1. QCD: the Final Frontier of Standard Model Physics
Xiangdong Ji
Tsung-Dao Lee Inst, Shanghai
& University of Maryland
July, 25, 2017

2. Outline Why QCD is so difficult? How to make progress SM successes
Strongly coupled QCD systems
Constraint from relativity: frame-dependence
Constraint from relativity: QCD vacuum
How to make progress
Asking good questions
Experimental program (Jlab 12 GeV, EIC)
Solving the fundamental theory
Making the physics intuitive

3. Why is non-perturbative QCD the ultimate challenge of the Standard Model physics?

4. Standard model successes:
The standard model itself has been hugely successful in explaining many physics phenomena
Electroweak processes
High-energy QCD processes
Perturbation theory works! （LHC）

5. Standard model challenges
However, it remains a challenge to understand how QCD works at low energy, where theory becomes non-perturbative:
Guts of Strong Interactions!
Similar in nature to Condensed Matter Physics: the Lagrangian is known, but the solution is hard
High Tc, Hall effects, strongly coupled electron systems, etc

6. Why QCD is so difficult?
Strongly coupled: Similar to NR electron systems
Non-perturbative approximation methods must be devised.
Ab initio numerical simulations
Working Language?
Extra difficulty: Relativity
Center-of-mass and internal motion coupled
The QCD vacuum

7. Relativity: internal states are frame-dependent
The center-of-mass motion is part of the physics: the bound state has definite total momentum
Because the boost operator is dynamical, the internal states are different at different momenta!
𝑝 ′ =𝑈 𝐿 |𝑝〉
where 𝑝 ′ is different from |𝑝〉 dynamically!
The electromagnetic fields of a moving charge depends on its velocity or 𝛽=𝑣/𝑐

8. Elastic scattering: form factors

9. Relativity: QCD vacuum:
Hadron systems are built upon the QCD vacuum which in itself is extraordinary complex
Similar to a strongly-interacting fermi sea in Condensed Matter Systems, where Landau’s fermi liquid theory breaks down!
And the hadron physics phenomena occur as complex excitations of this vacuum.

10. Understanding the water waves
Hadron physics that we try to understand!
QCD vacuum that we don’t observe

11. Water-wave analogy going further
We know the basic interactions between water mols
but we don’t know how the state of water is formed, or how to calculate the properties of water.
how the wave excitations are formed on the top of it?
Low-energy effective theory: Navier-Stokes equation
To understand the waves, we just need to solve Novier- Stocks equation
Turbulences?
In hadron physics, a universal effective description of hadrons has not been found
Existing ones are partially effective in limited domains.
We are forced to start from scratch

12. How to make progress?

13. Step 1: Asking good questions

14. Important questions about the nucleon
How does the nucleon get its mass, giving the gluons and quarks are (nearly) masses?
Where does the proton spin come from?
What is the role of gluons inside the nucleon?
What is the internal landscape of the nucleon, if we don’t have an approximate QCD nucleon wave function. ….

15. The proton mass: at the heart of visible matter

18. Proton mass
To a good approximation, QCD is a theory without mass (quarks are nearly massless, gluons mass zero)
However does mass generate in QCD? It must be generated from the energy of the strong interaction theory!
M= E/c2
What are the possible energies? Why they are what they are?
How to measure them? what do they tell us about the strong interaction dynamics?

19. The spin structure of the nucleon
Spin-1/2 arises from a complicated many-body system
How is it distributed among different sources?
Two pictures about the proton spin:
Jaffe & Manohar, 1990
1 2 = ΔΣ+Δ𝐺+ ℓ 𝑞 𝑧 + ℓ 𝑔 𝑧
Parton picture for longitudinally polarized nucleon
X. Ji, 1996
1 2 = 𝐽 𝑞 + 𝐽 𝑔 = 1 2 ΔΣ+ 𝐿 𝑞 𝑧 + J g
Naturally relate to the partons in a trans. polarized nucleon
11/12/2018

20. Spin program has had important progress
We know fairly well about the part related to the quark helicity contribution, ∆∑ = (0.3±0.05)
However, the details on the flavor and sea structure of the polarization are still sketchy.
Contribution from small and large-x?
We know with reasonable errors about the gluon helicity contribution ∆G
The polarized proton collisions at RHIC have produced important information.
current data
w/ EIC data

21. The orbital motion:
Orbital motion of quarks and gluons must be significant inside the nucleons!
This is in contrast to the naive non-relativistic quark model, which was the motivation to introduce the color quantum number!
The orbital motion shall generate direct orbital AM which must contribute to the spin of the proton.
However, orbital motion can also give rise to a range of interesting physical phenomena.

22. What are the role of gluons in the nucleon?
Due to the strong coupling of QCD, the gauge particles play a much more important role in the nucleon structure than the photons in the hydrogen atom.
Gluon is known to constitute about ½ momentum of the nucleon, and it also has the key role giving rise to the nucleon mass and spin.
If we don’t understand the gluon, we don’t understand the nucleon!
This is similar to the case that we cannot claim to understand the nuclei without the neutrons
11/12/2018

23. An image of gluon?

24. Internal landscape of the nucleon
The internal structure of the nucleon has been explored historically with important milestones
O. Stern “for … and his discovery of the magnetic moment of the proton”. （Nobel prize, 1943)
R. Hofstadter “for … and for his thereby achieved discoveries concerning the structure of the nucleons” . (Nobel prize, 1961)
J.I . Friedman, H. W. Kendall and R. E. Taylor "for their pioneering investigations concerning deep inelastic scattering of electrons on protons and bound neutrons, which have been of essential importance for the development of the quark model in particle physics". (Nobel prize, 1990)
However, we are still cannot describe the inside of the nucleon in the same confidence as we do about the hydrogen atom.

