Baryon quadrupole and octupole moments

Transcription

1 Baryon quadrupole and octupole moments Alfons Buchmann University of Tübingen 1. How I came to know Prof. Ernest Henley 2. Collaboration with E. M. Henley 3. Baryon quadrupole moments 4. Baryon octupole moments 5. Summary INT Symposium Symmetries in Subatomic Physics In memory of E. M. Henley University of Washington, Seattle 2018

2 1. How I came to know Prof. Ernest Henley

3 21 August 1981

4 E. M. Henley, Humboldt Fellow (1984) Ernest Henley was the recipient of the Humboldt prize in In 1984 Prof. Henley made a research visit to the Johannes Gutenberg University, Mainz. He gave a series of lectures on Symmetries of Electroweak Interactions at the Students Workshop on Electromagnetic Interactions in Bosen (near Mainz) in 1984.

5 Students workshop on electromagnetic interactions (Bosen 1984) Ernest Henley

6 Walk with Prof. Henley around the lake in Bosen 6,8 km trail Discussion on exchange currents and current conservation (Topic of my diploma thesis)

7 E. M. Henley and Subatomic Physics My favorite textbook

8 E. M. Henley and the BMW At the time (1984), the BMW company provided Humboldt prize winners with a BMW car for their stay in Germany free of charge. Later they could take this car home at a reduced price. Ernest Henley was not too fond of this arrangement and said: I would have prefered a bicycle. Story related to me by Dr. Lothar Tiator, University of Mainz Coorganizer of the Students Workshop in Bosen, Germany

9 E. M. Henley in Tübingen As a Humboldt fellow, Prof. Ernest Henley repeatedly visited the University of Tübingen, where I worked as a postdoc ( ). During his visits in 1998 and 1999 Ernest and I discussed results on charge radii and quadrupole moments derived from a constituent quark model with exchange currents. We thought about whether these results could be generalized.

10 2. Collaboration with Prof. Ernest Henley

11 Beginning of collaboration with E.M. Henley Date: Thu, 29 Jul :59: From: To: Subject: saga Dear Alfons, July 29 I looked at the various Morpurgo articles and now understand things a lot better. I thought that you might be able to generalize his idea to meson-baryon couplings Do you want to look at the inherent Q? The easiest way to do so might be to factor out the Clebsch-Gordon coefficient (which vanishes for j=1/2). If I can get you here for a month or more, we might put something together with all this "stuff. Best regards Ernest

12 Collaboration with E. M. Henley ( ) A. B. and E. M. Henley, Pion-baryon couplings, Phys. Lett. B 484 (2000) 255 A. B. and E. M. Henley, Intrinsic quadrupole moment of the nucleon, Phys. Rev. C 63 (2001) A. B. and E. M. Henley, Quadrupole moments of baryons, Phys. Rev. D 65 (2002) A. B. and E. M. Henley, Baryon octupole moments, Eur. Phys. J. 35 (2008) 267 A. B. and E. M. Henley, Spin of ground state baryons, Phys. Rev. D 83 (2011) A. B. and E. M. Henley, Three-quark currents and baryon spin, Eur. Phys. J. 55 (2014) 749

13 What about higher multipole moments? Presently, very little is known about magnetic octupole moments of decuplet baryons and excited N* states 3. Baryon quadrupole moments Information needed to reveal structural details of spatial current distributions in baryons.

14 Purpose of this talk Review the work with E.M. Henley adressing the question: What is the shape of the proton and its first excited state + (1232)? prolate (cigar shaped) p u u d u d u oblate (pancake shaped) + u

15 Electromagnetic multipole moments Electromagnetic multipole moments (22 JJ poles) are directly connected with the charge and current distributions in baryons. In particular, the sign and size of the JJ = 2 and JJ = 3 charge quadrupole (C2) moments magnetic octupole (M3) moments provide information on the geometric shape of baryons not available from the corresponding leading multipole moments C0 and M1.

16 Classical charge multipole moments +q QQ 0 < 0 +q q +q q q +q +q = q q + q q +q q +q ρρ ~ q 0 + d 1 + Q 2 + Ω 3 + monopole dipole quadrupole C0 C1 C2 octupole C3 +q +q +q +q 2q = q + q +2q +q QQ 0 > 0 In quantum mechanics only even charge multipoles e.g. C0,C2, are allowed. q

17 Geometric shape of proton charge distribution nonspherical charge distribution of proton ρρ pp rr = ρρ pp (rr, θθ, φφ) angular charge distribution shape information How can one get information on the angular dependence of the proton charge distribution?

