1. Physics with Nuclei at an Electron-Ion Collider
Oleg Eyser
International Conference on the Structure of Baryons
Florida State University, Tallahasse, FL
May 16-20, 2016

2. Electron-Ion Collider Design
2012
2015
arXiv:
arXiv:
arXiv:
arXiv:

3. Electron-Ion Collider Design
JLEIC
Figure-8 ring-ring collider, use of CEBAF
Electrons 3−10 GeV
Protons 20−100 GeV, ions up to 40 GeV/𝑢
𝑠 ≈ 11−45 GeV
ℒ ≈1.1× 𝑐 𝑚 −2 𝑠 −1 /𝐴 at 𝑠 =35 GeV
eRHIC
Add ERL+FFAG recirculating electron rings to RHIC facility
Electrons 6.3−15.9 & 21.2 GeV
Ions up to 100 GeV/𝑢
𝑠 ≈ 20 − 93 GeV
ℒ ≈ 1.7× 𝑐 𝑚 −2 𝑠 −1 /𝐴 at 𝑠 =80 GeV

4. The Nucleus…
What is the fundamental quark-gluon structure of light and heavy nuclei?
Can we experimentally find and explore a universal regime of strongly correlated QCD dynamics?
What is the role of saturated strong gluon fields, and what are the degrees of freedom in this strongly interacting regime?
Can the nuclear color filter provide insight into propagation, attenuation and hadronization of colored probes.

5. QCD matter at an extreme gluon density
Deliverables
Observables
What we learn
Gluon momentum distribution 𝑔 𝐴 (𝑥, 𝑄 2 )
𝐹 2 , 𝐹 𝐿 , and 𝐹 2 𝑐ℎ𝑎𝑟𝑚
Nuclear wave function; 𝑄 2 evolution: onset of DGLAP violation; saturation; 𝐴-dependence of (anti-)shadowing
𝑘 𝑇 -dependent gluon distributions 𝑓 𝑥, 𝑘 𝑇 ; gluon correlations
Dihadron correlations
Non-linear QCD evolution/universality; saturation scale 𝑄 𝑆
Spatial gluon distribution 𝑓 𝑥, 𝑏 𝑇 ; gluon correlations
Diffractive dissociation 𝜎 𝑑𝑖𝑓𝑓 / 𝜎 𝑡𝑜𝑡 ; 𝑑𝜎/𝑑𝑡 and 𝑑𝜎/𝑑 𝑄 2 for vector mesons & DVCS
Non-linear QCD small-𝑥 evolution; saturation dynamics; black disk limit

6. Deep Inelastic Scattering
Lorentz invariants
𝑠= 𝑝+𝑘 2 =4∙ 𝐸 𝑝 ∙ 𝐸 𝑒
𝑄 2 =− 𝑞 2 =− 𝑘−𝑘′ 2
𝑥 𝐵 = 𝑄 2 2∙𝑝∙𝑞
𝑦= 𝑞∙𝑝 𝑘∙𝑝
𝑄 2 =𝑥∙𝑦∙𝑠
Other variables 𝑊 2 = 𝑝+𝑞 2 = 𝑄 2 ∙ 1− 1 𝑥
𝜈= 𝑞∙𝑝 𝑀 = 𝑦∙𝑠 2𝑀
In the collider frame
𝐸 𝑒 ′ = 𝐸 𝑒 ∙ 1−𝑦 + 𝑄 2 4∙ 𝐸 𝑒

8. Hadronization and energy loss (color neutralization and color propagation)
Jet correlations
𝑝 𝑇 -broadening
Gluon saturation, strong color fields
Strongly correlated nonlinear QCD (color glass condensate)
𝑄 𝑆 𝐴 2 =𝑐 𝑄 𝐴 𝑥 1/3

9. Large 𝑄 2 and lever arm for wide 𝑥-range
Reach low-𝑥 sea quark and gluon domination

10. Nuclear Structure Functions
𝑑 2 𝜎 𝑑𝑥𝑑 𝑄 2 = 4𝜋 𝛼 2 𝑥 𝑄 −𝑦+ 𝑦 𝐹 2 𝑥, 𝑄 2 − 𝑦 𝐹 𝐿 𝑥, 𝑄 2
𝜎 𝑟 = 𝑑 2 𝜎 𝑑𝑥𝑑𝑄 𝑥 𝑄 4 2𝜋[1+ 1−𝑦 2 ] = 𝐹 2 𝑥, 𝑄 2 − 𝑦 −𝑦 2 𝐹 𝐿 (𝑥, 𝑄 2 )
Pseudodata from Pythia + EPS09
Assume 3% systematic uncertainty
Moderate luminosity requirement

11. Inclusive Structure Functions
𝜎 𝑟 = 𝑑 2 𝜎 𝑑𝑥𝑑𝑄 𝑥 𝑄 4 2𝜋[1+ 1−𝑦 2 ] = 𝐹 2 𝑥, 𝑄 2 − 𝑦 −𝑦 2 𝐹 𝐿 (𝑥, 𝑄 2 )
(slight offsets for same 𝑄 2 at different 𝑠 )
Reaching into the expected gluon saturation regime

12. Gluon Structure Functions
Comparison with EPS09, saturation model & pQCD shadowing
Tagged charm → complementary to inclusive structure functions
7% systematic uncertainty

