1 Electromagnetic Excitation of Baryon Resonances

2 Electromagnetic Excitation of N*’s 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 A 3/2 A 1/2 S 1/2 and their Q 2 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 e e’ γvγv N N’,Λ N*,△ A 3/2, A 1/2,S 1/2  p  p   p  

3 Inclusive Electron Scattering ep → e’X  Resonances cannot be uniquely separated in inclusive scattering → exclusive processes Q 2 =-(e-e’) 2 ; W 2 = M X 2 =(e-e’+p) 2 (G E, G M )  (1232) N(1440) N(1520)N(1535)  (1620) N(1680) ep →ep

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 6 th resonance

Dispersion relations and Unitary Isobar Model  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: (contribution by Inna Aznauryan)

 The imaginary parts of the amplitudes are determined mainly by the resonance contributions:  For all resonances, except P 33 (1232), we use relativistic Breit-Wigner parameterization with energy-dependent width  Combination of DR, Watson theorem, and the elasticity of t 1+ 3/2 (πN ) up to W=1.43 GeV provide strict constraints on the M 1+ 3/2,E 1+ 3/2,S 1+ 3/2 multipoles of the P 33 (1232) (Δ(1232)). Dispersion relations and Unitary Isobar Model (continued)

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

Some points which are specific to high Q 2 From the analysis of the data at different Q 2 = GeV, we have obtained consistent results for f sub (t,Q 2 ) f sub (t,Q 2 ) has relatively flat behavior, in contrast with π contribution:

Some points which are specific to high Q 2 (continued)  The background of UIM we use at large Q 2 consists of the Born term and t-channel ρ and ω contributions  At high Q 2, a question can arise if there are additional t-channel contributions, which due to the gauge invariance, do not contribute at Q 2 =0, e.g. π(1300), π(1670), scalar dipole transitions for h 1 (1170), b 1 (1235), a 1 (1260) … Such contributions are excluded by the data.

Analysis (continued)  Fitted parameters: amplitudes corresponding to: P 33 (1232), P 11 (1440), D 13 (1520), S 11 (1535) F 15 (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): E 1+ =S 1+ =0

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

14 Multipole Ratios R EM, R SM before 1999 Sign? Q 2 dependence?  Data could not determine sign or Q 2 dependence

15 N ∆ electroproduction experiments after 1999 ReactionObservableWQ2Q2 Author, Conference, PublicationLAB p(e,e’p)π 0 σ 0 σ TT σ LT σ LTP S. Stave, EPJA, 30, 471 (2006) MAMI p(e,e’p)π H. Schmieden, EPJA, 28, 91 (2006) MAMI p(e,e’p)π Th. Pospischil, PRL 86, 2959 (2001) MAMI p(e,e’p)π 0 σ 0 σ TT σ LT σ LTP C. Mertz, PRL 86, 2963 (2001) C. Kunz, PLB 564, 21 (2003) N. Sparveris, PRL 94, (2005) BATES p(e,e’p)π 0 σ 0 σ TT σ LT σ LTP N. Sparveris, SOH Workshop (2006) N. Sparveris, nucl-ex/ MAMI p(e,e’p)π 0 A LT A LTP P. Bartsch, PRL 88, (2002) D. Elsner, EPJA, 27, 91 (2006) MAMI p(e,e’p)π 0 p(e,e’π+)n σ 0 σ TT σ LT σ LTP C. Smith, SOH Workshop (2006) JLAB / CLAS p(e,e’p)π 0 σ 0 σ TT σ LT K. Joo, PRL 88, (2001) JLAB / CLAS p(e,e’p)π 0 p(e,e’π+)n σ LTP ,0.65K. Joo, PRC 68, (2003) K. Joo, PRC 70, (2004) K. Joo, PRC 72, (2005) JLAB / CLAS p(e,e’π+)nσ 0 σ TT σ LT H. Egiyan, PRC 73, (2006) JLAB / CLAS p(e,e’p)π 0 16 response functions J. Kelly, PRL 95, (2005) JLAB / Hall A p(e,e’π+)nσ 0 σ TT σ LT σ LTP K. Park, Collaboration review JLAB / CLAS p(e,e’p)π 0 σ 0 σ TT σ LT M. Ungaro, PRL 97, (2006) JLAB / CLAS p(e,e’p)π 0 σ 0 σ TT σ LT , 4.0 V. Frolov, PRL 82, 45 (1999) JLAB / Hall C p(e,e’p)π 0 σ 0 σ TT σ LT , 7.5A. Villano, ongoing analysis JLAB / Hall C

