Vina Punjabi

Norfolk State University

2012 JLab Users Group Meeting June 4-6, 2012

Jefferson Lab, Newport News, VA

Nucleon Form Factors

Outline

Nucleon Form Factors (FF) two methods to obtain GE and GM Rosenbluth separation and double polarization Old and new results for GE and GM

Comparison of GE/GM and F2/F1 to theoretical model predictions, and flavor separation Discrepancy in ratio results and two-photon exchange Future of Nucleon FF at JLab with 12 GeV

Nucleon Elastic Form Factors

The Form Factors (FF) are fundamental quantities defined in context of single-photon exchange FF Describe internal structure of the nucleons Related to charge and magnetization distributions Investigation of FFs provide a powerful tool toward understanding of non-perturbative QCD and confinement

Spectacular experimental progress in past decade using New techniques / double polarization experiments Unexpected results that inspired theoretical progress Rigorous tests of nucleon models Input to nuclear structure and parity violation experiments New information on basic hadron structure as first moments of GPD, and their use to obtain contribution to proton spin with Ji’s orbital angular momentum sum rule, A. Afanasev, hep-ph/9910565

Robert Hofstadter Nobel prize 1961

For his pioneering studies of electron scattering in atomic nuclei and for his thereby achieved discoveries concerning the structure of the nucleons

It all started in the 1950’s

Elastic electron-proton scattering The proton is not a point-like particle, but has finite size

Connection to radius of the proton:

The New York Times, July 13, 2010.

It went from 0.8768±0.0069 fm to 0.8418±0.0007 fm

Proton Charge Radius Puzzle

The figure is from X. Zhan et al., PLB 705, 59 (2011)

Mainz

JLab

Mostly Hydrogen Lamb shift Muonic Hydrogen Lamb shift

“For a Proton, a Little Off the Top (or Side) Could Be Big Trouble”

Nucleon vertex:

F1 helicity conserving Dirac FF, F2 helicity non-conserving Pauli FF. F1p(0)=1 F1n(0)=0

F2p(0)= κp F2n(0)= κn

Alternately, the Sachs form factors

GE(Q2) = F1(Q

2) - F2(Q2) GM(Q

2) = F1(Q2) + F2(Q

2)

Nucleon Elastic Form Factors

)2(Q2

Fνq2M

μνiσ

+)2(Q1

Fμγ=p'p,

μΓ

Internal Nucleon structure is revealed from the Q2 evolution of F1 and F2

Rosenbluth Separation Method

Qattan et al.PRL 94, 142301 (2005)

• Measure angular dependence of cross section at fixed Q2

• ε-dependence of “reduced” cross section σR is linear with slope GE

2 and intercept τGM

2.

τ

2γm=2Qwith2

pm4/2Q=τ

………. Polarization ----- μ GEp/GMp=1

For recoil polarization, the two polarization components are in the reaction plane, no normal component:

Superior method: “ much smaller systematics” Form Factor ratio is independent of the electron polarization Pe and of the polarimeter analyzing power Ay (h is beam helicity ±1).

2M

Gε

τ2E

GoIand2eθtan

M2

)e'

Ee(E

Pt

P

MpG

EpG

+=+

-=

Polarization transfer in or spin-target asymmetry (N=p or n) two different techniques, but give same information

NeNe

Double polarization Method

Statistical uncertainty depends directly on both Pe and Ay.

Remaining systematics mostly from spin precession

,eNNe

The results from all published Rosenbluth separation data for GEp and GMp. The “scaling” apparent after dividing by the dipole FF, GD=(1+Q

2/0.71)-2 did not survive the emergence of double polarization results in 1999.

