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TMD Physics with SoLID -SIDIS

This document presents key findings from the Hall A Collaboration Meeting on Transverse Momentum Dependent (TMD) functions and their relation to nucleon spin structure. It discusses the importance of quark distribution and orbital angular momentum, emphasizing how TMDs provide a unified picture of nucleon structure through techniques like Semi-Inclusive Deep Inelastic Scattering (SIDIS). Results such as the Collins and Sivers effects are highlighted, along with new methodologies for exploring nucleon spin correlations. The development and application of novel experimental setups promise significant advancements in understanding the complexities of nucleon spin.

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TMD Physics with SoLID -SIDIS

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  1. TMD Physics with SoLID-SIDIS XinQian Caltech For the SoLID-Spin Collaboration Hall A Collaboration Meeting

  2. d2kT drz d3r TMD PDFs f1u(x,kT), .. h1u(x,kT)‏ GPDs/IPDs A Unified Picture of Nucleon Structure 6D Des. Wpu(x,kT,r ) Wigner distributions 3D imaging dx & Fourier Transformation d2kT d2rT Form Factors GE(Q2), GM(Q2)‏ PDFs f1u(x), .. h1u(x)‏ 1D X. Ji PRL 91 (03)‏

  3. J q Nucleon Spin Structure Nucleon’s spin Ji’s Sum Rule • Understand Nucleon Spin in terms of quarks and gluons (QCD) • Small contribution from quarks and gluons’ intrinsic spin ~30% from data “spin crisis” • Orbital angular momentum is important! • Parton transverse motion + Spin-orbit correlations Hall A Collaboration Meeting

  4. TMD f1u(x,kT)‏ Transverse Momentum Dependent PDFs Longitudinal Direction z Transverse Plane x-y Hall A Collaboration Meeting

  5. Nucleon Spin Leading-Twist TMD PDFs Quark Spin Very well known h1= Boer-Mulders f1 = Reasonably known h1L= Worm Gear (Kotzinian-Mulders) Helicity g1 = h1= Transversity f1T= g1T= h1T= Sivers Worm Gear Pretzelosity Spin-orbital (trans. mom.) correlation is important! Hall A Collaboration Meeting

  6. Access TMDs through Semi-Inclusive DIS f1 = Unpolarized Boer-Mulder h1= h1L= Transversity h1T = Polarized Target Sivers f1T= Pretzelosity h1T= Polarized Beam and Target g1 = g1T= SL, ST: Target Polarization; le: Beam Polarization Hall A Collaboration Meeting

  7. Semi-Inclusive DIS DXs ~ PDF X FF h tags struck quark’s flavor, spin and transverse momentum Fragmentation function (FF)‏ h Parton distribution function (PDF)‏ Current Fragmentation Hall A Collaboration Meeting

  8. Hall A Polarized 3He Target S S’ D ~90% ~1.5% ~8% High luminosity: L(n) = 1036 cm-2 s-120 mins spin flip with K/Rb hybrid cells ~55% in beam polarization 1o atm3He Some N2, Rb, K Oven 230 oC Polarized Laser 795 nm F = 3” Pumping Chamber 25 G Holding Field 40 cm Target Chamber Hall A Collaboration Meeting

  9. Collins effect • Access to transversity • Transversity links quak’s spin tonucleon spin • Collins FF links quark’s spin to hadron transverse momentum • Artru model • Based on LUND fragmentation picture. Hall A Collaboration Meeting

  10. Rich Physics in TMDs (Sivers Function) • Correlation between nucleon spin with quark orbital angular momentum Burkhardt : chromodynamic lensing Important test for Factorization Final-State-Interaction Hall A Collaboration Meeting

  11. Results on Neutron • Sizable Collins π+ asymmetries at x=0.34? • Sign of violation of Soffer’s inequality? • Data are limited by stat Needs more precise data! • Negative Siversπ+ Asymmetry • Consistent with HERMES/COMPASS • Independent demonstration of negative d quark Sivers function. X. Qian PRL 107 072003 (2011) Model (fitting) uncertainties shown in blue band Radiative correction, diffractive ρ production, and finalize systematic uncertainties before submission Hall A Collaboration Meeting