18 Angular momentum selection rules JJ ii + JJ oooo JJ ff Here: JJ oooo = 2 Nucleon Nucleon JJ ii = JJ ff = Q [2] 1 2 = Q N 0 elastic electron scattering 1/ /2 no spectroscopic quadrupole moment Nucleon JJ ii = 1 2 Delta JJ ff = Q [2] 1 2 = Q N Δ inelastic electron scattering 1/ /2 spectroscopic quadrupole moment exists

19 Nucleon excitation spectrum N*(1680) N*(1520) N*(1440) radial excitation C0, M1 N(939) (1232) CJ charge multipoles EJ electric multipoles MJ magnetic multipoles J=1/2 + J=3/2 - J=3/2 + J=5/2 +.

20 Inelastic electron-nucleon scattering e π pion N electro-pionproduction QQ...four-momentum transfer of virtual photon pp QQ pp + GG + CCC QQ 2 = 0 transition quadrupole moment e Q γ (1232) N Δ transition form factors N G N Δ M1, E 2,C2 (Q spectroscopic transition quadrupole moment QQ NN eeeeee = (3333) fm² 2 )

21 What about higher multipole moments? Presently, very little is known about magnetic octupole moments of decuplet baryons and excited N* states 3.1 Spectroscopic vs. intrinsic quadrupole moments Information needed to reveal structural details of spatial current distributions in baryons.

22 Intrinsic quadrupole moment QQ 00 To learn about the shape of a particle one has to determine its intrinsic quadrupole moment, defined with respect to a body-fixed frame QQ 0 = ρρ rr 3zz 2 rr 2 dd 3 rr If ρ concentrated along z-axis, 3zz 2 -term dominates QQ 0 > 0 z prolate If ρ concentrated in x-y plane, rrr -term dominates QQ 0 < 0 z oblate

23 Intrinsic vs. spectroscopic quadrupole moment laboratory frame spectroscopic q.m. body-fixed frame intrinsic q.m. cos θθ = JJ zz JJ 2 JJ = 1/2 QQ = 0 even if QQ 0 0. spectroscopic q.m. intrinsic q.m. deformed baryon with JJ = 0 or JJ = 1 2 in body-fixed frame QQ = PP 2 (cos θθ) QQ 0 = cos2 θθ 1 QQ 0 = 3 JJ zz 2 JJ JJ + 1 2JJ JJ + 1 QQ 0 Legendre function PP 2 prevents QQ 0 from being seen in lab., if JJ = 0 or JJ = 1 2.

24 Do intrinsic quadrupole moments exist? Critique Intrinsic quadrupole moments cannot be directly measured. Therefore, they do not exist. Heisenberg: An elephant in an S-state remains an elephant. The nuclear collective model of deformed nuclei (Bohr & Mottelson) shows: Nuclei with spins JJ = 0 and JJ = 1 can have intrinsic quadrupole moments 2 even though their spectroscopic quadrupole moments are zero. The sign of the intrinsic quadrupole moment determines the geometric shape of the nucleus, i.e. whether it is prolate or oblate.

25 Intrinsic quadrupole moment of J=0 & J=1/2 nuclei Due to the work of A. Bohr and B. Mottelson and others, the notion of intrinsic quadrupole moment of spin 0 and spin ½ nuclei is now generally accepted. Obtaining information on intrinsic quadrupole moments QQ 0 of nuclei from experimental data is possible!

26 Status prior to our investigation Model Quark model with pion cloud oblate Q =? (Vento & Rho, PLB 102 (1981) 97 Quark-diquark model prolate Q = fm 2 (Migdal, PLB 228 (1989) 167 QQ Chiral bag model (Ma & Wambach, PLB 132 (1983) 1 oblate Q =? Isobar model (Giannini et al., PLB 88 (1979) 13 oblate Q = 0.18 fm 2 Skyrme model (Rahimov et al., PLB 378 (1996) 12 prolate Q = fm 2 None of this models features a clear distinction between QQ 00 and QQ.

27 Model calculations of QQ 00 We have calculated the intrinsic quadrupole moment QQ 0 in three rather different nucleon models quark model pion-nucleon model collective model All three models lead to the same signs for the intrinsic quadrupole moments QQ 0 (pp) and QQ 0 +.

