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Electromagnetic Excitation of Baryon Resonances

Electromagnetic Excitation of Baryon Resonances. l g p =1/2. g. p. l g p =3/2. Electromagnetic Excitation of N*’s. e’. p, h, pp, K. γ v. e. N*,△. N ’, Λ. N. A 3/2 , A 1/2 ,S 1/2. Primary Goals: Extract electro-coupling amplitudes for known △,N* resonances in N π , N η , N ππ

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Electromagnetic Excitation of Baryon Resonances

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  1. Electromagnetic Excitation of Baryon Resonances

  2. lgp=1/2 g p lgp=3/2 Electromagnetic Excitation of N*’s e’ p, h, pp, K γv e N*,△ N’,Λ N A3/2, A1/2,S1/2 Primary Goals: • Extract electro-coupling amplitudes for known △,N* resonances in Nπ, Nη, Nππ • Partial wave and isospin decomposition of hadronic decay • Assume em and strong interaction vertices factorize • Helicity amplitudes A3/2 A1/2 S1/2 and their Q2 dependence • Study 3-quark wave function and underlying symmetries • Quark models: relativity, gluons vs. mesons. • Search for “missing” resonances predicted in SU(6) x O(3) symmetry group

  3. Inclusive Electron Scattering ep→e’X (GE, GM) ep→ep N(1680) N(1440) D(1232) N(1520) N(1535) D(1620) Q2=-(e-e’)2; W2 =MX2=(e-e’+p)2 • Resonances cannot be uniquely separated • in inclusive scattering → exclusive processes

  4. W-Dependence of selected channels at 4 GeV e’ Measurement of various final states needed to probe different resonances, and to determine isospin. From panels 2 and 3 we can find immediately the isospins of the first and second resonances. The big broad strength near 1.35 GeV in panel 3, and not seen in panel 2 hints at another I=1/2 state. From panels 3 and 4 we see that there are 5 resonances. Panel 5 indicates there might be a 6th resonance. 1 2 3 4 5

  5. Dispersion relations and Unitary Isobar Model (contribution by Inna Aznauryan) • Using two approaches allows us to draw conclusions on the model dependence of the extracted results. • The main uncertainty of the analysis is related to the real parts of amplitudes which are built in DR and UIM in conceptually different way:

  6. Dispersion relations and Unitary Isobar Model (continued) • The imaginary parts of the amplitudes are determined mainly by the resonance contributions: • For all resonances, except P33(1232), we use relativistic Breit-Wigner parameterization with energy-dependent width • Combination of DR, Watson theorem, and the elasticity of t1+3/2(πN ) up to W=1.43 GeV provide strict constraints on the M1+3/2,E1+3/2,S1+3/2 multipolesof the P33(1232) (Δ(1232)).

  7. Fixed-t Dispersion Relations for invariant Ball amplitudes (Devenish & Lyth) γ*p→Nπ Dispersion relations for 6 invariant Ball amplitudes: Unsubtracted Dispersion Relations (i=1,2,4,5,6) Subtracted Dispersion Relation

  8. Some points which are specific to high Q2 • From the analysis of the data at different Q2 = 1.7-4.2 GeV,we have obtained consistent results for fsub(t,Q2) • fsub(t,Q2) has relatively flat behavior, in contrast with π contribution:

  9. Some points which are specific to high Q2 (continued) • The background of UIM we use at large Q2 consists of the Born term and t-channel ρ and ω contributions • At high Q2, a question can arise if there are additional t-channel contributions, which due to the gauge invariance, do not contribute at Q2=0, e.g. π(1300), π(1670), scalar dipole transitions for h1(1170), b1(1235), a1(1260) … • Such contributions are excluded by the data.

  10. Analysis (continued) • Fitted parameters: amplitudes corresponding to: P33(1232), P11(1440) , D13(1520) , S11(1535) F15 (1680) • Amplitudes of other resonances, in particular those with masses around 1700 MeV, were parameterized according to the SQTM or the results of analyses of previous data • Including these amplitudes into the fitting procedure did not change the results

  11. γNΔ(1232) Transition

  12. N-Δ(1232) Quadrupole Transition SU(6): E1+=S1+=0

  13. NΔ - in Single Quark Transition N(938) Δ(1232) N(938) Δ(1232) C2 M1 Magnetic single quark transition. C2 Coulomb single quark transition.

  14. Sign? Q2 dependence? • Data could not determine sign or Q2 dependence Multipole Ratios REM, RSM before 1999

  15. N ∆ electroproduction experiments after 1999

  16. Pion Electroproduction Structure Functions ½ + : J =l + - : J =l - ½ • Structure functions extracted from fits to f* distributions for each (Q2 ,W, cosθ*) point. • LT and TT interference sensitive to weak quadrupole and longitudinal multipoles.

