Dynamical study of N-  transition with N(e,e'  ) Shin Nan Yang Department of Physics National Taiwan University Collaborators: G.Y. Chen, J.C. Chen (NTU) S.S. Kamalov (Dubna) D. Drechsel, L. Tiator (Mainz)  Motivations  Model for  * N !  N ² DMT (Dubna-Mainz-Taipei) dynamical model  Results  Summary International Conference on QCD and Hadronic Physics, Beijing, June 16-20, 2005

 lectromagnetic properties of the  ²  , Q  ….. of the  E.g.,  + p !  +  0 + p  + p !  +  + p ( A2/TAPS) ²  N ! ,  Q N !  in the  * N !  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 ,  > >  > 0.4 (Dillon and Morpurgo)

 * 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 Q 2 =0, recent experiments give, R EM = E2/M1 ' -2.5 %, ( indication of a deformed  pQCD predicts that, as Q 2 ! 1 ¦ hadronic helicity conservation: A 1/2 À A 3/2 ¦ scaling: A 1/2 » Q -3, A 3 /2 » Q -5, S 1 + » Q -3 ) R EM = E 1+ (3/2) /M 1+ (3/2) ! 1, R SM = S 1+ (3/2) /M 1+ (3/2) ! const. What region of Q 2 correspond to the transition from nonperturbative to pQCD descriptions?

Two aspects of the problem 1)Theoretical prediction lattice QCD QCD-motivated models, e.g., constituent quark models, bag models, skyrmion 2)Extraction from experiments dispersion relation effective Lagrangian approach dynamical model

To order e, the t-matrix for  * N !  N is written as t  (E) = v  + v  g 0 (E) t  N (E), (1) where, v  = transition potential, two ingredients t  N (E) =  N t-matrix, g 0 (E) =. v  and t  N 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|, q E : photon and pion on-shell momentum Dynamical model for  * N !  N v , t  N

Both on- & off-shell

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) = then we obtain t  = t  B + t   with t  B (E) = v  B + v  B g 0 (E) t  N (E) t   (E) = v   + v   g 0 (E) t  N (E) t  = e i  33 |t  | t  B (E) = e i  33 |t  B (E)| t   (E) = e i  33 |t   (E)| Fermi-Watson theorem

Gauge invariance is maintained by the following substitution where is the electromagnetic current corresponding to the background contribution v B   With R  N (q E, q’;E) obtained from a meson-exchange model

In resonant channels, the total multipole amplitude is the sum of the background and resonant contributions A  (W,Q 2 ) = A B  (W,Q 2 ) + A R  (W,Q 2 ). If a bare resonance like is assumed in the dynamical model, A R  (W,Q 2 ) is given by A R  (W,Q 2 ) =, where f  N  = f 0  N  + f 0  N  g 0 t B  N = dressed  N !  vertex, f 0  N  = bare  N  vertex

DMT Model

 N Model Three-dimensional Bethe-Salpeter formulation with driving term, with pseudovector  NN coupling, given by

MAID DMT

In DMT, we approximate the resonance contribution A R  (W,Q 2 ) by the following Breit-Winger form with f  R = Breit-Winger factor describing the decay of the resonance R  R (W) = total width M R = physical mass  ( W) = to adjust the phase of the total multipole to be equal to the corresponding  N phase shift  (  ). Note that

A 1/2 (10 -3 GeV -1/2 ) A 3/2 Q N !  (fm 2 ) N ! N !  PDG LEGS MAINZ DMT -134 (-80) -256 (-136) (0.009) (1.922) SL -121 (-90) -226 (-155) (0.001) (2.188) Comparison of our predictions for the helicity amplitudes, Q N ! , and  N !  with experiments and Sato-Lee’s prediction. The numbers within the parenthesis in red correspond to the bare values.

 For electric (  =E) and Coulomb (  = S) multipoles, with X   (0) = 1.  X E and X S : to be determined by the experiments. X    1  violation of the scaling law  For N * (1440) resonance: two parameters X P11 M and X P11 S No Scaling (electroproduction)

Parameters determined from global fit to: Recent Jlab differential cross section data on p(e, e’  0 )p in 1.1 < W < 1.4 GeV 751 points at Q 2 = points at Q 2 = 4.0 (GeV/c) 2 Violation of the scaling assumption: X  E (MAID00) = 1 - Q 2 /3.7 X  E (DM) = 1 + Q 4 /2.4 X  S (MAID00) = 1 + Q 6 /61 X  S (DM) = 1 - Q 2 /0.1

Hadronic helicity conservation A 1/2 >> A 3/2 ??

scaling: A 1/2 ~ Q -3 A 3/2 ~ Q -5 S 1/2 ~ Q -3

Summary  DMT dynamical model describes well the existing data on pion photo- and electroproduction data from threshold up to 1 GeV photon lab. energy.  The DMT model predicts  N !  =  N, Q N !  = fm 2, and R EM = -2.4%, all in close agreement with experiments.  dressed  is oblate  The bare  is almost spherical. The oblate deformation of the dressed  arises almost exclusively from the pion cloud.

 The recent Jlab data for the electroproduction of the  (1232) resonance via p(e,e’p)  0 have been re-analyzed with DMT model. In contrast to previous finding, we find At Q 2 = 4.0 (GeV/c) 2, A  3/2 is still as large as A  1/2, implying that hadronic helicity conservation is still not yet observed in this region of Q 2. R EM, starting from a small and negative values at the real photon point, actually exhibits a clear tendency to cross zero and change sign as Q 2 increases. | R EM | is strongly increases with Q 2. S  1/2 and A  1/2, but not A  3/2, start exhibiting scaling behavior at about Q 2 ≥ 2.5(GeV) 2. It appears likely that the onset of scaling behavior might take place at a lower momentum transfer than that of hadron helicity conservation.

The End

 Model dependence of v  and t  N should be further studied v B  : PV or PV + PS ? form factors, gauge invariance consistency between  N and   coupling constants, e.g,   = 6.5 (DMT), 2.2 (SL) off-shell behaviors of v  and t  N

Hadronic helicity conservation A 1/2 >> A 3/2

Model dependence in v , t  N