28 What about higher multipole moments? Presently, very little is known about magnetic octupole moments of decuplet baryons and excited N* states 3.2 Quark model Information needed to reveal structural details of spatial current distributions in baryons.

29 One-gluon exchange potential quark hyperfine interaction causes N- mass splitting quark tensor force causes D state admixture in N and wave functions V gluon 1 π ( ) = αs 1+ σi σ j δ(r) 3 σi rˆ σ j rˆ σi σ j r mq 3 4mq r central tensor Analogous to Fermi-Breit interaction in QED

30 N(939) Single-quark transition Δ(1232) C2 C2

31 Single quark charge density 3 ρρ [1] = ee ii ee iiqq rr ii ii=1 ee ii quark charge qq photon momentum ee ii QQ pp + = bb aa SSbb DD aa DD bb SS With typical D-state probabilities in the N(939) and Δ(1232) of PP DD (NN) PP DD ( ) , QQ pp + is too small to account for the experimental NN Δ quadrupole moment. Which degrees of freedom are missing?

32 Two-quark charge density σ i m i σ j m j ee ii quark charge σσ ii quark spin mm ii quark mass qq photon momentum e i ee ii = 1 2 λλ 3ii λλ 8ii γ 2-quark operator ρρ [2] αα ss 3 ρρ [2] ~ ii 3 16 mm (ee ii ee iiqq rr ii σσ ii qq σσ jj rr + (ii jj)) 1 qq rr 3 ii<jj After angular momentum recoupling we can rewrite this as 3 ρρ [2] = BB ii jj ee ii 2 σσ ii σσ jj 3 σσ iiii σσ jjzz σσ ii σσ jj scalar (J=0) tensor (J=2)

33 Double spin flip mechanism C2 QQ pp + = rr nn 22 Simultaneously flipping the spin of two quarks via one-gluon exchange current A. J. Buchmann, E. Hernandez, A. Faessler, Phys. Rev. C55 (1997) 448

34 Neutron charge radius & N quadrupole moment 3 ρρ [2] = BB ee ii 2 σσ ii σσ jj 3 σσ iiii σσ jjzz σσ ii σσ jj ii jj two-body charge density scalar (J=0) tensor (J=2) neutron charge radius rr 2 nn = 56 nn ρρ JJ=0 [2] 56 nn = 4 BB N transition quadrupole moment QQ pp + = 56 + ρρ JJ=2 [2] 56 pp = 2 2 BB more general derivation independent of qq interaction QQ pp + = 1 2 rr nn 2 Neutron charge radius rr nn 2 and QQ pp +are dominated by the same degrees of freedom A. J. Buchmann and E. M. Henley, PRC 63 (2001)

35 Comparison with experiment Theory (quark model with two-body e.m. currents) pp QQ pp +: = GG + CCC QQ 2 = 0 = 1 2 rr nn 2 AJB and E. M. Henley, PRC 63 (2001) With the experimental rr nn 2 our theory gives QQ pp + = 1 2 rr nn 2 = fm 2 Experimental results QQ NN = 0.108(9) fm² LEGS: Blanpied et al., Phys. Rev. C 64 (2001) QQ NN = (33) fm² MAID: Tiator et al., Eur. Phys. J. A 17 (2003) 357

36 Spectroscopic quadrupole moment of the proton Clebsch-Gordan coefficients pp = uuuuuu uuuuuu dddddd 16 2 mixed sym. mixed sym uuuuuu dddddd 12 mixed antisym. mixed antisym. (3 σσ iiii σσ jjzz σσ ii σσ jj ) = QQ pp = pp QQ [2] pp = BB = 0 The spectroscopic quadrupole moment of the proton is zero!

37 Intrinsic quadrupole moment of the proton Renormalize all Clebsch-Gordan coefficients in the spin part to 1. pp = uuuuuu uuuuuu dddddd uuuuuu dddddd Clebsch-Gordan coefficients renormalized to 1 This amounts to undoing the averaging over the all spin directions. QQ 0 pp : = pp QQ [2] pp = 2BB = 4BB = rr nn 2 > 0 prolate Analogously we obtain for the 1232 QQ 0 + = QQ + = rr nn 2 QQ 0 + = QQ 0 pp < 0 oblate