  17. The Power of Interference I Im(S1+)Im(M1+) Large P33(1232) Small sLT ~ Re(L*T) = Re(L)Re(T) + Im(L)Im(T) • Unpolarized structure function • Amplify small resonant longitudinal multipole by interfering with a large resonance transverse multipole

  18. Typical Cross Sections vs cos q* andf* Q2 = 0.2 GeV2 W=1.22 GeV

  19. NΔ(1232) - Small Q2 Behavior Structure Functions Preliminary → Legendre expansion

  20. Structure Functions - Invariant Mass W

  21. Legendre Expansion of Structure Functions Resonant Multipoles Non-Resonant Multipoles Truncated multipole expansion (M1+ dominance) Resonance mass is not always at the peak!

  22. How about π+ electroproduction? π+ electroproduction is less sensitive to the Δ(1232) multipoles, and more sensitive to higher mass resonances e.g. P11(1440), D13(1520), S11(1535) (as well as to background amplitudes). The resonant NΔ multipoles cannot be extracted from a truncated partial wave expansion using only π+n data.

  23. lp= 1+ multipoles π+n channel has more background than pπ0 which makes it more difficult to measure the small quadrupole terms.

  24. π+ electroproduction at Q2=0.20 GeV2 CLAS

  25. CLAS, MAMI results for E1+/M1+ and S1+/M1+ pπ0 only pπ0 and nπ+ CLAS UIM Fit Truncated multipole expansion MAMI PRELIMINARY (N. Sparveris, SOH Workshop, Athens, Apr 06)

  26. Comparison to lattice QCD calculations C. Alexandrou et al, PRL 94, 021601 (2005) ■ CLAS 06 Quenched Lattice QCD GM* : Good agreement at Q2=0 but somewhat ‘harder’ form factor compared to experiment. S1+/M1+: Undershoots data at low Q2 Linear chiral extrapolations may be naïve.

  27. Comparison with Theory Quenched Lattice QCD - E1+/M1+: Good agreement within large errors. - S1+/M1+: Undershoots data at low Q2. - Linear chiral extrapolations may be naïve and/or dynamical quarks required Dynamical Models - Pion cloud model allows reasonable description of quadrupole ratios over large Q2 range. What are we learning from E/M, S/M? Shape of pion cloud? Deformation of N, △ quark core? Need to isolate the first term or go to high Q2 to study quark core.

  28. High Q2 NΔ Transition

  29. NΔ(1232) – Short distance behavior Complete angular distributions in Qp and fp ,in full W & Q2 range. Q2=3GeV2 cosqp f

  30. UIM Fit to pπ0 diff. cross section lp= 1+ multipoles

  31. NΔ Multipole Ratios REM, RSM in 2007 K. Joo, et al., PRL88 (2002); J. Kelly et al., PRL95 (2005); M. Ungaro, et al., PRL97 (2006) • Most precise baryon form factor measurement: dREM, dRSM < 0.01. • REM remains small and negative at -2% to -3.5% from 0 ≤ Q2≤ 6 GeV2. • No trend towards sign change or asymptotic behavior. Helicity conservation - REM→ +100(%). • RSM negative and increase in magnitude. Helicity conservation - RSM→ constant.

  32. NΔ Transition Form Factors - GM 1 GD = (1+Q2/0.71)2 * • 1/3 of G*M at low Q2 is due • to vertex dressing and pion • cloud contributions. bare vertex dressed vertex pion cloud Meson contributions play a role even at relatively high Q2.

  33. Sign? Q2 dependence? • Data could not determine sign or Q2 dependence Multipole Ratios REM, RSM before 1999

  34. Deviation from spherical symmetry of the D(1232) in LQCD (unquenched). NΔ Multipole Ratios REM, RSM in 2007 • There is no sign for asymptotic pQCD behavior in REM and RSM. • REM < 0 favors oblate shape of D(1232) and prolate shape of the proton. Dynamical models attribute the deformation to contributions of the pion cloud at low Q2.

  35. e / e / e e So what have we learned about the Δ resonance? • Its magnetic transition form factor drops much faster with Q2 (as we probe it at shorter distances) than the magnetic form factor of the proton. • The quadrupole contributions seems to originate mostly from the pion contributions to the wave function. The electric E1+ follows closely the magnetic M1+ multipoles. No sign of onset of asymptotic behavior up to shortest distances. • Within large statistical uncertainties qLQCD describes E1+/M1+. • S1+/ M1+ is well described by qLQCD at sufficiently high Q2 but deviates at low Q2. Deformation of N, △ quark core? Shape of pion cloud? Answer will depend on wavelength of probe. With increasing resolution, we are mapping out the shape of the Δ vs the distance scale. But it is unclear how high in Q2 we need to go.

  36. CLAS12 (projected) NΔ Multipole Ratios - Future Program • With the JLab energy upgrade to 12 GeV the accessible Q2 range for the NΔ transition form factors will be doubled to 12 GeV2. • Since the Δ form factors drop so rapidly with Q2, a direct measurement of all final state particles maybe required to uniquely identify the final state.

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