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Polarization Observables and Hadron Structure (1)

Polarization Observables and Hadron Structure (1). Egle Tomasi-Gustafsson Saclay, France. MOTIVATIONS. In the traditional view, the atom’s nucleus appears as a cluster of nucleons - protons and neutrons. A deeper view reveals quarks and gluons inside the nucleons.

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Polarization Observables and Hadron Structure (1)

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  1. Polarization Observables and Hadron Structure (1) Egle Tomasi-GustafssonSaclay, France Egle Tomasi-Gustafsson Gomel, July 31, 2007

  2. MOTIVATIONS • In the traditional view, the atom’s nucleus appears as a cluster of nucleons - protons and neutrons. A deeper view reveals quarks and gluons inside the nucleons. • CEBAF’s continuous, energetic beams of probing electrons let physicists examine how the two view fit together. Ultimately, the process of bridging the views will yield a complete understanding of nuclear matter…. 2002…. Istitutional plan Egle Tomasi-Gustafsson Gomel, July 31, 2007 Istitutional plan

  3. GENERAL PLAN • Lecture 1 • Introduction-Motivations • How to measure proton form factors? • Recent Results • Lecture 2 • Consequences • Space and time-like regions • Asymptotics • Two photon exchange • Radiative corrections Model Independent Statements Egle Tomasi-Gustafsson Gomel, July 31, 2007

  4. PLAN • Introduction-Motivations • How to measure form factors? • Unpolarized method (Rosenbluth separation) • Recoil polarization • Experiment (Polarimetry) • Results Egle Tomasi-Gustafsson Gomel, July 31, 2007

  5. Proton Form Factors Over a period of time lasting at least 2000 years, Man has puzzled over and sought an understanding of the composition of matter… F1 F2 Q2=1 GeV2 Egle Tomasi-Gustafsson Gomel, July 31, 2007

  6. Hadron Electromagnetic Form factors • Characterize the internal structure of a particle ( point-like) • Elastic form factors contain information on the hadron ground state. • In a P- and T-invariant theory, the EM structure of a particle of spin S is defined by 2S+1 form factors. • Neutron and protonform factors are different. • Deuteron: 2 structure functions, but 3 form factors. • Playground for theory and experiment. Egle Tomasi-Gustafsson Gomel, July 31, 2007

  7. Space-like and time-like regions • FFs are analytical functions. • In framework of one photon exchange, FFs are functions of the momentum transfer squared of the virtual photon, t. t<0 t>0 Scattering Annihilation _ _ e- + h => e- + h e+ + e- => h+ h Form factors are real in the space-like region and complex in the time-like region. Egle Tomasi-Gustafsson Gomel, July 31, 2007

  8. How to measure? Egle Tomasi-Gustafsson Gomel, July 31, 2007

  9. Electromagnetic interaction • The electromagnetic vertex is known (what about radiative corrections ?). • The strong vertex contains the hadron structure. • Validity of one-photon exchange at large t? Observables: differential cross section, polarization observables One photon-exchange Egle Tomasi-Gustafsson Gomel, July 31, 2007

  10. Proton Form Factors ...before Dipole approximation: GD=(1+Q2/0.71 GeV2)-2 Rosenbluth separation/ Polarization observables Egle Tomasi-Gustafsson Gomel, July 31, 2007

  11. Dipole Approximation • Classical approach • Nucleon FF (in the Breit system) are Fourier transform of the charge or magnetic distribution. Dipole approximation: GD=(1+Q2/0.71 GeV2)-2 • The dipole approximation corresponds to an exponential density distribution. • ρ = ρ0exp(-r/r0), • r02= (0.24 fm)2, <r2> ~(0.81 fm) 2  m2D=0.71 GeV2 Egle Tomasi-Gustafsson Gomel, July 31, 2007

  12. Dipole Approximation and pQCD Dimensional scaling • Fn(Q2)= Cn [1/( 1+Q2/mn) n-1], • mn=n2 , <quark momentum squared> • n is the number of constituent quarks • Setting 2 =(0.471±.010) GeV2(fitting pion data) • pion: F(Q2)= C[1/ (1+Q2/0.471 GeV2)1], • nucleon: FN(Q2)= CN [1/( 1+Q2/0.71GeV2)2], • deuteron: Fd(Q2)= Cd [1/( 1+Q2/1.41GeV2)5] Politzer (1974), Chernyak & Zhitnisky (1984), Efremov & Radyuskin (1980) Matveev (1985), Brodsky & Lepage (1989) Egle Tomasi-Gustafsson Gomel, July 31, 2007

