QCD: the Final Fronti er of Standard Model Physics Xiangdong Ji Tsung-Dao Lee Inst, Shanghai & University of Maryland July, 25, 2017 Outline 1. Why QCD is so difficult? a.

b. c. d. SM successes Strongly coupled QCD systems Constraint from relativity: frame-dependence Constraint from relativity: QCD vacuum 2. How to make progress a.

b. c. d. Asking good questions Experimental program (Jlab 12 GeV, EIC) Solving the fundamental theory Making the physics intuitive Why is non-perturbative QCD the ultimate challe

nge of the Standard Mo del physics? Standard model successes: The standard model itself has been hugel y successful in explai ning many physics p henomena Electroweak process es

High-energy QCD pr ocesses Perturbation theory works! LHC Standard model challenges However, it remains a challenge to understand how QCD works a t low energy, where theory beco mes non-perturbative: Guts of Strong Interactions!

Similar in nature to Condensed Matter Physics: the Lagrangian i s known, but the solution is har d High Tc, Hall effects, strongly cou pled electron systems, etc Why QCD is so difficult? Strongly coupled: Similar to NR electron systems Non-perturbative approximation methods must b

e devised. Ab initio numerical simulations Working Language? Extra difficulty: Relativity 1. Center-of-mass and internal motion coupled 2. The QCD vacuum Relativity: internal states a re frame-dependent The center-of-mass motion is part of the physics: th e bound state has definite total momentum

Because the boost operator is dynamical, the intern al states are different at different momenta! where is different from dynamically! The electromagnetic fields of a moving charge depends on its velocity or Elastic scattering: form fac tors Relativity: QCD vacuum: Hadron systems are built upon the QCD vacuum wh

ich in itself is extraordinary complex Similar to a strongly-interacting fermi sea in Con densed Matter Systems, where Landaus fermi li quid theory breaks down! And the hadron physics phenomena occur as compl ex excitations of this vacuum. Understanding the water w aves Hadron physics that we

try to understand! QCD vacuum that we dont observe Water-wave analogy going further We know the basic interactions between water mols but we dont know how the state of water is formed, or ho w 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-Stoc ks equation Turbulences? In hadron physics, a universal effective description of h adrons has not been found Existing ones are partially effective in limited domains. We are forced to start from scratch

How to make progr ess? Step 1: Asking good questions Important questions about the nucleon 1. How does the nucleon get its mass, giving the glu ons and quarks are (nearly) masses? 2. Where does the proton spin come from?

3. What is the role of gluons inside the nucleon? 4. What is the internal landscape of the nucleon, if we dont have an approximate QCD nucleon wave function. 5. . The proton mass: at the heart of visible mat Proton mass To a good approximation, QCD is a theory without mass (quarks are nearly massless, gluons mass zer

o) However does mass generate in QCD? It must be ge nerated from the energy of the strong interaction t heory! M= E/c2 What are the possible energies? Why they are what they are? How to measure them? what do they tell us about t he strong interaction dynamics? The spin structure of th

e Spin-1/2 nucleon arises from a complicated many-body syst em How is it distributed among different sources? Two pictures about the proton spin: Jaffe & Manohar, 1990 Parton picture for longitudinally polarized nucleon X. Ji, 1996 Naturally relate to the partons in a trans. polarized nucleon

02/12/2020 19 Spin program has had imp ortant progress We know fairly well about the part related to the quark helicity contri

bution, = (0.3) However, the details on the flavor and sea structure of the polarization are still sketc hy. Contribution from small and large-x? We know with reasonable errors ab out the gluon helicity contribution G The polarized proton collisions at RHIC have produced important information.

current data w/ EIC data The orbital motion: Orbital motion of quarks and gluons must be signifi cant inside the nucleons! This is in contrast to the naive non-relativistic quark mod el, which was the motivation to introduce the color quan

tum 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 rang e of interesting physical phenomena. What are the role of gluons in the nucleon? Due to the strong coupling of QCD, the gauge partic les play a much more important role in the nucleon

structure than the photons in the hydrogen atom. Gluon is known to constitute about momentum of the nucleon, and it also has the key role giving ris e to the nucleon mass and spin. If we dont understand the gluon, we dont underst and the nucleon! This is similar to the case that we cannot claim t o understand the nuclei without the neutrons 02/12/2020 22

An image of gluon? Internal landscape of the nucleon The internal structure of the nucleon has been explore d 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 conc

erning the structure of the nucleons . (Nobel prize, 1961) J.I . Friedman, H. W. Kendall and R. E. Taylor "for their pioneering i nvestigations concerning deep inelastic scattering of electrons on protons and bound neutrons, which have been of essential import ance 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 hy drogen atom.