38 Interpretation in quark model Two-quark spin-spin operators are repulsive for quark pairs with spin 1. In the neutron, both down quarks are in a spin 1 state, and are repelled more strongly than an up-down pair. elongated (prolate) charge distribution negative neutron charge radius rr nn 2 positive intrinsic quadrupole mom. QQ 0 In the 0, all quark pairs have spin 1. Equal distance between down-down and up-down pairs. planar (oblate) charge distribution vanishing 0 charge radius rr 2 0 negative intrinsic quadrupole mom. QQ 0 d n J=1/2 u intrinsic quadrupole moment QQ 0 nn = rr nn2 > 0 QQ 0 ( 0 ) = rr nn2 < 0 d u d 0 J=3/2 d AJB and E. M. Henley, PRC 63 (2001)

39 What about higher multipole moments? Presently, very little is known about magnetic octupole moments of decuplet baryons and excited N* states 3.3 Pion-nucleon and collective model Information needed to reveal structural details of spatial current distributions in baryons.

40 Interpretation in pion-nucleon model QQ ππ = ee ππ 16 ππ 5 rr ππ 2 YY 0 2 rr ππ rr ππ distance between core and pion rr ππ pion preferentially emitted along spin direction z YY 0 1 rr ππ pion preferentially emitted in equatorial x-y plane QQ pp 0 = rr 2 nn > 0 QQ + 0 = rr 2 nn < 0 prolate oblate More details in: A. J. Buchmann and E. M. Henley, PRC 63 (2001) YY 1 1

41 Interpretation in collective model J total angular momentum K projection of J onto z-axis R collective orbital angular momentum QQ = 3 KK2 JJ JJ + 1 JJ + 1 (2JJ + 3) QQ 0 spectroscopic quadrupole moment intrinsic quadrupole moment Consider the Δ(1232) with J=3/2 as a collective rotation of the nucleon with intrinsic angular momentum K=1/2. Insert QQ + = rr nn 2 for the spectroscopic quadrupole moment QQ 0 pp = 5 rr nn 2 > 0 overestimate due to crudeness of the model

42 Interpretation in collective model Estimate deviation from spherical symmetry For given rr pp = fm Q 0 = rr 2 nn = fm², calculate half axes aa and bb. QQ 0 = 2 5 aa2 bb 2 = 4 5 RR2 δδ RR = 1 2 aa + bb = 5 3 rr pp 2 δδ = 2 aa bb aa + bb aa/bb = 1.13 big! compare with deuteron aa/bb = 1.05 AJB and E. M. Henley, PRC 63 (2001)

43 What about higher multipole moments? Presently, very little is known about magnetic octupole moments of decuplet baryons and excited N* states 3.4 Broken SU(6) spin-flavor symmetry Information needed to reveal structural details of spatial current distributions in baryons.

44 SU(6) spin-flavor symmetry analysis SU(6) spin-flavor symmetry combines SU(3) multiplets with different spin and flavor to SU(6) spin-flavor supermultiplets. Gürsey, Radicati, Sakita (1964)

45 SU(6) spin-flavor supermultiplet S baryon supermultiplet 56 dimensional T 3 56 = 8, , 4 flavor spin flavor spin dimensionality in spin space 2JJ + 1

46 General spin-flavor operator OO OO = AA OO 1 + BB OO 2 + CC OO 3 one-body two-body three-body Constants AA, BB, CC are determined from experiment. OO kk allowed operators in spin-flavor space kk = 1,2,3 How are the spin-flavor operators constructed? Operators are built from the 35 generators of the SU(6) group: σσ ii 3, λλ jj 8, σσ ii λλ jj 24 σσ ii spin operator λλ jj flavor operator Ex.: Charge operator QQ = 1 2 λλ λλ 8 Gell-Mann Nishijima relation transforms as a flavor 8 rep.

47 SU(6) spin-flavor symmetry and its breaking Due to the SU(6) symmetry, there is a connection between observables of different tensor rank JJ e.g. between charge radii (JJ = 0) and quadrupole moments (JJ = 2). Example: Multipole expansion of ρρ [2] in spin-flavor space 3 ρρ [2] = BB ee ii 2 σσ ii σσ jj 3 σσ iiii σσ jjzz σσ ii σσ jj ii jj scalar (J=0) tensor (J=2) The prefactors of the spin scalar (+22) and spin tensor 11 terms are determined by the SU(6) group algebra.