  13. Polarized/Unpolarizedmethods Egle Tomasi-Gustafsson Gomel, July 31, 2007

  14. Rosenbluth separation (1950) • Elasticepcross section (1-γ exchange) • point-like particle:  Mott Linearity of the reduced cross section! Egle Tomasi-Gustafsson Gomel, July 31, 2007

  15. Rosenbluth separation Contribution of the electric term =0.5 =0.8 …to be compared to the absolute value of the error on s and to the size and e dependence of RC =0.2 Egle Tomasi-Gustafsson Gomel, July 31, 2007

  16. The Rosenbluth data (SLAC) L. Andivahis et al. Phys. Rev. D 50, 5491 (1994) Egle Tomasi-Gustafsson Gomel, July 31, 2007

  17. The polarization method (1967) The polarization induces a term in the cross section proportional to GE GM Polarized beam and target or polarized beam and recoil proton polarization Egle Tomasi-Gustafsson Gomel, July 31, 2007

  18. The polarization method (exp) The simultaneous measurement of Pt and Pl reduces the systematic errors Egle Tomasi-Gustafsson Gomel, July 31, 2007

  19. HADRON POLARIMETRY Egle Tomasi-Gustafsson Gomel, July 31, 2007

  20. Hadron Polarimetry • Polarized beams • Polarized targets • Polarimeters Egle Tomasi-Gustafsson Gomel, July 31, 2007

  21. Hadron Polarimetry Working principle: measurement of the azymuthal asymmetry in a secondary scattering Large cross section (statistical errors) Large analyzing power (systematic errors) Vector polarization: inclusive scattering on light targets: p+C → one charged particle +X Tensor polarization: exclusive scattering: d+p → d+p (elastic scattering) d+p → p+p+n (charge exchange reaction) Egle Tomasi-Gustafsson Gomel, July 31, 2007

  22. Charge exchange reaction Idea from I. Pomeranchuk (1938) The deuteron is a bound np system in T=0, S=1 state ( l=0 or 2). Selecting a pair of protons in relative s-state, requires a spin-flip due to Pauli principle, anti-symmetric total wave function Large tensor analyzing power! d +p → (pp) + n Egle Tomasi-Gustafsson Gomel, July 31, 2007

  23. Vector Polarimeter Inclusive reaction: p(d)+C 1 Charged particle+X Egle Tomasi-Gustafsson Gomel, July 31, 2007

  24. Proton polarimeter Inclusive reaction: p+C 1 Charged particle+X • Calibration: analyzing powers • Measurement: polarization Egle Tomasi-Gustafsson Gomel, July 31, 2007

  25. HADRON POLARIMETRY • The Efficiency • The Figure of merit: • The Error on the Polarization Measurement Egle Tomasi-Gustafsson Gomel, July 31, 2007

  26. Polarimetry at 4-5 GeV Pomme polarimeter ... ...JINR -LHE synchrophasotron Egle Tomasi-Gustafsson Gomel, July 31, 2007

  27. HYPOM Analyzing powers Figure of merit Egle Tomasi-Gustafsson Gomel, July 31, 2007

  28. The experimental set-up • Trigger on proton: background, target walls and pion electroproduction • The solid angle is defined by the proton Egle Tomasi-Gustafsson Gomel, July 31, 2007

  29. JLab - HALL A Egle Tomasi-Gustafsson Gomel, July 31, 2007

  30. The HALL A-calorimeter Electron detection • Assembled a 1.35 x 2.55 m2 calorimeter • 17 rows and 9 columns of 15x15 lead-glass blocks Egle Tomasi-Gustafsson Gomel, July 31, 2007

