When is the color force non-zero? x 2 (2 g 1 ( x, Q 2 ) + 3 g 2 ( x, Q 2 )) dx = 0 W.R. Armstrong October 11, 2019 5 / 13
proton: PRL 122, 022002 (2019) neutron E01-012 (Resonance) E155x 0.01 E99-117 + E155x (combined) 0 -0.01 n 2 d -0.02 Lattice QCD Sum Rules Chiral Soliton -0.03 Bag Models RSS (Resonance) Elastic Contribution (CN) -0.04 1 2 3 4 5 2 2 2 Q [GeV /c ] Existing data W.R. Armstrong October 11, 2019 6 / 13
proton: PRL 122, 022002 (2019) neutron E01-012 (Resonance) 0.03 0.01 E155x MIT Bag Lattice E99-117 + E155x (combined) 0.025 CM Bag This Work SLAC This Work (with low-x) Chiral Soliton RSS 0 0.02 Sum Rules 2 2 SANE Q = 2.8 GeV elastic 2 2 SANE Q = 4.3 GeV 0.015 -0.01 0.001 n 2 d 0 0.01 -0.001 -0.02 -0.002 Lattice QCD -0.003 0.005 Sum Rules -0.004 Chiral Soliton -0.03 -0.005 Bag Models 0 RSS (Resonance) -0.006 3 3.5 4 4.5 5 5.5 Elastic Contribution (CN) − 0.005 -0.04 1 2 3 4 5 − 2 2 2 Q [GeV /c ] 0.01 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 Neutron from d n 2 experiment: D.Flay, et.al. PRD.94(2016)no.5,052003 2 2 Q [GeV ] SANE and d n 2 Result • d 2 dips around Q 2 ∼ 3 GeV 2 for proton and neutron W.R. Armstrong October 11, 2019 6 / 13
proton: PRL 122, 022002 (2019) neutron E01-012 (Resonance) 0.03 0.01 E155x MIT Bag Lattice E99-117 + E155x (combined) 0.025 CM Bag This Work SLAC This Work (with low-x) Chiral Soliton RSS 0 0.02 Sum Rules 2 2 SANE Q = 2.8 GeV elastic 2 2 SANE Q = 4.3 GeV 0.015 -0.01 0.001 n 2 d 0 0.01 -0.001 -0.02 -0.002 Lattice QCD -0.003 0.005 Sum Rules -0.004 Chiral Soliton -0.03 -0.005 Bag Models 0 RSS (Resonance) -0.006 3 3.5 4 4.5 5 5.5 Elastic Contribution (CN) − 0.005 -0.04 1 2 3 4 5 − 2 2 2 Q [GeV /c ] 0.01 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 Neutron from d n 2 experiment: D.Flay, et.al. PRD.94(2016)no.5,052003 2 2 Q [GeV ] SANE and d n 2 Result • d 2 dips around Q 2 ∼ 3 GeV 2 for proton and neutron • Is this an isospin independent average color force? W.R. Armstrong October 11, 2019 6 / 13
proton: PRL 122, 022002 (2019) neutron E01-012 (Resonance) 0.03 0.01 E155x MIT Bag Lattice E99-117 + E155x (combined) 0.025 CM Bag This Work SLAC This Work (with low-x) Chiral Soliton RSS 0 0.02 Sum Rules 2 2 SANE Q = 2.8 GeV elastic 2 2 SANE Q = 4.3 GeV 0.015 -0.01 0.001 n 2 d 0 0.01 -0.001 -0.02 -0.002 Lattice QCD -0.003 0.005 Sum Rules -0.004 Chiral Soliton -0.03 -0.005 Bag Models 0 RSS (Resonance) -0.006 3 3.5 4 4.5 5 5.5 Elastic Contribution (CN) − 0.005 -0.04 1 2 3 4 5 − 2 2 2 Q [GeV /c ] 0.01 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 Neutron from d n 2 experiment: D.Flay, et.al. PRD.94(2016)no.5,052003 2 2 Q [GeV ] SANE and d n 2 Result • d 2 dips around Q 2 ∼ 3 GeV 2 for proton and neutron • Is this an isospin independent average color force? • Updated Lattice calculations are long over due! W.R. Armstrong October 11, 2019 6 / 13
