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Adam J. Sarty Saint Mary’s University

Measurement of the Coulomb quadrupole amplitude in the γ * p → Δ (1232) reaction in the low momentum transfer region (E08-010). Adam J. Sarty Saint Mary’s University. representing David Anez (SMU & Dalhousie U., PhD student) Doug Higinbotham (Jefferson Lab) Shalev Gilad (MIT)

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Adam J. Sarty Saint Mary’s University

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  1. Measurement of the Coulomb quadrupole amplitude in the γ*p→Δ(1232) reaction in the low momentum transfer region (E08-010) Adam J. Sarty Saint Mary’s University representing David Anez(SMU & Dalhousie U., PhD student) Doug Higinbotham(Jefferson Lab) ShalevGilad(MIT) Nikos Sparveris(spokesperson Emeritus!) Experiment proposal spear-headed by Nikos 2 years ago … he has handed it over for us to complete!

  2. E08-010: A short/little few-day “N D” Experiment! • Currently Scheduled to Run for 6 days: • April 3-8, 2011 • “squeezed” in between and “SRC” (E07-006) and “x>2” (E08-014) experiments. • The focus on low Q2 allows the high rates / short run • Personnel from this experiment will clearly be linked into the other two experiments. • Let me now overview the physics goals of the experiment, and give a few of the particulars.(Start with a general review …)

  3. * p0 D(1232) p p Where/How the Physicscomes in: * : EM Multipolarity of transition (Electric, Magnetic, Scalar) (Dipole, Quadrupole, etc.) Vertex #1 : Nucleon Structure model enters here: * + p   (CQM or “pion cloud” Bag Model, etc.) Vertex #2 : (1232) Model for decay PLUS 0p reaction Dynamics Lp value for nomenclature of transition amplitude determined here.

  4. * p0 D(1232) p p Where/How the Physicscomes in: * : EM Multipolarity of transition (Electric, Magnetic, Scalar) (Dipole, Quadrupole, etc.) Vertex #1 : Nucleon Structure model enters here: * + p   (CQM or “pion cloud” Bag Model, etc.) Vertex #2 : (1232) Model for decay PLUS 0p reaction Dynamics Lp value for nomenclature of transition amplitude determined here. NOTE: any full model for the reaction hasto deal with separating the desiredResonant excitation from “Other Processes”)

  5. Understanding the Nomenclature: #1 – the incident photonWhat “kind” (MULTIPOLE) of Photon can Excite p  ? * + p  (1232) ( Lgp ½+ = 3/2+ ) • Conserve Parity: Final p is +, so … pinitial= (pg)(pproton) = (pg)(+) = + • So photon’s parity is Even. • Recalling Parity of EM Multipoles: • Electric: EL = (-1)L • Magnetic: ML = (-1)L+1 • Scalar (or Coulomb): CL = (-1)L • So… Lgp= 1+  M1 (magnetic dipole) OR Lgp= 2+  E2, C2 (quadrupole)

  6. Understanding the Nomenclature: #2 – the N final stateEnsuring the intermediate state was (or could be!) resonance of interest - we’re interested here in the (1232) (1232)  p + p0 Jp= 3/2+ [ (½+ 0- )s l] So, Constraints on l: (the relative angular momentum of the pp0 pair in Final State) • Can have: l+ ½ = 3/2 (i.e. l = 1)orl– ½ = 3/2 (i.e. l = 2) • MUST conserve Parity: final p = + pfinal= (pp)(pproton) (-1)l = (+)(-) (-1)l + = (-1) l +1… so: l = ODD  l = 1 Sp = ½+

  7. Understanding the Nomenclature: #3 – The final labeling Joining the Photon and N angular momentum constraints(focusing still on (1232) resonance) • The full Multipole label for a specific *N  N transition amplitude carries information about the constraints on the initial virtual-photon  final pion-nucleon angular momentum …

  8. Understanding the Nomenclature: #3 – The final labeling Joining the Photon and N angular momentum constraints (focusing still on (1232) resonance) • The full Multipole label for a specific *N  N transition amplitude carries information about the constraints on the initial virtual-photon  final pion-nucleon angular momentum …Example:The dominant “Spherical” (single-quark spin-flip) transition amplitude is labeled M1+ l = 1 Magnetic photon(must be M1) J = l+ 1