25. Step 2: Learning from experimental data (Jlab 12 GeV, EIC)

26. Importance of a robust experimental program (Jlab 12 GeV)
Experiments provides the fountain of ideas for understanding the strong interactions!
How Nature solves the QCD
Possible effective descriptions
New phenomena in QCD systems
We have learnt a great deal through experimental data from the past
SLAC, MIT-Bates, Jefferson Lab 6 GeV, RHIC, LHC, etc.

27. High-energy electron scattering
At Jlab-12 GeV and EIC, the structure of the protons and neutrons will be studied with a highly-virtual photon probe.
Deep-inelastic (traditional）
Deeply-virtual but elastic (“new”)
The probe is hard (high-momentum) and relativistic, the nucleon is examined with this
probe in the infinite momentum frame (light-cone correlations)

28. Deep-inelastic scattering
The quarks are struck by the virtual photon and form a high-energy jet, separated from the remnant of the nucleon
Inclusive DIS
Parton distributions
Semi-inclusive DIS, measure additional hadrons in final state
Pt-dependent parton distributions

29. Transverse momentum dependent parton distributions (TMDPD）
Partons transverse momentum can be probed through semi-inclusive processes.
Complete momentum spectrum of single particle, similar to ARPES in Condensed Matter Physics
Important to probe the single particle dynamics inside the nucleon.
Similar processes are important to probe the gluon saturation (two jets)
(F. Yuan et al)

30. New: “Deep-elastic scattering” (deeply-virtual elastic process)
A new class of processes found useful in studying the nucleon structure (1996)
Can probe generalized parton distributions: internal landscape of the nucleon! Q2 t

31. Building a comprehensive understanding of the structure
Parton Distributions
Form factors:

32. Building a comprehensive understanding of the structure
Parton Distributions
Generalized parton distributions
Form factors:

33. Gluon tomography at small x (GPDs， EIC）
11/12/2018

34. Two different frames: static and infinite momentum
Physics is independent of frame?
Physical equations are covariant (take the same form) in different frame.
However, the physics content can differ, e.g., the electromagnetic fields of a moving charge.
The high-energy probes at JLab 12 GeV can be analyzed with two different pictures, similar to quantum mechanical
Schrodinger picture
Heisenberg picture

35. Step 3: Solving the fundamental theory

36. Theoretical approaches
Build a static frame picture, and calculate time- dependent correlations （’70s，’80s）
Boost wave functions to infinite momentum frame.
Light-front quantization (‘90s)
Advocated by K. Wilson and S. Brodsky et al
Very difficult to make systematic approximations
Lattice QCD, calculate moments of parton distributions (’00s)
Need all experimental x information
Higher moments are difficult

37. Recent theory advances
It has been realized in 2013 that the Large momentum frame (Feynman) or Schrodinger picture interpretation of the parton physics provides a hope in lattice calculations
Large momentum effective field theory, or LaMET
X. Ji, Phys. Rev. Lett. 110, (2013)
arXiv: [hep-ph].
X. Ji, Sci. China Phys. Mech. Astron. 57, 1407 (2014),
arXiv: [hep-ph].

38. Infinite momentum frame (Feynman picture)
In which, the nucleon is moving at the near speed of light (Lorentz contraction)
The high-energy probe studies the static correlation function (similar to many-body physics) in a fast moving system
Feynman parton model 𝜉3 𝜉0 Z

39. Large momentum effective field theory (LaMET, 2013)
Large but not infinite momentum nucleons are created on QCD lattices.
Static quark and gluon correlation functions of various types can be calculated in such a nucleon state using standard lattice QCD approach.
These lattice correlations can be matched directly to Jlab or EIC observables through QCD perturbation theory.
There are severable groups in the world pursuing this approach

40. Recent progress
Several preliminary lattice QCD calculations have been explored. The results are encouraging.
Renormalization properties of the quasi- distributions are finally understood on lattice. Non- perturbative matchings between lattice observables and physical quantities can be made.
Progress has been made in creating large momentum states on lattice
Specialized lattices for such calculations shall be created in the future.

41. Polarized quark distribution from lattice
J.W.Chen et al, Nucl. Phys. B911 (2016)

42. Gluon Helicity G in the proton
First lattice calculation of gluon polarization, made possible by LaMET. Kentucky group:
Phys. Rev. Lett. 118, (2017)

43. Step 4: Making the physics intuitive

44. How do we make an intuitive picture of the proton?
The picture shall in the infinite momentum frame as also all the info we learn in high-energy electron scattering is directly related to this frame.
The longitudinal direction is in the momentum space.
Transverse coordinates can be either in coordinate and momentum space
3 = 1+2

45. Toward a better and fun picture?
Elastic form factors in transverse plane
Feynman parton distributions in x,
TMD PD, (x, 𝑘 ⊥ ) , Parton saturation?
GPDs, (x, 𝑏 ⊥ ), gluon radius?
Wigner distributions in (x, 𝑏 ⊥ ,𝑘 ⊥ )
Quantum coherence?
Quantum entanglement?
QCD Wave functions?

46. Outlook
Interesting phenomena are the ultimate drive for understanding the strong interaction physics in non-perturbative domain
The solution of the problem requires high precision experimental data and innovative lattice QCD calculations
Ultimately the understanding of the phenomena needs a good intuitive picture (language) of physics.