Summary of Rosenbluth Data for Proton

Q2 (GeV2)

Neutron Form Factors

From elastic and quasi elastic electron-deuteron scattering cross sections

Before the double polarization Experimental era started

Summary of Double Polarization Results for Proton Form Factor Ratio

Linear decrease observed in first two GEp experiments seems to slow down in GEp-III

Neutron Form Factors

All polarization results, including new JLab Hall A data

Polarization and cross section Data, including JLab Hall B data

Low Q2 Region New results from Jlab, MIT for GEp/GMp in low Q2 region. Significant differences between various experiments

Preliminary

Punjabi et al., et al., Phys. Rev. C 71, 055202 (2005) [Erratum-ibid. C 71, 069902 (2005)] C.B. Crawford et al. Phys. Rev. Lett. 98,052301 (2007) Paolone et al. Phys. Rev. Lett. 105, 072001 (2010) Ron et al. Phys. Rev. C 84 (2011) 055204 X. Zhan et al. Phys. Lett. B 705 (2011) 59

Just completed GEp polarization experiment to Q2 ≤ 0.03 GeV2 at JLab in hall A

The dashed curve is Kelly fit, solid curve is global fit by Arrington et al.

VMD-based models describe all four nucleon FFs well (Lomon, Bijker) rCQM, show importance of relativistic dynamics, allow to separate dynamical from nucleon structure effects (Chung, Miller, Gross, Boffi, Cardarelli, Pace, De Milo) pQCD predict logarithmic scaling behavior of F2/F1 at intermediate Q2 (Belitsky, Ji, Yuan), related to quark orbital angular momentum Dyson-Schwinger equations, as continuum approach to QCD (Roberts, Cloet et al.) GPD, show a connection to OAM of quarks in nucleon (Ji), FF provide important constraints on GPD’s, allow flavor separation for “dressed” quarks in nucleon (Miller) Lattice QCD models very good progress now and will get better in future

GEp/GMp Ratio Compared to Predictions from Theoretical Models

Current Status of all Four Form Factors

Figure is from Puckett et al., Phys. Rev. C 85, 045203 (2012)

Dyson-Schwinger Equations

Interpreting experiments with GeV electromagnetic probes requires Poincaré covariant treatment of baryons, covariant dressed-quark Faddeev equation, correlations in Faddeev amplitude quark orbital angular momentum – essential to that agreement

Well suited to Relativistic Quantum Field Theory Non Perturbative, continuum approach to QCD Hadrons as composites of Quarks and Gluons

I.C. Clöet et al., Few-Body Syst. 46, 1 (2009) D.J. Wilson et al., Phys. Rev. C 85 (2012) 025201

GPDs and Electromagnetic FF

Modified Regge Parametrization for H and E (Guidal et al., (2005)

The first moments of GPDs are related to the elastic FF (Ji, 97)

Scaling of F2p/F1p The F2/F1~1/Q

2 pQCD scaling prediction – does not agree with data Modified pQCD scaling prediction by Belitsky et al, F2/F1~ ln

2(Q2/Λ2)/Q2 includes quark angular momentum component, shows scaling starting at Q2 of 2 GeV2 with Λ~0.3 GeV

Scaling of F2n/F1n

The F2/F1~1/Q

2 pQCD scaling shows good agreement with data starting at Q2 of 1 GeV2

The logarithmic pQCD scaling prediction by Belitsky et al. better agreement for the proton, with Λ~0.3 GeV but not for neutron

Transverse Charge Densities

Miller, PRL 99, 112001 (2007)

Charge density ρ(b) of partons in the transverse plane is a two-dimensional Fourier transform of the F1 form factor It is calculated in the infinite momentum frame, from the measured FF

Note that F2n/κn ~ F2p/ κp

F1n is negative because GEn~0 and GMn is negative.

Dirac and Pauli form factors separately

Polynomial fit to the data to use for flavor separation

Quark Flavor separation (I) Assume hadron current: <p|euūγμu+edđγμd|p>

and isospin symmetry:

Then the Fermi and Dirac form factors of the “dressed” quarks in the nucleon are:

See for example: Cates, de Jager, Riordan, Wojtsekhowski, PRL 106 252003, (2011)

d2pF=u

2nF,u

2pF=d

2nF

d1pF=u

1nF,u

1pF=d

1nF

2n2F+

2pF=d

2pF

2nF+

2p2F=u

2pF

1n2F+

1pF=d

1pF

1nF+

1p2F=u

1pF

Quark Flavor separation (II)

scaling behavior not anticipated from pQCD

interference of axial-vector and scalar di-quark produces the zero in the Dirac form factor of the d quark in the proton F1p

d

Wilson, Cloët, Chang, Roberts, Phys. Rev. C 85, 025205 (2012)

