Electromagnetic N →  (1232) Transition

1. Electromagnetic N → (1232) Transition Shin Nan Yang Department of Physics National Taiwan University Pascalutsa, Vanderhaeghen, SNY, Physic.Reports 437 (2007) 125, hep-ph/0609004. Lattice QCD Journal Club, NTU, April 20, 2007

2. Motivation • low energies ─ChPT • high energies, high momentum transfer─ pQCD • medium energies ․LQCD ․Phenomenology : hadron models, reaction theory QCD Hadronic phenomena Δ(1232) physics

3. : 1st, most prominent and non-overlapping resonance Discovered by Fermi in 1952 inπp scatterings 1232 2

4. Properties of (1232) • M = 1232 MeV,  = 120 MeV • I(JP) = • Electromagnetic properties of the  ?

5. Electromagnetic properties of the D 1.mD, QD ….. of the D E.g., g + p →g + p0 + p p + p →g + p + p ( A2/TAPS) (A2/TAPS, MAMI) 1980’s

6. |GE2| << |GM1| GM1, GE2 photo- and electro-production of pion

7. Parity and angular momentum of multipole radiation • electric multipole of order (l,m), parity = (-1)l • magnetic multipole of order (l,m), parity = (-1)l+1 Allowed multipole orders are l = 1 and 2, with parity = +

8. S S S D (deformed) (S=1/2, L=2) J=3/2

9. helicity conserving

10. Jones-Scadron f.f’s

12. 2 m N →D ,Q N →D in the g* N →D transition E.g.,  + N → + N , e + N → e + N +  For electroproduction, Coulomb quadrupole transition C2 is allowed, in addition to magnetic dipole M1 and electric quadrupole E2 transitions. Q N →  =  Q,  > 0 1.13 >  > 0.4 (Dillon and Morpurgo)

14. * N → transition • In a symmetric SU(6) quark model the electromagnetic excitation of the  could proceed only via M1 transition. • If the  is deformed, then the photon can excite a nucleon into a  through electric E2 and Coulomb C2 quadrupole transitions. • At Q2 = 0, recent experiments give, Rem = E2/M1  -2.5 %, ( indication of a deformed  ) • pQCD predicts that, as Q2→∞ hadronic helicity conservation: A1/2 A3/2 scaling: A1/2 Q-3, A3/2 Q-5, S1+ Q-3 Rem = E1+(3/2)/M1+(3/2) → 1, Rsm = S1+(3/2)/M1+(3/2)→ const. What region of Q2 correspond to the transition from nonperturbative to pQCD descriptions?

15. Two aspects of the problem • Theoretical predictions • QCD-motivated models, e.g., constituent quark models, bag models, skyrmion • lattice QCD, large-Nc • Extraction from experiments • dispersion relation • dynamical model • effective field theory

16. SU(6) constituent quark model Both N and ∆ are members of the [56]-plet and the three quarks are in the (1s)3 states • In a symmetric SU(6) quark model the e.m. excitation of the  could proceed only via M1 transition • large-Nc QCD has an exact SU(6) spin-flavor symmetry • If the  is deformed, then the photon can excite a nucleon into a  through electric E2 and Coulomb C2 quardrupole transitions. • At Q2 =0, recent experiments give, • REM = E2/M1 ≈ -2.5 %, (MAMI, LEGS) • ( indication of a deformed  )

17. In constituent quark model, Tensor force Fermi contact term D-state component -0.8% < REM < -0.3% Too small !!

18. EMR：E2/M1 RATIO (Theory) SU（6）： 0.0 MIT bag model： 0.0 Large Nc : 0.0 Non. rel. quark model： -0.8% ~ -0.3% Relativized quark model： -0.1% Cloudy bag model -2.0 to -3.0% Chiral constituent quark model -1.0 to -4.0% Skyrme model： -2.5 to -6.0% PQCD： -100% LQCD pion cloud models

19. QCD: hadron helicity conservation at high Q2 and scaling

20. Lattice QCD Alexandrou et al , PR D 66, 094503 (2002)

22. Alexandrou et al., PR D 94, 021601 (2005)

23. Pascalutsa and Vanderhaeghen, PR D 73, 034003 (2006)

24. Extraction from experiments • dispersion relation (analyticity, crossing symmetry) • dynamical model (SL, DMT, DUO) • effective field theory (QCD symmetry, perturbative) SL: Sato-Lee DMT: Dubna-Mainz-Taipei DUO: dynamical Utrecht-Ohio

25. Dynamical model for * N → N Both on- & off-shell two ingredients v , t N

26. In resonant channel like (3,3), resonance  excitation plays an important role. If a bare  is assumed such that the transition potential v consists of two terms v (E)=vB + v(E), where vB = background transition potential v(E) =

27. DMT Model(Dubna-Mainz-Taipei)

28. N Model (Taipei-Argonne) Three-dimensional Bethe-Salpeterformulation with driving term, with pseudovector  NN coupling, given by

30. Chiral effective theory in the Δ-resonance region (D. Phillips, V. Pascalutsa, M. Vanderhaeghen) 1. Chiral relativistic Lagrangian of π, N, and Δ 2. The Lagrangian is organized in powers of electromagntic coupling e, plus the number of derivatives of pion and photon field 3. Power counting for the γπamplitude: δ-expansion scheme. 4. Dressed Δ propagator = (p-Δ-Σ)-1 .

31. Only electric eNN coupling contributes in NLO

32. MAID DMT

35. Photoproduction Threshold electromagnetic production • LET (Gauge Inv. + PCAC)： Electroproduction

36. HBChPT：a low energy effective field theory respecting the symmetries of QCD, in particular, chiral symmetry perturbative calculation － crossing symmetric DMT：Lippman-Schwinger type formulation with potential constructed from chiral effective lagrangian unitarity－ loops to all orders What are the predictions of DMT?

37. Cooper-Jennings reduction scheme

39. bare excitation K-matrix Pion cloud effects

40. full

41. Experimentally, it is only possible to extract the contribution of the following process, = + dressed vertex bare vertex

42. Comparison of our predictions for the helicity amplitudes, QN → and N → with experiments and Sato-Lee’s prediction. The numbers within the parenthesis in red correspond to the bare values. Q N→ =  Q > 0, 1.13 >  > 0.4 (Dillon and Morpurgo)  is oblate !!!

43. For electroproduction : Q2-dependent