  31. Proton momentum and scattering angle Egle Tomasi-Gustafsson Gomel, July 31, 2007

  32. Identify coincidence events Good separation peak/background Egle Tomasi-Gustafsson Gomel, July 31, 2007

  33. Identify elastic events In-plane and out-of-plane angular correlation Angles measured in the calorimeter and in the spectrometer Egle Tomasi-Gustafsson Gomel, July 31, 2007

  34. Identify elastic events After angular selection Egle Tomasi-Gustafsson Gomel, July 31, 2007

  35. Focal plane polarimeter Ptfpp and Pnfppare the physical asymmetries at the FPP Egle Tomasi-Gustafsson Gomel, July 31, 2007

  36. Azymuthal distribution Q2=5.6 GeV/c2 Egle Tomasi-Gustafsson Gomel, July 31, 2007

  37. Discussion of the results Egle Tomasi-Gustafsson Gomel, July 31, 2007

  38. THE RESULTS Linear deviation from dipole mGEpGMp Jlab E93-027 , E99-007Spokepersons:Ch. Perdrisat, V. Punjabi, M. Jones, E. Brash M. Jones et ql. Phys. Rev. Lett. 84,1398 (2000) O. Gayou et al. Phys. Rev. Lett. 88:092301 (2002) Egle Tomasi-Gustafsson Gomel, July 31, 2007

  39. Nucleon models... • Skyrme Models (Soliton) • Vector Dominance Models (G-K, IJL…) • Perturbative QCD • (Relativistic) Constituent Quark Model • Di-quark models • GPD • …….. Egle Tomasi-Gustafsson Gomel, July 31, 2007

  40. Comparison with theory Egle Tomasi-Gustafsson Gomel, July 31, 2007

  41. Issues • Simultaneous description of the four nucleon form factors... • ...in the space-like and in the time-like regions • Consequences for the light ions description • When pQCD starts to apply? • Source of the discrepancy Egle Tomasi-Gustafsson Gomel, July 31, 2007

  42. The nucleon form factors E. T.-G., F. Lacroix, Ch. Duterte, G.I. Gakh,EPJA (2005) Electric Magnetic VDM : IJL F. Iachello..PLB 43, 191 (1973) proton Hohler NPB 114, 505 (1976) Extended VDM (G.-K. 92): E.L.Lomon PRC 66, 045501 2002) Bosted PRC 51, 409 (1995) neutron Egle Tomasi-Gustafsson Gomel, July 31, 2007

  43. The neutron Form Factor Egle Tomasi-Gustafsson Gomel, July 31, 2007

  44. Electric NEUTRON Form Factor • Smaller than for proton, but not so small • New results, also based on polarization method Egle Tomasi-Gustafsson Gomel, July 31, 2007

  45. The reaction d(e,e’n)p - Ax • The KHARKOV model: • - Impulse Approximation • - Deuteron structure • - Kinematics: proton spectator • - Polarization observables G.I. Gakh, A. P. Rekalo, E. T.-G. Annals of Physics (2005) Egle Tomasi-Gustafsson Gomel, July 31, 2007

  46. The reaction d(e,e’n)p - Ax Select the quasi-elastic Kinematics Large dependence of the asymmetry on GEn! Polarized electron beam, polarized target or neutron polarimeter G.I. Gakh, A. P. Rekalo, E. T.-G. Annals of Physics (2005) Egle Tomasi-Gustafsson Gomel, July 31, 2007

  47. Neutron electric form factor Phys. Rev. C 70, 025202 (2004) Longitudinally polarized electrons, polarized target: a method similar to the polarization method, which takes into account the deuteron structure. Real Amplitudes, functions of q, W, Q2 Egle Tomasi-Gustafsson Gomel, July 31, 2007

  48. GEn from e-deuteron elastic scattering • GEn > GEp starting from 2 GeV2 ! E. T-G. and M. P. Rekalo, Europhys. Lett. 55, 188 (2001) Egle Tomasi-Gustafsson Gomel, July 31, 2007

  49. The IA deuteron structure E. T-G. and M. P. Rekalo, Europhys. Lett. 55, 188 (2001) Egle Tomasi-Gustafsson Gomel, July 31, 2007

  50. Polarization Observables and Hadron Structure (2) Egle Tomasi-GustafssonSaclay, France Egle Tomasi-Gustafsson Gomel, July 31, 2007

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