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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 -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. 14

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

14. 17

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

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

17. 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

18. 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

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

20. 26

21. MAID DMT 27

22. 28

23. 29

24. 30

25. 31

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

27. For electroproduction : Q2-dependent 33

28. 34

29. 35

30. 36

31. 37

32. 38

33. 39

34. 40

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

36. 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

37. 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