48 Spin-flavor selection rule for the 56-plet Ground state baryon observable OO [RR] must satisfy the following selection rule OO = 56 OO [RR] 56 Selection rule OO 00 only if OO [RR] transforms according to one of the irreducible representations RR contained in the product = body 1-body 2-body 3-body

49 SU(3) x SU(2) decomposition of 35-plet Decompose one-body SU(6) tensor 35 into SU(3) and SU(2) subtensors 35 = 8,1 + 8,3 + 1,3 scalar JJ = 0 vector JJ = 1 First entry: dimension of SU(3) flavor operator Second entry: dimension of SU(2) spin operator (2JJ + 1) Example: Charge multipole operator transforms as flavor 8. Charge multipoles transform as J=even tensors in spin space. The 35 dim. irrep does not contain a 5-dim. rep. (8,5) in spin space necessary for a rank J = 2 quadrupole moment operator. Therefore, first order SU(6) symmetry breaking one-quark operators cannot produce nonvanishing quadrupole moments.

50 SU(3) x SU(2) decomposition of 405-plet Decompose two-body SU(6) tensor 405 into SU(3) and SU(2) subtensors 405 = 1,1 + 8,1 + 27, ,3 + 10,3 + 10, ,3 + 1,5 + (8,5) + (27,5) scalar JJ = 0 vector JJ = 1 tensor JJ = 2 First entry: dimension of SU(3) flavor operator Second entry: dimension of SU(2) spin operator (2JJ + 1) Example: Charge multipole operator transforms as flavor 8 and as a spin tensor with rank J=even. The spin scalar (8,1) and spin tensor (8,5) are the only components of the SU(6) tensor 405 that contribute to the two-body charge density ρ [2].

51 SU(6) Wigner-Eckart Theorem [405] [405] OO = 56 ff ρρ 2 μμ 56ii = 56 ρρ 2 56 (SU(6) CG coefficient) reduced matrix element has the same value for the entire 56 multiplet provides relations between different components μμ of the 405 tensor and of different members of the 56 multiplet Explains the prefactors ( 2) for the spin scalar (charge radii) and ( 1) for the spin tensor (quadrupole moment) operators Explains why the matrix elements of the spin scalar and the spin tensor operators taken between the 56 dimensional representation are related. 3 [405] ρρ 2,(8,1) ~ BB ee ii σσ ii σσ jj ii jj 3 [405] ρρ 2,(8,5) ~ BB ee ii (3 σσ iiii σσ jjzz σσ ii σσ jj ) ii jj AJB, Proceedings of NSTAR 2009 Workshop, Chin. Phys. C 33, 1257 (2009)

52 What about higher multipole moments? Presently, very little is known about magnetic octupole moments of decuplet baryons and excited N* states 4. Baryon octupole moments Information needed to reveal structural details of spatial current distributions in baryons.

53 Magnetic octupole moment Ω The magnetic octupole moment Ω measures the deviation of the magnetic moment distribution from spherical symmetry. Ω > 0 magnetic moment density is prolate Ω: = 3 8 dd3 rr rr JJ rr zz 3zz2 rr 2 Ω < 0 magnetic moment density is oblate

54 SU(3) x SU(2) decomposition of the 2695-plet 2695 = (1, 7) + (1, 3) + (8, 7) + 2(8, 5) + 2(8, 3) + (8, 1) + 10, , , , 3 + (10, 1 + (10, 1) + 27, , , , 1 + (35, 5) + (35, 5) + (35, 3) + (35, 3) + (64, 7) + (64, 5) + (64, 3) + (64, 1). no one-quark and no two-quark octupole moment operator unique three-quark octupole moment operator 88, 77 3 Ω = CC ii jj kk ee ii 3 σσ iiii σσ jjjj σσ ii σσ jj σσ kk three-body op. OO 1 NN cc 2 A.J.B. and E.M. Henley, EPJA 35, 267 (2008)

55 Magnetic octupole moments Ω Baryon ΩΩ(rr = 11) ΩΩ(rr 11) 4CC 4CC CC 4CC ++ 8CC 8CC Σ 4CC 4CC(1 + r + r 2 )/3 Σ 0 0 2CC(1 + r 2r 2 )/3 Σ + 4CC 4CC(1 + 2r r 2 )/3 Ξ 4CC 4CC(r + r 2 + r 3 )/3 Ξ 0 0 2CC(2r r 2 r 3 )/3 Ω 4CC 4CCr 3 A.J.B. and E.M. Henley, EPJA 35, 267 (2008) rr = mm uu mm ss SU(3) breaking parameter