Fixed Target Technology A quick overview of polarized fixed targets Dynamic Nuclear Polarization (DNP) solid Metastability-exchange optical pumping (MEOP) gas Spin exchange optical pumping (SEOP) gas Atomic Beam Source (ABS) internal gas Polarized nucleon targets DNP � p Solid frozen target NH 3 , butanol, LiH ABS � Internal target (Hermes) p From � DNP � n d From 3 � SEOP � n He From 3 � MEOP � n He W.R. Armstrong October 11, 2019 7 / 13
Polarized Target Dilution Factor Example: Polarized NH3 Target Dilution Polarized NH3 • Packing faction of NH 3 about 60% • Takes into account scattering from unpolarized material in target. Ammonia beads • Need to know target geometry Liquid 4 He and material. e − beam • Function of x and W ∼ 3 cm 0.3 N p σ p ( x, W ) f ( x, W ) = 0.25 N p σ p + � i N i σ i ( x, W ) 0.2 0.15 0.1 0.05 W.R. Armstrong October 11, 2019 8 / 13 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
Collider Benefits Proton Deuteron 3 He p n p p p n • No dilution from • Polarized neutron or • Polarized neutron extra material proton • No dilution from windows, cryogenics, molecular structure, ... • Forward spectator tagging to identify struck nucleon. • Arbitrary ion polarization direction W.R. Armstrong October 11, 2019 9 / 13
Collider Benefits Fixed Target Ion Collider Dilution NH 3 : f ≃ 0 . 12 proton: no dilution 3 He: f ≃ 0 . 92 / 3 neutron: f ≃ 1 / 3 Spectator Tagging Very difficult Possible with forward detectors L ≃ 10 34 s − 1 cm − 2 Luminosity NH 3 : Beam current limited to 100 nA → L ≃ 10 35 s − 1 cm − 2 better dilution compensates for lower 3 He: L ≃ 10 37 s − 1 cm − 2 luminosity NH 3 : physically rotated 5T magnet � , ⊥ polarization Bunch by bunch ion spin rotation? leads to different rates/backgrounds in detectors for same kinematics 3 He: weak field, dual Helmholtz coils for easy rotation. W.R. Armstrong October 11, 2019 10 / 13
Polarized Heavy Ions Polarized EMC Effect R ≃ g A 1 /g p 1 Clo¨ et, et.al., Phys.Rev.Lett. 95 (2005) 052302 Tagging to identify struck system • Full tagging of spectator system (A-1) • Identify struck nucleon to eliminate dilution of nucleus • Would like many polarized ions beyond 3 He W.R. Armstrong October 11, 2019 11 / 13
Laser Driven Source 25 Years Ago at Argonne Recent Developments • Hybrid SEOP → K and Rb ( M.V. Romalis PRL 105, 243001 (2010) ) • Readily available high power diode lasers for pumping Rb (795 nm) • Successful polarized 3 He program at JLab. Beginning to investigate general purpose hybrid SEOP to polarize heavier ions such as 21 Ne. W.R. Armstrong October 11, 2019 12 / 13
Summary • Nuclear polarization is key for unraveling QCD at the EIC • All polarization directions equally important , especially for imaging program • Extreme forward tagging will significantly improve the science extracted with each polarized ion electron collision • Nuclear polarization is needed to investigate Polarized EMC Effect • A general purpose laser driven source may provide polarized heavy ions W.R. Armstrong October 11, 2019 13 / 13
Thank You! W.R. Armstrong October 11, 2019 13 / 13
Backup W.R. Armstrong October 11, 2019 0 / 1
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