Future Opportunitiesat an

Electron-Ion Collider

Oleg Eyser

Brookhaven National Laboratory

2

Exploring the Glue that Binds Us All

Questions at the next QCD frontiero How are the sea quarks and gluons, and their spins,

distributed in space and momentum inside the nucleon?o Where does the saturation of gluon densities set in?o How does the nuclear environment affect the distribution of

quarks and gluons and their interactions in nuclei?

An Electron-Ion Collidero Electron beams for precision measurementso Polarized nucleon beamso Heavy ion beams of different specieso Kinematic reach into the gluon dominated regimeo Dedicated hermetic detector setup

3

The Structure of the Nucleon

What is the dynamical origin of sea quarks and gluons inside the proton?

How does the proton spin originate at the microscopic level?

How is hadron structure influenced by chiral symmetry and its breaking?

How does confinement manifest itself in the structure of hadrons?

4

Partonic Descriptions of the Nucleon

5

Deep Inelastic Scattering

Lorentz invariants

𝑠=(𝑝+𝑘 )2=4 ∙𝐸𝑝 ∙𝐸𝑒

𝑄2=−𝑞2=− (𝑘−𝑘 ′ )2

𝑥𝐵=𝑄2

2∙𝑝 ∙𝑞

𝑦=𝑞 ∙𝑝𝑘 ∙𝑝

In the collider frame

𝐸𝑒′ =𝐸𝑒 ∙ (1− 𝑦 )+ 𝑄2

4 ∙𝐸𝑒

𝑄2=𝑥 ∙ 𝑦 ∙𝑠

Other variables

𝑊 2=(𝑝+𝑞)2=𝑄2 ∙ (1−1 /𝑥 ) 𝜈=𝑞 ∙𝑝𝑀

=𝑦 ∙𝑠2𝑀

6

Structure Functions

𝑑2𝜎𝑑𝑥𝑑𝑄2=

4 𝜋𝛼2

𝑥𝑄4 [(1− 𝑦+ 𝑦 2

2 )𝐹2 (𝑥 ,𝑄2 )− 𝑦2

2𝐹 𝐿 (𝑥 ,𝑄2 )] 𝜎 𝑟=𝐹 2 (𝑥 ,𝑄2 )− 𝑦 2

1+ (1− 𝑦 )2𝐹 𝐿 (𝑥 ,𝑄2 )

12 [ 𝑑2𝜎⇆

𝑑𝑥𝑑𝑄2−𝑑2𝜎⇉

𝑑𝑥𝑑𝑄2 ]≃ 4𝜋𝛼2

𝑄4 𝑦 (2− 𝑦 )𝑔1 (𝑥 ,𝑄2 )

𝐹 2 (𝑥 ,𝑄2 )=𝑥∑𝑒𝑞2 [𝑞 (𝑥 ,𝑄2 )+𝑞 (𝑥 ,𝑄2 ) ] 𝑔1 (𝑥 ,𝑄2 )=𝑥∑𝑒𝑞

2 [Δ𝑞 (𝑥 ,𝑄2)+Δ𝑞 (𝑥 ,𝑄2 ) ]

7

Longitudinal Spin Structure

8

Longitudinal Spin Structure

9

Quark TMD Distributions in SIDIS

𝑧=𝑃h ∙𝑃𝑞 ∙𝑃

10

Quark TMD Distributions

11

Spatial Imaging of Nucleons

𝑓 ⇑ (𝑥 ,𝑏𝑇 )= 𝑓 (𝑥 ,𝑏𝑇2 )+

(𝑆𝑇 ×𝑏𝑇 )𝑧

𝑀𝜕

𝜕𝑏𝑇2 𝑒 (𝑥 ,𝑏𝑇

2 )

𝐸 (𝑥 , 𝜉 , 𝑡 )𝐻 (𝑥 ,𝜉 ,𝑡 )

Fourier transform of at 𝜉=0𝑒 (𝑥 ,𝑏𝑇

2 )𝑓 (𝑥 ,𝑏𝑇

2 )

Exclusive processes

Resolution scale 𝑄2 𝑀𝑉2 +𝑄2

𝑉

12

Deeply Virtual Compton Scattering

13

Towards Spatial Imaging

Combine with next slide???

14

Gluon Distributions

15

The Nucleus: A Laboratory for QCD

What is the role of strong gluon fields, parton saturation effects, and collective gluon excitations in nuclei?

Can we experimentally find evidence of non-linear QCD dynamics in the high-energy scattering off nuclei?

What are the momentum/spatial distributions of gluons and sea quarks in nuclei?

Are there strong color fluctuations inside a large nucleus?

16

High Gluon Densities in Nuclei

17

Lepton-Nucleus Scattering

u.r. boost amplifies the gluon densities in nucleus ()

18

Nuclear PDFs

𝑑2𝜎𝑑𝑥𝑑𝑄2=

4 𝜋𝛼2

𝑥𝑄4 [(1− 𝑦+ 𝑦 2

2 )𝐹2 (𝑥 ,𝑄2 )− 𝑦2

2𝐹 𝐿 (𝑥 ,𝑄2 )]

Expect strong non-linear effects in FL from higher twist contributionsDipole model from Bartels et al.

𝑅2/𝐿 (𝑥 ,𝑄2 )= 𝐹 2/𝐿𝐴 (𝑥 ,𝑄2 )

𝐴 ∙𝐹 2 /𝐿𝑝 (𝑥 ,𝑄2 )

Quantify by

19

Nuclear PDFs

20

Di-hadron Correlations

PRD 83, 1 5005 (2011)PRL 106, 022301 (2011)

Prediction in CGC framework Expected experimental significance

GeV

with EPS09 (nPDF shadowing)PYTHIA6 (partons, showers, fragmentation)DPMJet-III (nuclear geometry)

21

Diffractive Scattering

Rapidity gap

|𝑡|≈𝑘2𝜃2

Black disc limit Non-linear amplify in e+A

22

Exclusive Vector Meson Production

Fix momentum transfer

23

Spatial Gluon Distribution

24

Precision Measurement of

25

ERL eRHIC

Electron beam energy 10 GeVProton beam energy 250 GeVIon beam energy 100 GeV/AElectron beam polarization 80%Proton beam polarization 70%

26

MEIC

Electron beam energy 5 GeVProton beam energy 60 GeVIon beam energy 40 GeV/AElectron beam polarization 80%Proton beam polarization 70%

27

DIS Kinematics

Scattered electron

5 GeV x 50 GeV10 GeV x 100 GeV20 GeV x 250 GeV

28

SIDIS Kinematics

Non-exclusive pion

29

DVCS Kinematics

Photon in lab. frame

5 GeV x 100 GeV 10 GeV x 100 GeV 20 GeV x 100 GeV

30

Detector Layout

SolenoidEM-CalorimeterDual Rad. RICHAero RICH/DIRC/HR-ToFTrackingMicro-Vertex Tracking

31

32

arXiv:1212.1701http://www.bnl.gov/npp/docs/EIC_White_Paper_Final.pdf

33

Longitudinal Spin Structure

34

Transverse Momentum Dependence

35

Spatial Imaging DVCS

36

Saturation Scale QS

The ultra-relativistic boost amplifies the gluon densities in a nucleus

𝑄𝑠2 (𝑥 ) ( 𝐴𝑥 )

13

𝑅 𝐴13

37

Diffractive Cross Section