Parton distribution functions PDFs in the EIC era

Parton distribution functions (PDFs) in the EIC era Pavel Nadolsky CTEQ collaboration Southern Methodist University Dallas, TX, USA HUGS’ 2019 Summer School Jefferson Laboratory June 5, 2019

The Electron-Ion Collider aims to study the inner structure of nucleons and nuclei at an unprecedented level of detail Do we trust QCD theory to this level of accuracy? Will the extremely elaborate experiments provide us with reliable information? The global analysis of PDFs is an active research area exploring these questions 2019 -06 -05 P. Nadolsky, HUGS'2019 program 2

Outline of the lectures 1. Intuitive introduction to the parton model and QCD factorization 2, 3. Factorization in deep-inelastic scattering Rich quantum field theory [using slides by Wu-Ki Tung] Elaborate large-scale data analysis 4, 5. Determination and modern applications of PDFs Focus on the simplest case of collinear factorization for unpolarized cross sections 2019 -06 -05 P. Nadolsky, HUGS'2019 program 3

References • CTEQ summer school lectures – each lecturer covers the subject from a complementary viewpoint! http: //www. physics. smu. edu/scalise/cteq/#Summer Many textbooks… • • • J. C. Collins, Foundations of perturbative QCD, (Cambridge University Press, 2013) Handbook on Perturbative QCD http: //www. physics. smu. edu/scalise/cteq/handbook/v 1. 1/handbook. pdf. J. Campbell, J. Huston, and F. Krauss, The Black Book of Quantum Chromodynamics (Oxford University Press, 2017). … and reviews • J. Gao, L. Harland-Lang, J. Rojo (2018), “The Structure of the Proton in the LHC Precision Era, " Phys. Rept. 742, 1 (2018), ar. Xiv: 1709. 04922 [hep-ph]. • K. Kovarik, P. Nadolsky, D. Soper, Hadron structure in high-energy collisions, ar. Xiv: 0905. 06957 • … 2019 -06 -05 P. Nadolsky, HUGS'2019 program 4

PDFs are important for both nuclear and high-energy physics

Coordinated Theoretical Experimental study of QCD Initiated around 1990 to stimulate interactions between • Experimentalists and theorists, especially at the newly built Tevatron • High-energy physics and hadronic physics communities This is achieved by various initiatives: • Global analysis (the term coined by J. Morfin and Wu-Ki Tung) constrains PDFs or other nonperturbative functions with data from diverse hadronic experiments CT 18 • Workshops and summer schools • Annual Wu-Ki Tung award for junior researchers working on intersections of experiment and theory [nominate by August 15 each year] 2019 -06 -05 P. Nadolsky, HUGS'2019 program 2019: new experiments (LHC, EIC, LHe. C, …)! New 6 objectives!

PDFs are provided by several groups in various formats Which PDF set is the best for your calculation?

Frontiers of the PDF analysis Experiment New collider and fixed-target measurements Theory Precision PDFs, specialized PDFs Statistics Hessian, Monte-Carlo techniques, neural networks, reweighting, meta-PDFs… 2019 -06 -05 Significant advances on all frontiers will be necessary to meet the targets of future experiments P. Nadolsky, HUGS'2019 program 8

Now I have questions for you From time to time, I will ask questions to check if you are following me. Just answer what you can. Write your answers on the paper. Please raise your hand if you are • an undergraduate student • a postdoc • you took a course on quantum field theory • you took other particle physics courses 2019 -06 -05 P. Nadolsky, HUGS'2019 program 9

QCD versus the parton model A 1 -minute poll for everyone Can you define in 1 -2 sentences: 1. What is quantum chromodynamics (QCD)? 2. What is the parton model? Are they the same? Choose: 3: If you can define both 4: If you can define neither 2019 -06 -05 P. Nadolsky, HUGS'2019 program 10

Parton model vs. QCD: definitions Nucleon quarks 2019 -06 -05 P. Nadolsky, HUGS'2019 program 11