16 Pion Electroproduction Structure Functions Structure functions extracted from fits to  * distributions for each (Q 2,W, cosθ * ) point. LT and TT interference sensitive to weak quadrupole and longitudinal multipoles. + : J = l + ½ - : J = l - ½

17 Unpolarized structure function –Amplify small resonant longitudinal multipole by interfering with a large resonance transverse multipole The Power of Interference I  LT ~ Re(L*T) = Re(L)Re(T) + Im(L)Im(T) Large Small P 33 (1232) Im(S 1+ ) Im(M 1+ )

18 Typical Cross Sections vs cos  * and  * Q 2 = 0.2 GeV 2 W=1.22 GeV

19 NΔ(1232) - Small Q 2 Behavior Structure Functions → Legendre expansion

20 Structure Functions - Invariant Mass W

21 Legendre Expansion of Structure Functions Resonant Multipoles Non-Resonant Multipoles (M 1+ dominance) Resonance mass is not always at the peak! Truncated multipole expansion

22 How about π + electroproduction? π+ electroproduction is less sensitive to the Δ(1232) multipoles, and more sensitive to higher mass resonances e.g. P 11 (1440), D 13 (1520), S 11 (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 l    multipoles π + n channel has more background than pπ 0 which makes it more difficult to measure the small quadrupole terms.

24 π + electroproduction at Q 2 =0.20 GeV 2 C LAS

25 CLAS, MAMI results for E 1+ /M 1+ and S 1+ /M 1+ pπ 0 only pπ 0 and nπ + CLAS UIM Fit Truncated multipole expansion MAMI PRELIMINARY (N. Sparveris, SOH Workshop, Athens, Apr 06)

26 Comparison to lattice QCD calculations ■ CLAS 06 Quenched Lattice QCD GM* : Good agreement at Q 2 =0 but somewhat ‘harder’ form factor compared to experiment. S1+/M1+: Undershoots data at low Q 2 Linear chiral extrapolations may be naïve. C. Alexandrou et al, PRL 94, (2005)

27 Comparison with Theory Quenched Lattice QCD - E 1+ /M 1+ : Good agreement within large errors. - S 1+ /M 1+ : Undershoots data at low Q 2. - Linear chiral extrapolations may be naïve and/or dynamical quarks required Dynamical Models - Pion cloud model allows reasonable description of quadrupole ratios over large Q 2 range. Deformation of N, △ quark core? Shape of pion cloud? What are we learning from E/M, S/M? Need to isolate the first term or go to high Q 2 to study quark core.

28 High Q 2 NΔ Transition

29 NΔ(1232) – Short distance behavior Complete angular distributions in   and    in full W & Q 2 range.  Q 2 =3GeV 2 cos  

30 l    multipoles UIM Fit to pπ 0 diff. cross section

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

32 NΔ Transition Form Factors - G M Meson contributions play a role even at relatively high Q 2. *  1/3 of G * M at low Q 2 is due to vertex dressing and pion cloud contributions. bare vertex dressed vertex pion cloud

33 Multipole Ratios R EM, R SM before 1999 Sign? Q 2 dependence?  Data could not determine sign or Q 2 dependence

34  There is no sign for asymptotic pQCD behavior in R EM and R SM.  R EM < 0 favors oblate shape of  (1232) and prolate shape of the proton. NΔ Multipole Ratios R EM, R SM in 2007 Deviation from spherical symmetry of the  (1232) in LQCD (unquenched). Dynamical models attribute the deformation to contributions of the pion cloud at low Q 2.

35 So what have we learned about the Δ resonance? e e / Shape of pion cloud? Deformation of N, △ quark core? e e / 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 Q 2 we need to go.  Its magnetic transition form factor drops much faster with Q 2 (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 E 1+ follows closely the magnetic M 1+ multipoles. No sign of onset of asymptotic behavior up to shortest distances.  Within large statistical uncertainties qLQCD describes E 1+ /M 1+.  S 1+ / M 1+ is well described by qLQCD at sufficiently high Q 2 but deviates at low Q 2.

36 NΔ Multipole Ratios - Future Program CLAS12 (projected)  With the JLab energy upgrade to 12 GeV the accessible Q 2 range for the NΔ transition form factors will be doubled to 12 GeV 2.  Since the Δ form factors drop so rapidly with Q 2, a direct measurement of all final state particles maybe required to uniquely identify the final state.