56 Magnetic octupole moment Ω in pion model Ω ππ = 16 ππ 5 rr ππ 2 YY 0 2 rr ππ ττ zz NN σσ zz NN + JJ zz = 3 Ω 2 ππ + JJ zz = 3 2 = 2 15 ββ 2 rr 2 ππ μμ NN = rr 2 nn μμ NN < 0 Ω + = fm 3 μμ NN = 1 nuclear magneton 2MM NN rr ππ distance between core and pion ββ nucleon core pion admixture Ω + < 0 magnetic moment distribution is oblate A.J.B. and E.M. Henley, EPJA 35, 267 (2008)

57 Determine constant C in pion model Ω + = 4CC = fm 3 CC = Ω Ω = 4CC rr 3 = fm³ Comparison with other models Ω( + ) = fm³ (Ramalho, Peña, Gross, PLB 678, 355 (2009)) Ω(Ω ) = fm³ (Aliev, Aziz, Savici, PLB 681, 240 (2009)) Models agree in sign but not in magnitude.

58 Magnetic octupole moment relations The 10 diagonal decuplet baryons are described by just one parameter C. There are 9 relations between them. 6 of these do not depend on the flavor-symmetry breaking parameter rr. Ω Δ + = Ω Δ Ω Δ 0 = 0 Ω Δ ++ = 2 Ω Δ Ω Σ + Ω Σ =2 Ω Σ 0 3 Ω Ξ Ω Σ = Ω Ω Ω Δ Ω Ξ Ω Ξ = Ω Σ Ω Σ + A.J.B. and E.M. Henley, Eur. Phys. J. A 35, 267 (2008)

59 5. Summary

60 Results obtained with E. M. Henley Three very different nucleon models agree concerning the sign of the intrinsic quadrupole moments QQ 00 of the proton and its first excited state + (1232). u u d p d u u + prolate (cigar-shaped) u oblate (pancake shaped) QQ 0 pp = rr nn2 > 0 QQ 0 + = rr nn2 < 0 rr nn 2 = fm 2 experimental neutron charge radius

61 Magnetic octupole moment Ω of the Δ Spectroscopic octupole moment of the + Ω + = fm 3 Intrinsic octupole moment of the proton and + Ω 0 pp = rr nn 2 μμ NN > 0 Ω 0 + = rr nn 2 μμ NN < 0 Ω 0 pp Ω 0 + > 0 proton magnetic moment distribution is prolate < 0 + magnetic moment distribution is oblate Best chance to get information on Ω is from exp. N N*(1680) M3 transition amplitude.

62 Implications for other observables The intrinsic deformation of the nucleon may be seen in other observables, e.g. spin structure of the nucleon AJB. and E. M. Henley, Spin of ground state baryons, Phys. Rev. D 83, (2011) AJB. and E. M. Henley, Three-quark currents and baryon spin, Eur. Phys. J. 55, 749 (2014) πnδ and πδ Δ couplings AJB and E. M. Henley, Pion-baryon couplings, Phys. Lett. B 484, 255 (2000) AJB and S. Moszkowski, Phys. Rev. C 87, (2013) atomic hydrogen spectroscopy AJB, Nucleon deformation and atomic spectroscopy, Can. J. Phys. 83, 455 (2005) AJB, Nonspherical proton shape and hydrogen hyperfine splitting, Can. J. Phys. 87, 773 (2009)

63 Prof. Ernest Henley was a man of the highest scientific and personal integrity, which was reflected in his humanity, empathy, and modesty.

64 What about higher multipole moments? Presently, very little is known about magnetic octupole moments of decuplet baryons and excited N* states Back up material Information needed to reveal structural details of spatial current distributions in baryons.

65 What about higher multipole moments? Presently, very little is known about magnetic octupole moments of decuplet baryons and excited N* states Form factor relations Information needed to reveal structural details of spatial current distributions in baryons.