First hint of discrepency from GEp-I experiment with the Rosenbluth cross section data

GEp/GMp Crisis: discrepancy in the data

Discrepancy confirmed beyond any doubt in next two GEp experiments

“The discrepancy is a serious problem as it generates confusion and doubt about the whole methodology of lepton scattering experiments”

P.A.M. Guichon ,M.Vanderhaeghen, PRL 91, 142303 (2003) P.G. Blunden, W. Melnitchouk and J.A. Tjon, PRL 91, 142304 (2003)

Double-polarization JLab 2-γ Experiment

COZ BLW nuclear distribution Amplitudes: Kivel and Vanderhaeghen GPD Afanasev et al. Hadronic Blunden et al. SF Bystritskiy et al, shifted down.

lp

tp

2ε

ε)+τ(1- =

MpG

EpG

pμ In Born approximation

Measured average μpGEp/GMp=0.6923±0.0059 at Q2=2.5 GeV2 for 3 values of ε, unprecedentedly small error bars. published: M. Meziane et al. PRL 106, 132501 (2011)

Evaluate the box and crossed-box TPE diagrams explicitly incorporate the hadronic structure of the nucleon, parametrized through hadronic electromagnetic form factors

Arrington, Blunden, Melnitchouk, PPNP 66, 782 (2011)

1) Novosibirsk has preliminary results: This is run I: Q2=2.0 GeV2; Run II at Q2=1.6 GeV2 and ε<0.5 yet to come. Older data shown with Q2<2 GeV2

A.V. Gramolin et al, arXiv:1112.5369 Solid curve, Blunden et al Phys. Rev. C 72, (2005) 034612 for these data; dashed, same for future data. 2) JLab Hall B, currently in data analysis phase. 3) Olympus at DESY, currently in data taking mode

Current Attempts to Determine the Two-γ Contribution from the e+p/e-p Cross Section Ratio

(dσ+-dσ-)/(dσ++dσ-) = 1-2 dσ2γ/(dσ++dσ-)

After the 12 GeV upgrade Measure GEp/GMp to Q

2 of 12 GeV2 with new large acceptance Super Bigbite Spectrometer (SBS) in hall A to be built with single dipole and GEM trackers. Measure GEn to Q

2 = 10 GeV2 and GMn to 13.5 GeV2.

SBS capabilities derived from using a large open-geometry dipole magnet together with a detector package with direct view of target GEM-based tracking system able to tolerate very high rates

Setup for GEp-V

Recoil proton polarization measured using the large-acceptance SBS double polarimeter with large GEM trackers (50 × 200 cm2) together

with a highly segmented hadron calorimeter. Electron detected in coincidence by a large EM calorimeter, ‘‘BigCal”. Efforts underway to replace BigCal by Shashlik type HERA-B calorimeter, “NewCal”, for much better radiation hardness.

L = 8·1038 cm−2s−1

High calorimeter thresholds to reject background Coincidence rate ≤ 5 kHz

40 cm LH2 target

Coordinate

detector

Anticipated statistical uncertainties for approved GEp-V with 45 days of beam.

GEp-V Projected Errors with SBS

Setup for GEn-II and GMn

A polarized 3He target is somewhat equivalent to a polarized neutron target, except for nuclear corrections, small polarization of protons and other “minor” problems.

Polarized 3He

GEn-II and GMn Projected Errors with SBS

GEn in Q2 range will be close to

other form factors Red points - with SBS in Hall A Blue points – with CLAS12 in Hall B

Concluding Remarks

• High-Q2 surprise in GEp/GMp, have led to a fundamental change in picture of the internal structure of the proton, strong impact on theoretical progress

• no evidence for two-photon exchange effects in ratio obtained from polarization observables.

• The new results from double polarization method for proton and neutron, together with further results following the 12 GeV upgrade, will provide answers to a number of open questions crucial to our understanding of fundamental nucleon properties, and the nature of QCD in the confinement regime

• Since Hofstadter’s first experiments 50 years ago, we have discovered many new features about the structure of the proton and neutron.

Thank you for your attention