13. Nuclear Effects in Nuclei
Structure function
𝑅 2,𝐿 =𝑥 𝐹 2,𝐿 𝐴 (𝑥, 𝑄 2 )/𝐴𝑥 𝐹 2,𝐿 𝑝 (𝑥, 𝑄 2 )
Parton distribution function
𝑅 𝑖 =𝑥 𝑓 𝑖 𝐴 (𝑥, 𝑄 2 )/𝐴𝑥 𝑓 𝑖 𝑝 (𝑥, 𝑄 2 ) →
𝑒+𝐶
∫ℒ𝑑𝑡=10 𝑓 𝑏 −1
𝑒+𝑃𝑏
∫ℒ𝑑𝑡=10 𝑓 𝑏 −1

14. Jet/Particle Correlations
Transverse momentum dependence
Gluon correlations in CGC models
Nonlinear evolution
Pseudodata: PYTHIA, DPMjet, FLUKA, EPS09 & energy loss
𝑝 𝑇 𝑡𝑟𝑖𝑔 >2 GeV 𝑐
1 GeV 𝑐 < 𝑝 𝑇 𝑎𝑠𝑠𝑜𝑐 < 𝑝 𝑇 𝑡𝑟𝑖𝑔

15. Away-side Particle Correlations
Relative two-particle yield on away-side: 𝐽 𝑒𝐴 = 1 𝐴 𝜎 𝑒𝐴 𝑝𝑎𝑖𝑟 / 𝜎 𝑒𝐴 𝜎 𝑒𝑝 𝑝𝑎𝑖𝑟 / 𝜎 𝑒𝑝
Requires measurement of 𝑒+𝑝 baseline
( 𝑥 𝑓𝑟𝑎𝑔 : parton momentum fraction from hadron pair)
𝐽 𝑑𝐴 scales with binary collisions, not 𝐴 1/3

16. Diffractive Scattering𝒌′ 𝒌
𝐌 𝐗 𝐩 𝐩′
Colorless exchange
𝑡= 𝑝−𝑝′ 2
𝑀 𝑋 2 = 𝑝− 𝑝 ′ +𝑘−𝑘′ 2
Rapidity gap
𝜂= − 1 2 ln tan 𝜃 2
Rapidity gap: hermetic detector
Coherent/incoherent: 𝑛, 𝛾 in zero degree calorimeter, spectator tagging in Roman pots
𝑡 ≈ 𝑘 2 𝜃 2

17. Diffractive Cross Section
Colorless: very sensitive to gluon distribution
𝜎 𝑑𝑖𝑓𝑓 / 𝜎 𝑡𝑜𝑡 ≈15% at HERA
uncertainties scaled by factor 10!

18. Exclusive Vector Meson Production
Diffractive pattern is related to the size of the illuminated object → 𝑑𝜎/𝑑𝑡
Nucleon is not a “black disk”
Probes can have different sizes
𝑒+𝐴→ 𝑒 ′ + 𝐴 ′ +𝜙,𝜌,𝐽/Ψ
Diffractive is not necessarily elastic scattering
𝜙,𝜌→
𝐽/𝜓→
𝑡 ≈ 𝑘 2 𝜃 2

19. Spatial Gluon Distribution
Pseudodata: SARTRE event generator (bSat dipole model, tuned to HERA data)
𝜙 is more sensitive to saturation effects
Fourier transform 𝑑𝜎/𝑑𝑡 at small 𝑡: spatial gluon distribution

20. Coherent Diffractive Scattering
Pseudodata: SARTRE event generator
Reuquires 𝑒+𝑝 baseline
Scaled with 𝐴 4/3 (dilute limit at large 𝑄 2 )
Deviations at low 𝑄 2 due to denser gluon regime
∫ℒ𝑑𝑡≈1 𝑓 𝑏 −1

21. Quark Hadronization
Deliverables
Observables
What we learn
Transport coefficients in nuclear matter
Production of light and heavy hadrons and jets in semi-inclusive DIS
Color neutralization: mass dependence of hadronization; Multiple scattering and mass dependence of energy loss; Medium effect of heavy quarkonium production
Fluctuations of the nuclear density
Azimuthal modulation of light and heavy meson production in semi-inclusive DIS
Color fluctuations: connection to heavy ion physics
What is the time scale for hadronization and color neutralization?
Clean environment to address nuclear modification
Well-controlled kinematic variables
Wide range in virtual photon energy: 30<𝜈<2800 GeV
Multidifferential observables
Energy loss model
Absorption model

22. Analyzer: Color Propagation
color neutralization and pre-hadron attenuation
harder fragmentation of heavy flavor mesons
Pseudodata based on Nucl. Phys. A740, 211 (2004), Nucl. Phys. A761, 67 (2005)
Suppression from medium induced energy loss and attenuation of pre-hadrons

23. Complementarity 𝑝+𝐴 / 𝑒+𝐴
Directly probing gluons
Large cross-sections
Initial state effects
Cold nuclear matter energy loss
Ridge
Flow coefficients 𝑣 𝑛
Particle correlations
Transverse momentum dependence
High precision
Partonic kinematics ( 𝑄 2 , 𝑥, 𝜈)
Photoproduction
Tagging of high 𝑁 𝑐ℎ events
Ridge
Flow coefficients 𝑣 𝑛
Particle correlations
Transverse momentum dependence
Spatial distributions

24. Summary An electron-ion collider will…
be complementary to existing heavy ion colliders
allow the study of spatial and momentum dependent distributions of gluons and sea quarks in light and heavy nuclei
enable measurements of diffractive processes in which the system is left intact and the color neutral exchanges are mainly sensitive to the gluon densities
deliver precision measurements for the study of a novel strongly correlated regime of QCD
provide access to color propagation and neutralization in the transition from partons to hadrons with an unprecented kinematic reach (𝜈) and in heavy flavor production