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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.

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Parton distribution functions (PDFs) in the EIC era

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  1. 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

  2. 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 P. Nadolsky, HUGS'2019 program

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

  4. 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/v1.1/handbook.pdfJ. • 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), arXiv:1709.04922 [hep-ph]. • K. Kovarik, P. Nadolsky, D. Soper, Hadron structure in high-energy collisions, arXiv:0905.06957 • … P. Nadolsky, HUGS'2019 program

  5. PDFs are important for both nuclear and high-energy physics

  6. 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 • 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] CT18 2019: new experiments (LHC, EIC, LHeC,…)! New objectives! P. Nadolsky, HUGS'2019 program

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

  8. Frontiers of the PDF analysis Significant advances on all frontiers will be necessary to meet the targets of future experiments P. Nadolsky, HUGS'2019 program

  9. 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 graduate student • a postdoc • you took a course on quantum field theory • you took other particle physics courses P. Nadolsky, HUGS'2019 program

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

  11. Parton model vs. QCD: definitions The parton model is an order-of-magnitude model describing scattering on a highly boosted composite quantum particle (parent, or target) in terms of scatterings on the particle’s constituents (partons). The parton model invokes only basic QFT properties, such as Lorentz invariance and weakness of short-distance parton interactions. To accurately predict scattering rates, a more fundamental theory is needed. QCD, the fundamental gauge theory of the Standard Model Lagrangian, is such quantitative fundamental theory. Nucleon quarks P. Nadolsky, HUGS'2019 program

  12. The inner world of a hadron The structure of the hadron drastically changes as the resolution of the “microscope” (scattering process) increases P. Nadolsky, HUGS'2019 program

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

  14. 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 themby starting with simple examples P. Nadolsky, HUGS'2019 program

  15. Our “electroweak microscopes”:three instructive processesto 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

  16. Hadrons 1.hadrons at LEP View in the frame Hadrons Simplest Feynman diagram

  17. 1.hadrons at LEP Notations: is the 4-momentum of the boson’ and are Lorentz invariants is the invariant mass of Z In the c.m. (lab) frame, the boson is at rest, initial-state EM radiation is neglected P. Nadolsky, HUGS'2019 program

  18. 1.hadrons at LEP , where is the part of that is orthogonal (in the covariant sense) to the quark’s and antiquark’s momenta: If quark masses are negligible compared to the other energy scales ( P. Nadolsky, HUGS'2019 program

  19. 1.hadrons at LEP When only a pair is produced, the quark and anti-quark momenta are exactly back-to-back in the lab frame and equal in the magnitude: When additional radiation is emitted, and are misaligned by an angle This angle in the c.m. frame can be expressed as . That is, is an indicator of the additional radiation Recoil (extra particles) P. Nadolsky, HUGS'2019 program

  20. 2. at the Large Hadron Collider and Tevatron aka “Drell-Yan process” View in the AB c.m. frame Simplest Feynman diagram P. Nadolsky, HUGS'2019 program

  21. 2. at the Large Hadron Collider and Tevatron The same Lorentz-invariant definitions apply: , P. Nadolsky, HUGS'2019 program

  22. 2. at the Large Hadron Collider and Tevatron In the lab frame (AB c.m. frame), the boson moves with 4-momentum is naturally interpreted as the transverse momentum of the vector boson in the lab frame But, an angular variable can be also constructed in DY process. It indicates additional radiation and is an analog of the non-collinearity angle in hadroproduction P. Nadolsky, HUGS'2019 program

  23. 3.(SI)DIS at Jefferson Lab, HERA, EIC,… View in the c.m. frame Simplest diagram: P. Nadolsky, HUGS'2019 program

  24. 3.(SI)DIS at Jefferson Lab, HERA, EIC,… View in the c.m. frame To get the Breit (brick-wall) frame: Boost in the direction to make momentum of purely spacelike b) Flip the axis P. Nadolsky, HUGS'2019 program

  25. 3.(SI)DIS at Jefferson Lab, HERA, EIC,… View in the c.m. frame Now a silly question to you: Why did I draw hadrons as disks, not circles? P. Nadolsky, HUGS'2019 program

  26. 3.(SI)DIS at Jefferson Lab, HERA, EIC,… View in the c.m. frame Answer: All rapidly moving particles are highly Lorentz-contracted. (Ultra-thin pancakes) Their longitudinal size practically does not matter. But, the interaction depends on the transverse positions of the particles (impact parameter ) P. Nadolsky, HUGS'2019 program

  27. Space-time diagrams: rest frame of an event E E World lines of light signals (at angles and ) P. Nadolsky, HUGS'2019 program

  28. Space-time diagrams: rest frame of an event E Cartesian coordinates Absolute future E World lines of light signals (at angles and ) Absolute past P. Nadolsky, HUGS'2019 program

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

  30. Space-time diagrams: Light-cone coordinates

  31. World-line of a point moving with The world line must be within to the axis

  32. Reference frame moving with As , both and axes align with the or axis;

  33. 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) P. Nadolsky, HUGS'2019 program

  34. Here is a scalar wave from a radiating point source at rest: The wave from the point source is spherical: ; . Assume no attenuation (no energy loss from the wave) Question (sketch on the paper for 1 minute): How will the wave change if the source quickly moves to the right (in the direction of the arrow?) z P. Nadolsky, HUGS'2019 program

  35. A wave of a source moving with (to the right) The wave is distorted by the Doppler effect The forward wave has dependence (contracted wave fronts, ) The backward wave has dependence (extended wave fronts, ) z P. Nadolsky, HUGS'2019 program

  36. A wave of a source moving with (to the right) Waves radiated in the “past” in the proton’s rest frame have compressed into a small interval the “future” has extended into a large By Heisenberg uncertainty principle, the boosted object in the +z direction has large and small (small and large for an object boosted in the direction) This is the first indication that the the and dependence of relativistic interactions can be separated (factorized) z P. Nadolsky, HUGS'2019 program

  37. Relativistic transformations, higher-spin fields I just described the effect of a Lorentz transformation on a spin-0 field : Frame K Frame K’ Higher-spin fields transform as SU(N) spin-1 field: SU(N) spin-1/2 field: Same intuition about factorization at applies. Mathematical realization beyond the leading order is non-trivial. P. Nadolsky, HUGS'2019 program

  38. 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 P. Nadolsky, HUGS'2019 program

  39. Physical intuition behind factorization • Relative speeds of hadrons are close or equal to speed of light • Particles appear time-dilated and Lorentz-contracted along their directions of motion • Naturally described in terms of light-cone coordinates • Partons appear frozen inside parent hadrons • Partons collide pair-wise, nearly independently and instantaneously asymptotic freedom at P. Nadolsky, HUGS'2019 program

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

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