Step 2: Learning from experime ntal data (Jlab 12 GeV, EIC) Importance of a robust experi mental program (Jlab 12 GeV) Experiments provides the fountain of ideas for unders tanding the strong interactions! How Nature solves the QCD Possible effective descriptions

New phenomena in QCD systems We have learnt a great deal through experimental dat a from the past SLAC, MIT-Bates, Jefferson Lab 6 GeV, RHIC, LHC, etc. High-energy electron scatt ering At Jlab-12 GeV and EIC, the structure of the protons and neutrons will be studied with a highly-virtual p hoton 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 c orrelations) Deep-inelastic scattering The quarks are struck by the virtual photon and for

m 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 Transverse momentum dependen

t parton distributions (TMDPD Partons transverse momentum can be probed through semi-inclusive proces ses. Complete momentum spectrum of sin gle particle, similar to ARPES in Conde nsed Matter Physics Important to probe the single particle dynamics inside the nucleon. Similar processes are important to pr obe the gluon saturation (two jets)

(F. Yuan et al) New: Deep-elastic scatteri ng (deeply-virtual elastic process) A new class of processes found useful in studying the nucle on structure (1996) Q2 t

Can probe generalized parton distributions: internal landsc ape of the nucleon! Building a comprehensive understanding of the struct ure Parton Distributions Form factors:

Building a comprehensive understanding of the struct ure Parton Distributions Generalized parton distributions Form factors:

Gluon tomography at small x (GPDs EIC 02/12/2020 33 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 electro magnetic fields of a moving charge. The high-energy probes at JLab 12 GeV can be analy zed with two different pictures, similar to quantum mechanical Schrodinger picture Heisenberg picture

Step 3: Solving the fundam ental theory Theoretical approaches Build a static frame picture, and calculate time-dep endent 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 distributi ons (00s) Need all experimental x information Higher moments are difficult Recent theory advances It has been realized in 2013 that the Large momentum fra me (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, 262002 (2013) arXiv:1305.1539 [hep-ph]. X. Ji, Sci. China Phys. Mech. Astron. 57, 1407 (2014), arXiv:1404.6680 [hep-ph]. Infinite momentum frame (Feynman picture) In which, the nucleon is moving at the near speed o f light (Lorentz contraction)

The high-energy probe studies the static correlation function (similar to many-body physics) in a fast mo ving system 0 0 Feynman parton model Z 3

Large momentum effective field theory (LaMET, 2013) Large but not infinite momentum nucleons are crea ted on QCD lattices. Static quark and gluon correlation functions of vario us types can be calculated in such a nucleon state u sing standard lattice QCD approach. These lattice correlations can be matched directly t o Jlab or EIC observables through QCD perturbation theory.

There are severable groups in the world pursuing th is approach Recent progress Several preliminary lattice QCD calculations have b een explored. The results are encouraging. Renormalization properties of the quasi-distributio ns are finally understood on lattice. Non-perturbati ve matchings between lattice observables and physi cal quantities can be made. Progress has been made in creating large momentu

m states on lattice Specialized lattices for such calculations shall be cre ated in the future. Polarized quark distribution from lattice J.W.Chen et al, Nucl. Phys. B911 (2016) 246-273 Gluon Helicity G in the proton First lattice calculation of gluon polarization,

made possible by LaMET. Kentucky group: Phys. Rev. Lett. 118, 102001 (2017) Step 4: Making the physics intui tive How do we make an intuiti ve picture of the proton? The picture shall in the infinite momentum frame a s also all the info we learn in high-energy electron s

cattering is directly related to this frame. The longitudinal direction is in the momentum s pace. Transverse coordinates can be either in coordina te and momentum space 3 = 1+2 Toward a better and fun pic ture? Elastic form factors in transverse plane

Feynman parton distributions in x, TMD PD, (x, ) , Parton saturation? GPDs, (x, ), gluon radius? Wigner distributions in (x, ) Quantum coherence? Quantum entanglement? QCD Wave functions? Outlook Interesting phenomena are the ultimate drive for u nderstanding the strong interaction physics in nonperturbative domain

The solution of the problem requires high precision experimental data and innovative lattice QCD calcul ations Ultimately the understanding of the phenomena ne eds a good intuitive picture (language) of physics.