Model Independent Nucleon results Gerald A. Miller University of Washington “Everything that rises”, Martin Puryear

Blind men and the elephant

Physicists and the nucleon Soliton s s pion u d gluon

Experimental Observables/outline Tranverse Momentum Distributions form factors TMDs GPDs Generalized Parton Distributions

Experimental Observables/outline Nucleon TMDs form factors Shape charge density spin GPDs Aim: unified picture (including spin)

What is a form factor? How to tell how big something is? Look e’ Deep Inelastic Scattering q(x) q P e Proton

What is a form factor? How to tell how big something is? Proton Look P+q Elastic e’ Non rel form factor -old q P e Proton

Elastic electron scattering from a nucleon j=<e’||e> J=<p’||p> Deep inelastic scattering Nucleon vertex: 1990 Nobel Prize Dirac Pauli Form factors describing nucleon shape/structure 1961 Nobel Prize Cross section for scattering from a point-like object

Expectations- Pre Jlab Proton QF2 /F1 GE/GM Q2 Q2 old helicity conservation

Jlab Jlab QF2 /F1 GE/GM QF2/F1 GE/GM Q2 Q2 Proton

Meaning of elastic form factors-I Old Interpretation- Breit frame GE is helicity flip matrix element of J0 Interpretation: GE(Q2) = Fourier trans. of charge density Relativistic : wave function is frame dependent, initial and final states differ interpretation of Sachs FF is wrong

Light cone coordinates/Infinite momentum frame

Relativistic formalism- kinematic subgroup of Poincare Lorentz transformation –transverse velocity v k- such that k2 not changed Just like non-relativistic with k+ as mass

Model- Impulse Approximation Frank, Jennings, Miller ‘95 g carry orbital angular momentum

Ratio of Pauli to Dirac Form Factors Frank,Jennings, Miller theory1995, data 2000 Model flat curve due to orbital ang. mom.

Orbital angular momentum and proton shape Shape of proton?? Wigner Eckart-no quadrupole moment spin dependent densities SDD Non-relativistic example

 s r

Shapes of the proton three vectors n, K, S MODEL , HOW TO MEASURE?

Field theoretic SDD Transverse Momentum Distributions TMDs Probability for momentum K, and spin direction n. Matrix elements depend on three vectors n, K, S, equal time Transverse Momentum Distributions TMDs x=K+/P+ Mulders & Tangerman ’96

Polarized TMD Quark Distributions Nucleon Unpol. Long. Trans. Quark Unpol. Long. Trans. Boer, Mulders, Tangerman (96&98) 21

Field theoretic SDD Transverse Momentum Distributions TMDs Probability for momentum K, and spin direction n. Matrix elements depend on three vectors n, K, S, equal time Transverse Momentum Distributions TMDs x=K+/P+ Mulders & Tangerman ‘96 i+5~+i ~ 0 i Integrate: SDD over Kz ; TMD over x: non-spherical nature of proton related to

Model-Transverse spin-dependent densities Lattice calcs have done GPD, not TMD

Measure :e, p  e’,  X ST e’  e Cross section has term proportional to cos 3 Boer Mulders ‘98

Summary of SDD SDD are closely related to TMD’s If is not 0, proton is not round. Experiment can show proton ain’t round. The Proton

Journey to the center of the neutron: charge density π- p center is + center is + One gluon exchange also gives positive central charge density d u d

e-i q b

Parameterizations of nucleon form factors hep-ex/0602017

Results BBBA Kelly Negative

Negative F1 means central density negative GeV2 Why?

quark orbital angular momentum Generalized Parton Distributions : yield 3-dim quark structure of nucleon Burkardt (2000,2003) Belitsky,Ji,Yuan (2004) Elastic Scattering transverse quark distribution in coordinate space DIS longitudinal quark distribution in momentum space DES (GPDs) fully-correlated quark distribution in both coordinate and momentum space quark orbital angular momentum

relate:high x, high Q2 , low b

Input distribution x Neutron- dv dominates at high x (b=0) ????

Neutron charge distribution vs x high x: d dominates at small b

Neutron ρ(b,x) x=0.3 x=0.1 x=0.5 d dominates at high x, low b

Neutron Interpretation b

How does the proton spin? Quark spin Crisis : polarized (beam and target) DIS experiments Total quark spin contribution is about 30%

Ultimate goal of spin physics Spin sum rule 30 % Quark spin, Best known In the naïve quark model, the proton spin is carried by the quark spin. However, the EMC and other DIS experiments found that the quark spin only contribute 30% to the proton spin. Where is the rest of the proton spin. To understand the proton spin sum rule is the ultimate goal of the proton spin physics. Of course, in the QCD, we not only have quarks, but also gluons, and all the quarks and gluons have orbital motion inside nucleon. So, for a complete spin sum rule, we should have quark spin, gluon spin, and orbital angular momenta from quarks and gluons. Among these contributions, the quark spin is best known from EMC and other DIS experiments, and can be written as integral of the polarized quark or quark helicity distirbutions. Similarly, the gluon spin contribution can also be written as integral of polarized gluon distribution, or gluon helicity distribution. The orbital angular momentum part is the most difficult part. So far, we know little about them. In this talk, I am going to focus these three contribution terms, and hope to present you the current status and future perspective of the proton spin physics, from my personal perspective for sure. Gluon spin, Poorly known Orbital Angular Momentum of quarks and gluons, Little known 41 7/17/2018 41

