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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

5

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

9

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

04/19/23 33Mueller, et al., 1304.0077

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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