Nucleon Form Factors. Vina Punjabi Norfolk State University JLab Users Group Meeting June 4-6, 2012 Jefferson Lab, Newport News, VA

Transcription

1 Nucleon Form Factors Vina Punjabi Norfolk State University 2012 JLab Users Group Meeting June 4-6, 2012 Jefferson Lab, Newport News, VA

2 Outline Nucleon Form Factors (FF) two methods to obtain G E and G M Rosenbluth separation and double polarization Old and new results for G E and G M Comparison of G E /G M and F 2 /F 1 to theoretical model predictions, and flavor separation Discrepancy in ratio results and two-photon exchange Future of Nucleon FF at JLab with 12 GeV

3 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/

4 It all started in the 1950 s 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 Elastic electron-proton scattering The proton is not a point-like particle, but has finite size

5 Proton Charge Radius Puzzle Mainz The figure is from X. Zhan et al., PLB 705, 59 (2011) JLab Mostly Hydrogen Lamb shift Muonic Hydrogen Lamb shift Connection to radius of the proton: The New York Times, July 13, It went from ± fm to ± fm For a Proton, a Little Off the Top (or Side) Could Be Big Trouble

6 Nucleon Elastic Form Factors Nucleon vertex: Γ μ F 1 helicity conserving Dirac FF, F 2 helicity non-conserving Pauli FF. F 1p (0)=1 F 1n (0)=0 F 2p (0)= κ p F 2n (0)= κ n Alternately, the Sachs form factors p,p' = γ μ iσ F (Q 2 )+ μν 1 2M F (Q 2 ) 2 G E (Q 2 ) = F 1 (Q 2 ) - F 2 (Q 2 ) G M (Q 2 ) = F 1 (Q 2 ) + F 2 (Q 2 ) q ν Internal Nucleon structure is revealed from the Q 2 evolution of F 1 and F 2

7 Rosenbluth Separation Method Qattan et al.prl 94, (2005) τ=q2/4m2 p with Q2= m2 γ τ Measure angular dependence of cross section at fixed Q 2 ε-dependence of reduced cross section σ R is linear with slope G E 2 and intercept τg M2.. Polarization μ G Ep /G Mp =1

8 Double polarization Method Polarization transfer in en en or spin-target asymmetry en en, (N=p or n) two different techniques, but give same information For recoil polarization, the two polarization components are in the reaction plane, no normal component: G Ep G Mp = - P (E e E ) e' tan P t + 2M θ 2 e and I o τ = G2 + G2 E ε M Superior method: much smaller systematics Form Factor ratio is independent of the electron polarization P e and of the polarimeter analyzing power A y (h is beam helicity ±1). Statistical uncertainty depends directly on both P e and A y. Remaining systematics mostly from spin precession

9 Summary of Rosenbluth Data for Proton The results from all published Rosenbluth separation data for G Ep and G Mp. The scaling apparent after dividing by the dipole FF, G D =(1+Q 2 /0.71) -2 did not survive the emergence of double polarization results in Q 2 (GeV 2 )

10 Neutron Form Factors From elastic and quasi elastic electron-deuteron scattering cross sections Before the double polarization Experimental era started

11 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

12 Neutron Form Factors All polarization results, including new JLab Hall A data Polarization and cross section Data, including JLab Hall B data

13 Low Q 2 Region New results from Jlab, MIT for G Ep /G Mp in low Q 2 region. Significant differences between various experiments Preliminary Punjabi et al., et al., Phys. Rev. C 71, (2005) [Erratum-ibid. C 71, (2005)] C.B. Crawford et al. Phys. Rev. Lett. 98, (2007) Paolone et al. Phys. Rev. Lett. 105, (2010) Ron et al. Phys. Rev. C 84 (2011) X. Zhan et al. Phys. Lett. B 705 (2011) 59 Just completed GEp polarization experiment to Q GeV 2 at JLab in hall A The dashed curve is Kelly fit, solid curve is global fit by Arrington et al.

14 G Ep /G Mp Ratio Compared to Predictions from Theoretical Models 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 F 2 /F 1 at intermediate Q 2 (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

15 Current Status of all Four Form Factors Figure is from Puckett et al., Phys. Rev. C 85, (2012)

16 Dyson-Schwinger Equations Well suited to Relativistic Quantum Field Theory Non Perturbative, continuum approach to QCD Hadrons as composites of Quarks and Gluons D.J. Wilson et al., Phys. Rev. C 85 (2012) I.C. Clöet et al., Few-Body Syst. 46, 1 (2009) 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

17 GPDs and Electromagnetic FF The first moments of GPDs are related to the elastic FF (Ji, 97) Modified Regge Parametrization for H and E (Guidal et al., (2005)