World efforts for spin physics Current Lepton-nucleon scattering HERMES, COMPASS, JLAB Polarized proton-proton scattering, RHIC Future facilities Jlab-12GeV EIC JPARC (Japan) GSI-FAIR (Germany) RHIC@BNL pp@200GeV HERMES@ DESY e--p @27GeV SLAC E142-155 EMC@CERN COMPASS@CERN  p@160GeV Jefferson Lab e-p@6GeV There have been tremendous efforts around the world trying to pin down the proton spin problem. These experiments include the earlier experiments at SLAC, at CERN, and HERMES, and COMPASS, and Jefferson Lab. All these experiments are DIS experiments with lepton-nucleon scattering. We also have a polarized proton-proton collider, RHIC, at Brookhaven National Lab, Long island, New york. In the future, we will have electron-ion collider, JPARC, a hadron fixed target experiment, and GSI-FAIR, a ppbar collider. All these experiments have their unique coverage on the studies of quark spin, gluon spin, and orbital angular momenta from quarks and gluons. And they are complementary to each other as well. All these experiments have their unique coverage on q, g, Lq,g, and they are complementary 42 7/17/2018 42

Sea quark polarization One can measure the sea quark contribution to the spin of the proton through fragmentation of the polarized quark into mesons Major topic at JLab 12GeV HERMES, 2004 Semi-inclusive DIS small, so far 43 7/17/2018

GLUON SPIN From DIS measurements DIS can only indirect probe the gluon polarization, through the Q^2 evolution. Nevertheless, there have been attempts to study gluon polarization in ep collision by looking at particular final state, like heavy quark, hadron pair, and others. Keep in mind, the theoretical uncertainties in this determination are underestimate. 7/17/2018 44 44

Exciting results from RHIC-proton proton scattering Double longitudinal spin asymmetry STAR The gluon pol. is small, but the uncertainty is large. Future data will improve! arXiv:0710.2048 [hep-ex]

Hunting for Lq: Generalised Parton Distributions (GPDs) = 1/2 DS + Lz 30% ( H + E) x dx = Jq = 1/2 DS + Lz Ji,96 GPDs Can be measured in deeply virtual Compton scattering and other hard exclusive processes Related to form factors and parton distributions Comprehensive programs at JLab,HERMES,COMPASS DIS DVCS Parton Distributions Generalized Mueller et al.,94;Ji,96; Radyushkin ,96 46

Lattice Simulation of GPDs Ld + Lu cancel? Q2 evolution Thomas ‘08

Where are we now for the spin puzzle Quark spin 30 % Gluon spin 0-70%, <0? q G LG Lq 48 Proton Spin

Summary and conclude many try and this is solvable Form factors reveal transverse charge density (center of neutron negative) TMDs reveal momentum & spin distributions- proton not round if ≠0 GPDs reveal x, b distributions- high x quarks are at low b Spin of nucleon is not yet understood, many try and this is solvable Thanks for slides to Roy Holt, Marc Vanderhaeghen, Feng Yuan

Total neutron charge distribution x<0.23 total x>0.23 d dominates at high x, low b

The spin puzzle in horizon Gluon spin~ 0-70%, <0? RHIC, EIC, … Quark spin ~30% DIS, and pp coll. q G LG Lq Deeply Virtual Compton Scattering, Transverse spin physics, in DIS, pp coll. 7/17/2018 51

Summary We are in the early stages of a very exciting era of proton spin physics studies, where the future RHIC, JLAB, JPARC, FAIR, and EIC experiments will certainly play very important roles We will learn more about QCD dynamics and nucleon structure from these studies, especially for the quark orbital motion 52

Expectations- Pre Jlab QF2 /F1 GE/GM QF2/F1 GE/GM Q2 Q2 Proton

Spin density operator: d(r-rp) s . n PRB65, 144429 Canted ferromagnetic structure of UNiGe high magnetic fields Neutron magnetic scattering Neutron, B, crystal

RHIC spin unpol. u 55 7/17/2018

Global fit constrains the gluon spin from the RHIC data Polarized sea and gluon distributions RHIC spin asymmetries A number of important features: (1) \delta ubar is not equal to delta dbar, also different from delta sbar, they all have nontrivial behavior, especially for delta sbar; (2) gluon polarization is small, but with large uncertainties. In the kinmeatic range probed by RHIC experiments, the gluon polarization is constrained small. de Florian, Sassot, Stratmann and Vogelsang (0804.0422) 57

Naive Model of Nucleon Proton 2 u, 1 d, Neutron 2 d, 1 u Confined quarks move with zero orbital angular momentum “Spin Crisis” Quarks carry only 30 % of proton spin three ideas- u,d quarks surrounded by s s gluons carry angular momentum quarks carry orbital angular momentum

Proton- connect x and b high x-low b x<0.1 x>.5

Naive Quark Model of Proton, Neutron (nucleon) Proton 2 u(2/3 ), 1 d Neutron 2 d(-1/3) 1 u Confined quarks move with zero orbital angular momentum

Why study the nucleon? Neutrons protons made of quarks, gluons Quantum Chromodynamics QCD CONFINEMENT How does the nucleon stick together when struck by photon? Where is charge and magnetization density located? Origin of angular momentum? What is the shape of the proton?

How to study the proton? EXPERIMENTS Theory –numerical simulations lattice masses + … low Q2 eventually exact Phenomenology- symmetries, dynamical guesses, high Q2 Model independent techniques what the lattice will find

How proton holds together-high Q2 pQCD Feynman Non perturbative ∞ gluon exch g g

width in Brel ~independent of x

DSSV spin content The gluon pol. is small, but the uncertainty is large. Future data will improve this

DVCS with transversely polarized target from HERMES & Jlab JLab Hall A Jq input parameter in the GPD ansatz, need More sophisticted model for GPDs HERMES Jlab Hall A, 0709.0450; HERMES, 0802.2499

Definitions and high Q2 predictions old helicity conservation

Expectations- Pre Jlab QF2 /F1 GE/GM QF2/F1 GE/GM Q2 Q2 Proton