Gerald A. Miller, UW Definitions, model calculations Meaning of - PowerPoint PPT Presentation

Nucleon Form Factors and Related Matters Gerald A. Miller, UW • Definitions, model calculations • Meaning of form factors • Shape of the proton Talk based on personal interests. For other approaches see Cloet et al, Few Body Syst. 46 (2009) 1-36 Arrington et al, J.Phys. G34 (2007) S23-S52 Punjabi, Perdrisat et al, Eur.Phys.J. A51 (2015) 79 De Teramond et al PRL 120,182001

Why study the nucleon? • More than 99 % of matter we see made of neutron and proton • Neutrons protons made of quarks , gluon s • Quantum Chromodynamics QCD • CONFINEMENT, test QCD lattice • Size influences atomic physics tests of QED • 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? • Discover new phenomenon - proton G E /G M, neutron central charge density

What is a form factor? How to tell 
 how big something is? Proton • Look P+q e’ q P e Proton 3

What is a form factor? How to tell 
 how big something is? Proton • Look P+q e’ Non rel form factor -old q P e Proton 3 Structure factor


 
 
 
 
 
 
 How proton holds together-high Q 2 γ • pQCD γ Feynman 
 Non perturbative 
 ∞ gluon exch All reaction mechanisms included in light front wave function of proton 4 Need GPDs and color transparency to decide


 
 
 
 
 
 
 How proton holds together-high Q 2 γ • pQCD γ Feynman 
 Non perturbative 
 ∞ gluon exch All reaction mechanisms included in light front wave function of proton 4 Need GPDs and color transparency to decide


 
 
 
 
 
 
 How proton holds together-high Q 2 γ • pQCD γ Feynman 
 Non perturbative 
 ∞ gluon exch All reaction mechanisms included in light front wave function of proton 4 Need GPDs and color transparency to decide

Definitions i 5/34

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<latexit sha1_base64="l+aoSNMR3hTNqrwcLEBFfJwv8gM=">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</latexit> Before JLab QF 2 /F 1 G E /G M G E /G M QF 2 /F 1 Q 2 Q 2 New Phenomenon! Proton recoil polarization technique www.scholarpedia.org/article/Nucleon_Form_factors Punjabii, Perdrisat Conclusion -non-relativistic quark model is not correct Ω − Gell-Mann used non-rel to predict -Nobel 6

Q 2 Q 2 Relativistic quark model is needed Our prediction: M. R. Frank, B. K. Jennings, and G. A. Miller Phys. Rev. C 54, 920 – 1 August 1996 Our explanation - relativistic quark model needed Gerald A. Miller and Michael R. Frank Phys. Rev. C 65, 065205 – 7

Jlab QF 2 /F 1 G E /G M Q 2 Q 2 Relativistic quark model is needed Our prediction: M. R. Frank, B. K. Jennings, and G. A. Miller Phys. Rev. C 54, 920 – 1 August 1996 Our explanation - relativistic quark model needed Gerald A. Miller and Michael R. Frank Phys. Rev. C 65, 065205 – 7

Implement Relativity: Light front, Infinite momentum “ Time ” , x + = x 0 + x 3 , “ Evolve ” , p − = p 0 − p 3 “ Space ” , x − = x 0 − x 3 , “ Momentum ” , p + (Bjorken) x Bj = p + (quark) Transverse position, momentum b , p p + (traget) These variables are used in GPDs, TMDs, standard variables transverse boosts in kinematic subgroup Z d 2 p | p , λ i k → k − k + v | R = 0 , λ i = Momentum transfer in transverse direction then density is 2 Dimensional Fourier Trans form 8

Frank Jennings Miller PRC54, 920, 1996 Impulse Approximation 
 Three particles independent spatial variables Purpose of model wave function - learn phenomena Please know the difference between using wave functions and fits Models give predictions and fits do not 9

1996 Frank, Jennings, Miller G E /G M falls with increasing Q 2 10/34

Ratio of Pauli to Dirac Form Factors Theory 1996 Miller & Frank PRC 65, 920 Will flat trend continue? Data: Jones et al PRL 84,1398 Gayou et al, PRL 88, 092301 Puckett et al PRL 104,242301 11

Relativistic Explanation Lower component signature of relativistic effects Over range of existing data, future? 12

G E ≠ 0 PRD 24, 216 From 3D Fourier Transform of G E Updated : Miller, Phys.Rev. C66 (2002) 032201 With pion Good fits to other form factors mag. moments 13

1 PRC86,015208 Model proton wave function: quark-diquark Lorentz and rotationally invariant-more γ different forms! Light front variables Dirac spinors-orbital angular momentum 1 . 0 µ p G Ep /G Mp µ p G Ep /G Mp Venkat (2010) proton form factors 0 . 8 0 . 6 theory 0 . 4 0 . 2 Quark spin is 35 % of fit proton total angular 0 momentum − 0 . 2 − 0 . 4 0 2 4 6 8 10 12 14 16 18 20 14 Q 2 (GeV 2 )

Unified model of nucleon elastic form factors and implications for neutrino oscillation experiments Zhang, Hobbs, Miller arXiv: 1912:08479 • Axial current form factors needed for neutrino-nucleus interactions • Light front wave function model- includes Δ − π • Fit parameters to electromagnetic (vector) form factors • Compute axial form factors and consequences for neutrino-nucleus interactions physics /34 15

Vector FF’s: Light Front Quark Model (LFQM) arXiv: 1912:08479 Z-exp. Fit: Ye et al PLB 777, 8 (’18) 11 proton neutron 1.0 1.0 ( a ) ( a ) 0.8 0.8 0.6 0.6 p / G D 0.4 n / G D 0.4 0.2 G E G E 0.2 Z - exp. fit ( 2018 ) 0.0 Z - exp. fit ( 2018 ) LFQM 0.0 - 0.2 - 0.4 LFQM - 0.2 0 2 4 6 8 10 0 2 4 6 8 10 Q 2 ( GeV 2 ) Q 2 ( GeV 2 ) 1.15 1.3 ( b ) ( b ) 1.10 LFQM 1.2 1.05 Z - exp. fit ( 2018 ) 1.1 p / � p G D n / � n G D 1.00 1.0 0.95 0.9 G M Z - exp. fit ( 2018 ) G M 0.90 0.8 LFQM 0.85 0.7 0.6 0.80 0 2 4 6 8 10 Q 2 ( GeV 2 ) 0 2 4 6 8 10 12 Q 2 ( GeV 2 ) 1.0 Z - exp. fit ( 2018 ) 0.8 LFQM p / G M p 0.6 � p G E 0.4 0.2 0.0 16 0 2 4 6 8 10 Q 2 ( GeV 2 )