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Electromagnetic N →  (1232) Transition

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  1. Electromagnetic N → (1232) Transition • Motivations • Model for * N →  N DMT (Dubna-Mainz-Taipei) dynamical model • Results • Summary Shin Nan Yang Department of Physic, National Taiwan University Pascalutsa, Vanderhaeghen, SNY, hep-ph/0609004, Phys. Report “NEW TRENDS IN HEP”, Yalta, Crimea, Ukraine, September 16-23, 2006 1

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

  3. Properties of (1232) • M = 1232 MeV,  = 120 MeV • I(JP) = • Electromagnetic properties of the  ? 3

  4. Electromagnetic properties of the D 1mD, QD ….. of the D E.g., g + p →g + p0 + p p + p →g + p + p ( A2/TAPS) 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) 4

  5. * 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 quardrupole 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? 5

  6. 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 = + 6

  7. S S S D (deformed) (S=1/2, L=2) J=3/2 7

  8. Two aspects of the problem • Theoretical predictions • QCD-motivated models, e.g., constituent quark models, bag models, skyrmion • lattice QCD • Extraction from experiments • dispersion relation • dynamical model • effective field theory 8

  9. 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 • 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 %, • ( indication of a deformed  ) 9

  10. In constituent quark model, Tensor force Fermi contact term D-state component -0.8% < REM < -0.3% Too small !! 10

  11. 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 11

  12. Jones-Scadron f.f’s 12

  13. helicity conserving 13

  14. 14

  15. QCD: hadron helicity conservation at high Q2 and scaling 15

  16. Lattice QCD Alexandrou et al , PR D 66, 094503 (2002) 16

  17. 17

  18. Alexandrou et al., PR D 94, 021601 (2005) 18

  19. Pascalutsa and Vanderhaeghen, PR D 73, 034003 (2006) 19

  20. Extraction from experiments • dispersion relation (analyticity, crossing symmetry) • dynamical model (SL, DMT, DUO) • effective field theory (QCD symmetry, perturbative) 20

  21. Dynamical model for * N → N To order e, the t-matrix for * N → N is written as t(E) = v+ vg0(E) t N (E), where, v= transition potential, two ingredients t N (E) =  N t-matrix, g0 (E) = . Multipole decomposition of (1) gives the physical amplitude in channel =( , l , j) where (), R() :  N scattering phase shift and reaction matrix in channel  k=|k|, qE : photon and pion on-shell momentum v , t N pion cloud effects 21

  22. Both on- & off-shell 22

  23. 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) = 23

  24. DMT Model(Dubna-Mainz-Taipei) 24

  25. N Model (Taipei-Argonne) Three-dimensional Bethe-Salpeterformulation with driving term, with pseudovector  NN coupling, given by 25

  26. 26

  27. MAID DMT 27

  28. 28

  29. 29

  30. 30

  31. 31

  32. ….. .…….. tBγπK-matrix approx. _ _ _ _ tBγπ full 32

  33. For electroproduction : Q2-dependent 33

  34. 34

  35. 35

  36. 36

  37. 37

  38. 38

  39. 39

  40. 40

  41. Hadronic helicity conservation A1/2 >> A3/2? 41

  42. scaling: A1/2 ~ Q-3 A3/2 ~ Q-5 S1+ ~ Q-3 42

  43. Summary • Abundant precision data are now available from Bates (MIT), MAMI (Mainz), and Jlab on e.m. production of pion for Q2 ranging from 0.0 to 6.0 (GeV/c)2. • Existing data give clear indication of a deformed Δ. • DMT dynamical model describes well the existing data on pion photo- and electroproduction data from threshold up to 1 GeV photon lab. energy. it predicts N → = 3.516 N , QN → = -0.081 fm2 , and REM = -2.4%, all in close agreement with experiments.   is oblate bare  is almost spherical. The oblate deformation of the  arises almost exclusively from the pion cloud. 43

  44. Existing data between Q2 = 0-6 (GeV/c)2 indicate • hadronic helicity conservation and scaling are still not yet observed in this region of Q2 . • REM still remains negative. • | REM | strongly increases with Q2. • Impressive progress have been made in the lattice QCD calculation for N → Δ e.m. transition form factors • More data at higher Q2will be available from Jlab upgrade • Other developments: N →Δ generalized parton distributions (GPDs),two-photon exchange effects,chiraleffective field theory approach. . 44