66 N form factor relations pp GG + MMM QQ 2 = 2 GG nn MM QQ 2 μμ pp + = 2 μμ nn magnetic form factors Beg, Lee, Pais, 1964 pp GG + CCC QQ 2 = 3 2 QQ 2 GG CC nn QQ 2 QQ pp + = 1 2 rr nn 2 charge form factors AJB, Phys. Rev. Lett. 93 (2004)

67 Definition of C2/M1 ratio CCC MMM QQ2 : = qq MM NN 6 pp GG + CCC QQ 2 pp GG + MMM QQ 2 Insert form factor relations CCC MMM QQ2 = qq MM NN 2QQ 2 GG CC nn QQ 2 GG MM nn QQ 2 C2/M1 ratio expressed via neutron elastic form factors A. J. Buchmann, Phys. Rev. Lett. 93 (2004)

68 MAID 2007 analysis C2/M1(Q²)=S 1+ /M 1+ (Q²) MAID Buchmann 2004 MAID 2007 from: Drechsel, Kamalov, Tiator, EPJ A34 (2007) 69

69 MAID 2007 analysis MAID Buchmann 2004 MAID 2007 JLab data analysis MAID 2007 analysis of JLab data

70 What about higher multipole moments? Presently, very little is known about magnetic octupole moments of decuplet baryons and excited N* states Historical notes on the discovery of intrinsic quadrupole moments Information needed to reveal structural details of spatial current distributions in baryons.

71 Discovery of intrinsic quadrupole moments In 1934 Schüler and Schmidt found an anomously large isotope shift between the lines of 150 Sm and 152 Sm isotopes with nuclear spin I=0. intensity λ = 5321 Å 148 Sm 152 Sm 150 Sm 154 Sm ν [10-3 cm] shift between 150 Sm and 152 Sm is twice as large as between 152 Sm and 154 Sm cannot be explained by a mass or volume effect

72 Explanation by Brix and Kopfermann (1947) Idea The anomalously large isotope shift in Sm isotopes is connected with the big jump of spectroscopic quadrupole moments in Eu isotopes QQ( 151 Eu) = 150 fm 2 QQ( 153 Eu) = 320 fm 2 The huge quadrupole moments of 151 Eu and 153 Eu cannot be generated by the addition of a single proton. 151 Eu(I = 5 2) = 150 Sm I = 0 + p 153 Eu(I = 5 2) = 152 Sm I = 0 + p They must have been already present in the II = 00 nuclei 150 Sm and 152 Sm. Conclusion The 150 Sm and 152 Sm nuclei with nuclear spin II = 0 have the same intrinsic deformation as the 151 Eu and 153 Eu nuclei with spin II = 5/2. intrinsic quadrupole moment: QQ 0 (Eu) QQ 0 (Sm)

73 Effect of nuclear deformation on isostope shift δ E = IS 2π 3 Ze 2 Ψ e (0) 2 δ r 2 Ψ e (0) 2 = 1 π Z n a 0 3 Ψ e... electron wave function at r=0 a 0... Bohr radius 2 2 δ r = δ r + vol measured ~A 1/3 calculated 2 δ r def ~ δ Q 0 extracted rr 2 vvvvvv ~ AA 2/3 The Sm isotope shift is increased due to large change in nuclear deformation. The large δe IS between Sm isotopes is explained using δq 0 of Eu isotopes.

74 Effect of nonsphericity on nuclear charge radius measured charge radius ρ(r) r 0 b spherically symmetric deformed deformation contribution a volume contribution b r 0 a r deformed nucleus with I = 0 or 1/2 r 2 = dr r 2 ρ (r) Effect of deformation Larger charge radius but the same area (total charge).

75 What about higher multipole moments? Presently, very little is known about magnetic octupole moments of decuplet baryons and excited N* states N quadrupole moment in 11 NN CC Information needed to reveal structural details of spatial current distributions in baryons.

76 1/NN CC expansion of QCD processes NN CC... number of colors strong coupling αα SS QQ 2 = gg2 QQ 2 4ππ = 12ππ ~ 11 NN cc 2 NN ff ln QQ2 Λ 2 11 NN cc two-quark operator three-quark operator g ~ 1 g ~ 1 N C N C OO 1 NN cc 1 OO 1 NN cc 2

77 N quadrupole moment in 11 NN CC QQ pp + = BB NN CC 2 CC NN CC 2 rr nn 2 = BB NN CC 2 CC NN CC 2 NN CC + 5 (NN CC 1) 2 NN CC + 5 (NN CC + 3) NN CC including 3-body operators (C terms) QQ pp + = 1 2 rr nn 2 NN CC NN CC + 3 NN CC + 5 NN cc 1 1 for NN CC =3 and NN CC = indicative of a more general validity AJB, J. Hester, R. Lebed, PRD 66, (2002)