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

2. Blind men and the elephant

3. Physicists and the nucleon
Soliton
s s
pion u d
gluon

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

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

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

7. 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

8. 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

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

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

11. 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

12. Light cone coordinates/Infinite momentum frame

13. 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

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

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

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

18. 
s r

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

20. 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

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

22. 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

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

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

25. 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

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

28. e-i q b

29. Parameterizations of nucleon form factors
hep-ex/

30. Results
BBBA
Kelly
Negative

31. Negative F1 means central density negative
GeV2
Why?

32. 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

35. relate:high x, high Q2 , low b

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

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

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

39. Neutron Interpretationb

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

41. 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

42. 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)
DESY
SLAC E 
Jefferson Lab
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

43. 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

44. 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

45. 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:  [hep-ex]

46. 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

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

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

49. 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

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

51. 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

52. 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

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

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

55. RHIC spin
unpol. u 55
7/17/2018

57. 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 ( ) 57

58. 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

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

60. 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

61. 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?

62. 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

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

64. width in Brel ~independent of x

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

66. 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, ; HERMES,

67. Definitions and high Q2 predictions
old helicity conservation

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