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Nucleon Spin: Final Solution at the EIC
Feng Yuan Lawrence Berkeley National Laboratory
Next Big Thing in QCD
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References: INT-Write-Up, “Gluons and the quark sea
at high energies: distributions, polarization, tomography”, 500 pages, e-Print: arXiv:1108.1713 [nucl-th].
EIC-White Paper, “Electron-Ion Collider: Next QCD Frontier”,150 pages, e-Print: arXiv:1212.1701 [nucl-ex]
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QCD and Strong-Interactions QCD: Non-Abelian gauge theory
Building blocks: quarks (spin ½, mq, 3 colors;
gluons: spin 1, massless, 32-1 colors)
Asymptotic freedom and confinement
1( )
4a
q a sL i m F F g A
Clay Mathematics InstituteMillennium Prize Problem
Long distance:? Soft, non-perturbativeShort d
istance
hard, perturbative
Nonperturbative scale QCD~1GeV~1/Length
Understanding the nucleon
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Solving QCD Numeric simulation: Lattice QCD
BMW, Science, 2008LHPC, 2011
Understanding the nucleon
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Experimental probes Study the quark and gluon structure through low
and high-energy scatteringMatrix elements of local operators (e.g., form
factors) or operators on the light-cone (parton distributions)
High energy experiments perturbative QCD, factorization, universality
Sum rules:MomentumBjorkenNucleon spin…
Deep Inelastic Scattering
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Friedman Kendall Taylor
Bjorken Scaling: Q2InfinityFeynman Parton Model:Point-like structure in Nucleon
In particular DIS (Virtual Photon Q>>∧QCD)
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Leading Born Diagram
Higher Order Corrections:Gluon Momentum (divergence)
Collinear: xP, x-finiteSoft: xP+kt, x-small
P
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Factorization is essential to study nucleon structure
Universality of the parton distributions Predictive power of QCD
Collins-Soper-Sterman 85, Bodwin 85, …Ji-Ma-Yuan 04, Dominguez-Xiao-Yuan 10,…
EIC Proposals in US
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Basics Inclusive DIS
Parton distributions Semi-inclusive DIS, measure
additional hadron in final state Kt-dependence
Exclusive Processes, measure recoiled nucleon Nucleon tomography
Parity violating process
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Luminosity requirem
ent
Big questions
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kt-dependence crucial to the saturation
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QCD Phase structure of cold nuclei
Comprehensive study of small-x saturation at the EIC
Inclusive observable
Two-particle correlations
04/19/23 14xiao@EIC-Whitepaper
Diffractions
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Hadronization in cold nuclei vs hot matter
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Intensity Frontier (EW Physics)
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√S = 140GeV, 200fb-1
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Ultimate goal of spin physics?
Spin sum rule
Quark spin, Best known
Gluon spin,Start to know
Orbital Angular Momentumof quarks and gluons,Little known
Jaffe-Manohar, 90Ji, 96
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EMC experiment at CERN Polarized muon + p deep inelastic scattering,
Virtual photon can only couple to quarks with opposite spin, because of angular momentum conservation
Select q+(x) or q-(x) by changing the spin direction of the nucleon or the incident lepton
The polarized structure function measures the quark spin density
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Summary of the polarized DIS data
EIC kinematics
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Back to DIS
With EIC
In particular
Quark spin x2
glu
on
sp
in
Where is the rest of spin
Back to the angular momentum density
Energy-momentum tensors in quark and gluon
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Spin sum rule
Taking forward limit,
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Ji, 1996
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Q2
t
A new type of parton “distributions” contains much more information
Comprehensive program at JLab,HERMES,COMPASS and future EIC
Quark OAM: Quark OAM: LLqq
Generalized Parton Distributions in hard exclusive processes:
( H + E) x dx = JJqq = = 1/2 1/2 LLzz
Mueller et al.,94;Ji,96; Radyushkin ,96
(Ji 96)
Extract the GPDs
The theoretical framework has been well establishedPerturbative QCD corrections at NLO,
some at NNLO
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Mueller, et al., 1310.5394
Ju, Jd, Jg
EIC kinematics coverage
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Further decomposition of Jq
Quark spin explicitly OAM, twist-three nature
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Ji, Xiong, Yuan, PRL109, 152005 (2012); PRD 13;Hatta, Yoshita, JHEP 2012;Liuti, et al., 1310.5157
Related to the parton’s phase space Wigner Distributions
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Phase space distribution: Projection onto p (x) to get the momentum (probability) density
Quark orbital angular momentum
Well defined in QCD:Ji, Xiong, Yuan, PRL, 2012; PRD, 2013Lorce, Pasquini, Xiong, Yuan, PRD, 2012
Quark imaging from EIC
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Gluon Tomography toward small-x
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Nucleon tomography
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Transverse momentum dependent parton distribution
Straightforward extension Spin average,
helicity, and transversity distributions
PT-spin correlations Nontrivial
distributions, STXPT In quark model,
depends on S- and P-wave interference
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Quark Sivers function leads to an azimuthal asymmetric distribution of quark in the transverse plane
Alex Prokudin@EIC-Whitepaper
Where can we learn TMDs Semi-inclusive hadron production in
deep inelastic scattering (SIDIS) Drell-Yan lepton pair, photon pair
productions in pp scattering Dijet correlation in DIS Relevant e+e- annihilation processes …
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Novel Single Spin Asymmetries
U: unpolarized beamT: transversely polarized target
Semi-inclusive DIS
Sivers:
Collins:
EIC kinematics
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Precision of 3-D PDFs at EIC
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all order
factorization
04/19/23 42Similar calculations for pp collisions:Zhu HX, et al., PRL110 (2013) 082001
Conclusions: EIC
Great opportunities in nuclear science Ultimate machine for nucleon spin physics Unique place to investigate gluon
saturation Potential discovery in BSM physics
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TMDs in valence region
Quark Sivers function leads to an azimuthal asymmetric distribution of quark in the transverse plane
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Alex Prokudin@EIC-Whitepaper
Current Research Focused on
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Long. Momentum distributions
NucleonSpin
3D imagingTransverse-momentum-dependent and Generalized PDFs
QCD:Factorization,Universality,Evolution,Lattice, …
Access the GPDs Deeply virtual Compton Scattering
(DVCS) and deeply virtual exclusive meson production (DVEM)
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GPD
In the Bjorken limit: Q2>>(-t),∧2QCD,M2
Mueller, et al., hep-ph/0112108, 1310.5394
Nucleon tomography and Orbital angular momentum
Momentum PT
Factorization: Ji-Ma-Yuan 2004
Coordinate BT
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