  12. Double Spin Asymmetry: g1T • Leading twist TMD PDFs • T-even, Chiral-even • Dominated by real part ofinterference between L=0 (S) and L=1 (P) states • Imaginary part -> Sivers effect • First TMDs in Lattice calculation • arXiv:0908.1283 [hep-lat],Europhys.Lett.88:61001,2009 • arXiv:1011.1213 [hep-lat] , Phys.Rev.D83:094507,2011 Worm Gear g1T (1) n e’ S-P int. e TOT X g1T= P-D int. π Beam Helicity Light-Cone CQM by B. Pasquini B.P., Cazzaniga, Boffi, PRD78, 2008 Target Spin Hall A Collaboration Meeting

  13. Extract Neutron ALT J. Huang et al. PRL 108, 052001 (2012) • Neutron π+ data is sensitive to d , π- data also sensitive to u • Consist w/ model in signs, suggest larger asymmetry Hall A Collaboration Meeting

  14. SoLID-Spin: SIDIS on 3He/Proton @ 11 GeV E12-10-006:Single Spin Asymmetry on Transverse 3He @ 90 days E12-11-007:Single and Double Spin Asymmetry on 3He @ 35 days E12-11-108:Single and Double Spin Asymmetries on Transverse Proton @ 120 days White paper: Eur. Phys. J. Plus (2011) 126:2 • Key of SoLID-Spin program: • Large Acceptance + High Luminosity4-D mapping of asymmetriesTensor charge, TMDs … • Lattice QCD, QCD • Dynamics, Models Hall A Collaboration Meeting

  15. SoLID Setup for SIDIS • Tracking: GEM Tracker. • Shared R&D with Super BigBite • Electron Identification: • Large angle • E&M calorimeter • Forward angle • E&M calorimeter • Light gas Cerenkov • Pion identification: • Heavy Gas Cerenkov • TOF (Multi-gap Resistive Plate Chamber) • Fast pipeline DAQ (Similar to Hall D) • Polarized 3He and Polarized NH3 targets Hall A Collaboration Meeting

  16. Projections on Collins/Sivers Asymmetry (90 Days) Collins 1/48 bins 4-D Mapping of Asymmetries Tensor Charge Expected Improvement of Sivers Function From A. Prokudin Sivers 1/48 bins Hall A Collaboration Meeting

  17. Requirement of SIDIS • Kinematics Coverage: • 0.05 ~ 0.6 in x (valence) • 0.3 ~ 0.7 in z (factorization region) • PT up to ~ 1 GeV (TMD Physics) • Fixed target  Q2 coverage 1-8 GeV2 (~ 2 GeV2 in ΔQ2 at fixed x) • Luminoisity: • Unpolarized ~ 1037 N/cm2/s • Polarized 3He Target: • ~ 60% higher polarization • Fast spin flip (<20 mins) • Electron PID: • <1% Pion contamination (asymmetry point of view) • Pion PID: • <1% Kaons and Protons • <1% electron contamination • Optics of Reconstruction: • < a few % in δP/P. • < 1 mr in polar angle. • < 10 mr in azimuthal angle • ~ 1-2 cm vertex resolution • Similar precision required. • A factor of 2-3 better already achieved in MC. • DAQ: • ~ 3kHz Physics Coincidence • ~ 100 kHz Single electron • ~ 60 kHz Coincidence • Limits: 300 MB/s to tape. Hall A Collaboration Meeting

  18. Bright Future for TMDs • Electron Ion Collider: • The Next QCD Frontier - Understanding the glue that binds us all (arXiv:1212.1701) • Stage-I EIC • Proton Spin • The motion of quarks and gluons in the proton • Sea quark TMDs Gluon Sivers? • Test Collins-Soper Evolution at large x • The tomographic images of the proton • QCD matter at an extreme gluon density • Quark hadronization Hall A Collaboration Meeting

  19. Impact of Jlab12 + EIC Hall A Collaboration Meeting

  20. Summary • TMD physics plays a crucial role in understanding Nucleon Spin/Quark OAM • Neutron SSA and DSA has been measured for the first time in Hall A • TMD physics with SoLID-SIDIS • u/d tensor charge measurements • 4-D measurements in the valence region • Natural extensions at future EIC Hall A Collaboration Meeting

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