The inner world of a hadron Atom Nucleus Nucleon Quarks & gluons The structure of the hadron drastically changes as the resolution of the “microscope” (scattering process) increases 2019 -06 -05 P. Nadolsky, HUGS'2019 program 12

The inner world of a hadron Atom Nucleus Nucleon Quarks & gluons A short-distance probe (virtual photon, heavy boson, gluon) resolves increasingly small structures inside the nucleon. 2019 -06 -05 P. Nadolsky, HUGS'2019 program 13

A variety of nonperturbative functions can be introduced to describe the rich Internal structure of nucleons. Which core principles enable us to determine these functions? I will review them by starting with simple examples 2019 -06 -05 P. Nadolsky, HUGS'2019 program 14

Our “electroweak microscopes”: three instructive processes to probe the hadronic structure Involve scattering of an electroweak boson on quasi-free quarks (always perturbative) emerging from, and fragmenting into, nonperturbative hadronic states Lectures by Carlota Andres 2019 -06 -05 15

Hadrons Simplest Feynman diagram 2019 -06 -05 16

2019 -06 -05 P. Nadolsky, HUGS'2019 program 17

2019 -06 -05 P. Nadolsky, HUGS'2019 program 18

Recoil (extra particles) 2019 -06 -05 P. Nadolsky, HUGS'2019 program 19

aka “Drell-Yan process” View in the AB c. m. frame Simplest Feynman diagram P. Nadolsky, HUGS'2019 program 20

2019 -06 -05 P. Nadolsky, HUGS'2019 program 21

2019 -06 -05 P. Nadolsky, HUGS'2019 program 22

2019 -06 -05 P. Nadolsky, HUGS'2019 program 23

2019 -06 -05 P. Nadolsky, HUGS'2019 program 24

Now a silly question to you: Why did I draw hadrons as disks, not circles? 2019 -06 -05 P. Nadolsky, HUGS'2019 program 25

2019 -06 -05 P. Nadolsky, HUGS'2019 program 26

Space-time diagrams: rest frame of an event E E 2019 -06 -05 P. Nadolsky, HUGS'2019 program 27

Space-time diagrams: rest frame of an event E Cartesian coordinates Absolute future E Absolute past 2019 -06 -05 P. Nadolsky, HUGS'2019 program 28

Space-time diagrams: Light-cone coordinates provide an intuitive alternative to the Cartesian coordinates. They are especially convenient for various collider calculations. 2019 -06 -05 P. Nadolsky, HUGS'2019 program 29

Space-time diagrams: Light-cone coordinates 2019 -06 -05 30

31

32

Can you visualize radiation from a highly boosted object? For example, radiation of electromagnetic waves from a relativistic electron As a gauge theory, QCD is like quantum electrodynamics in many aspects Quarks are QCD-charged spin-1/2 fermions (analogs of electrons) Gluons are spin-1 bosons that carry the strong force (analogs of photons) 2019 -06 -05 P. Nadolsky, HUGS'2019 program 33

z 2019 -06 -05 P. Nadolsky, HUGS'2019 program 34

z 2019 -06 -05 P. Nadolsky, HUGS'2019 program 35

z 2019 -06 -05 P. Nadolsky, HUGS'2019 program 36

Relativistic transformations, higher-spin fields • 2019 -06 -05 P. Nadolsky, HUGS'2019 program 37

Relativistic transformations, higher-spin fields Factorization of coordinate/momentum, spin, and gauge degrees of freedom can be rigorously proved for simple (inclusive one-scale) observables for weakly interacting partons 38 2019 -06 -05 P. Nadolsky, HUGS'2019 program

Physical intuition behind factorization • 2019 -06 -05 P. Nadolsky, HUGS'2019 program 39

2019 -06 -05 P. Nadolsky, HUGS'2019 program 40

2019 -06 -05 P. Nadolsky, HUGS'2019 program 41

End of module 1 2019 -06 -05 P. Nadolsky, HUGS'2019 program 42