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

Electron-Ion Collider Design 2012 2015 arXiv:1209.0757 arXiv:1504.07961 arXiv:1212.1701 arXiv:1409.1633

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× 10 34 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× 10 33 𝑐 𝑚 −2 𝑠 −1 /𝐴 at 𝑠 =80 GeV

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.

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

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

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 0 2 𝐴 𝑥 1/3

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

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

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

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

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

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

Away-side Particle Correlations Relative two-particle yield on away-side: 𝐽 𝑒𝐴 = 1 𝐴 1 3 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

Diffractive Scattering 𝒌′ 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

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

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

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

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

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

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

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

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