  9. Understanding the Nomenclature: #3 – The final labeling Joining the Photon and N angular momentum constraints (focusing still on (1232) resonance) • The full Multipole label for a specific *N  N transition amplitude carries information about the constraints on the initial virtual-photon  final pion-nucleon angular momentum …Example:The dominant “Spherical” (single-quark spin-flip) transition amplitude is labeled M1+ and the smaller “Deformed” (quadrupole) transitions; E1+and S1+ (with E meaning “electric” and S “scalar” photon) The “S” can also be written “L” (“longitudinal”) – related by a kinematic factor to amplitudes written with “S” l = 1 Magnetic photon(must be M1) J = l+ 1

  10. Goal of these kind of “N D” Experiments:Quantify “non-spherical” Components of Nucleon wf Talking with a CQM view of a nucleon wave-function: • Dominant M1+ is a “spin-flip” transition;Nand D both “spherical”…L=0 between 3 quarks • BUT, the Quadrupole transitions (E1+ , S1+ ) “sample” the “not L=0” parts of the wavefunctions. • Consider writing wavefunctions like so: then,we can view the quadrupoletx as…

  11. Goal of these kind of “N D” Experiments:Quantify “non-spherical” Components of Nucleon wf • These Quadrupole transitions thus give insight into small L=2 part of wf. Phys. Rev.C63, 63 (2000)

  12. Goal of these kind of “N D” Experiments:Quantify “non-spherical” Components of Nucleon wf • These Quadrupole transitions thus give insight into small L=2 part of wf. • Such L=2 parts arise from “colour hyperfine interactions” between quarksIF the assumption is a “one-body interaction”: Phys. Rev.C63, 63 (2000)

  13. Goal of these kind of “N D” Experiments:Quantify “non-spherical” Components of Nucleon wf • These Quadrupole transitions thus give insight into small L=2 part of wf. • BUTL=2 transitions can also arise via interactions with virtual exchanged pions (the “pion cloud”): Phys. Rev.C63, 63 (2000)

  14. Goal of THIS“N D” Experiment:FOCUS ON LOW Q2 WHERE PION CLOUD DOMINATES • At low momentum transfer: the Pion Cloud dominates the “structure” of wavefunctions • These pion dynamics dictate the long-range non-spherical structure of the nucleon … and that is where we focus.

  15. NOW: to p( e , e’ p )0Measurements 18 Response Functions:Each with their own Unique/Independentcombination of contributing Multipole transition amplitudes

  16. NOW: to p( e , e’ p )0Measurements 18 Response Functions:Each with their own Unique/Independentcombination of contributing Multipole transition amplitudes • No polarization required for these Responses (R’s) • L and T via cross-sections at fixed (W,Q2) but different v’s (“Rosenbluth”) • LT and TT via cross-sections at different Out-Of-Plane angles  • We will extract just RLT (by left/right measurements) – and s0 – since LT term isvery sensitive to size of L1+ (see next slide…)

  17. NOW: to p( e , e’ p )0Measurements 18 Response Functions:Each with their own Unique/Independentcombination of contributing Multipole transition amplitudes For Example: decomp of 5 R’s (Drechsel & Tiator)

  18. Status of World Data at Low Q2(2 years old…from proposal)EMR ~ E2/M1 ratio CMR ~ C2/M1 ratio

  19. Status of World Data at Low Q2(2 years old…from proposal)EMR ~ E2/M1 ratio CMR ~ C2/M1 ratio We focus on getting CMR values in this region

  20. Where our Planned Results Fit(2 years old…from proposal)focus on: CMR ~ C2/M1 ratio at lowest Q2

  21. Where our Planned Results Fit(2 years old…from proposal)focus on: CMR ~ C2/M1 ratio at lowest Q2 • Q2 = 0.040 (GeV/c)2 • New lowest CMR value • θe = 12.5° • Q2 = 0.125 (GeV/c)2 • Validate previous measurements • Q2 = 0.090 (GeV/c)2 • Bridge previous measurements

  22. Step back to look at what weactually will measure:

  23. Finish with a Step back to look at what weactually will measure: Q2 = 0.040 GeV2 s0 LT Theta-pq W Q2 = 0.090 GeV2 s0 LT Theta-pq W

  24. Finish with a Step back to look at what weactually will measure: s0 LT W Theta-pq Q2 = 0.125 GeV2

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