18 Scaling of F 2p /F 1p The F 2 /F 1 ~1/Q 2 pqcd scaling prediction does not agree with data Modified pqcd scaling prediction by Belitsky et al, F 2 /F 1 ~ ln 2 (Q 2 /Λ 2 )/Q 2 includes quark angular momentum component, shows scaling starting at Q 2 of 2 GeV 2 with Λ~0.3 GeV

19 Scaling of F 2n /F 1n The F 2 /F 1 ~1/Q 2 pqcd scaling shows good agreement with data starting at Q 2 of 1 GeV 2 The logarithmic pqcd scaling prediction by Belitsky et al. better agreement for the proton, with Λ~0.3 GeV but not for neutron

20 Transverse Charge Densities Charge density ρ(b) of partons in the transverse plane is a two-dimensional Fourier transform of the F 1 form factor It is calculated in the infinite momentum frame, from the measured FF Miller, PRL 99, (2007)

21 Dirac and Pauli form factors separately Polynomial fit to the data to use for flavor separation F 1n is negative because G En ~0 and G Mn is negative. Note that F 2n /κ n ~ F 2p / κ p

22 Quark Flavor separation (I) Assume hadron current: <p e u ūγ μ u+e d đγ μ d p> and isospin symmetry: F d 1n = F u, 1p F u 1n = F d 1p F d 2n = F u, 2p F u 2n = F d 2p Then the Fermi and Dirac form factors of the dressed quarks in the nucleon are: F u 1p F u 2p = 2F 1p = 2F 2p + F 1n + F 2n F d 1p F d 2p = F 1p = F 2p + 2F 1n + 2F 2n See for example: Cates, de Jager, Riordan, Wojtsekhowski, PRL , (2011)

23 Quark Flavor separation (II) interference of axial-vector and scalar di-quark produces the zero in the Dirac form factor of the d quark in the proton F 1p d scaling behavior not anticipated from pqcd Wilson, Cloët, Chang, Roberts, Phys. Rev. C 85, (2012)

24 GEp/GMp Crisis: discrepancy in the data 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, (2003) P.G. Blunden, W. Melnitchouk and J.A. Tjon, PRL 91, (2003) First hint of discrepency from GEp-I experiment with the Rosenbluth cross section data Discrepancy confirmed beyond any doubt in next two GEp experiments

25 Double-polarization JLab 2-γ Experiment μ G p Ep G Mp = - τ(1+ ε) 2ε p t p l In Born approximation COZ BLW nuclear distribution Amplitudes: Kivel and Vanderhaeghen GPD Afanasev et al. Hadronic Blunden et al. SF Bystritskiy et al, shifted down. Arrington, Blunden, Melnitchouk, PPNP 66, 782 (2011) Evaluate the box and crossed-box TPE diagrams explicitly incorporate the hadronic structure of the nucleon, parametrized through hadronic electromagnetic form factors Measured average μ p G Ep /G Mp =0.6923± at Q 2 =2.5 GeV 2 for 3 values of ε, unprecedentedly small error bars. published: M. Meziane et al. PRL 106, (2011)

26 Current Attempts to Determine the Two-γ Contribution from the e + p/e - p Cross Section Ratio (dσ + -dσ - )/(dσ + +dσ - ) = 1-2 dσ 2γ /(dσ + +dσ - ) 1) Novosibirsk has preliminary results: This is run I: Q 2 =2.0 GeV 2 ; Run II at Q 2 =1.6 GeV 2 and ε<0.5 yet to come. Older data shown with Q 2 <2 GeV 2 A.V. Gramolin et al, arxiv: Solid curve, Blunden et al Phys. Rev. C 72, (2005) 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

27 After the 12 GeV upgrade Measure G Ep /G Mp to Q 2 of 12 GeV 2 with new large acceptance Super Bigbite Spectrometer (SBS) in hall A to be built with single dipole and GEM trackers. Measure G En to Q 2 = 10 GeV 2 and G Mn to 13.5 GeV 2. 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

28 Setup for GEp-V Coordinate detector 40 cm LH 2 target L = cm 2 s 1 High calorimeter thresholds to reject background Coincidence rate 5 khz Recoil proton polarization measured using the large-acceptance SBS double polarimeter with large GEM trackers ( cm 2 ) 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.

29 GEp-V Projected Errors with SBS Anticipated statistical uncertainties for approved GEp-V with 45 days of beam.

30 Setup for GEn-II and GMn Polarized 3 He A polarized 3 He target is somewhat equivalent to a polarized neutron target, except for nuclear corrections, small polarization of protons and other minor problems.

31 GEn-II and GMn Projected Errors with SBS G En in Q 2 range will be close to other form factors Red points - with SBS in Hall A Blue points with CLAS12 in Hall B

32 Concluding Remarks Since Hofstadter s first experiments 50 years ago, we have discovered many new features about the structure of the proton and neutron. High-Q 2 surprise in G Ep /G Mp, 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 Thank you for your attention