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

1232  1st, most prominent and non-overlapping resonance 2 Discovered by Fermi in 1952 in πp scatterings

Properties of  M  = 1232 MeV,   = 120 MeV I(J P ) = Electromagnetic properties of the  ? 3

 lectromagnetic properties of the  1  , 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) 4

 * 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 → ∞ hadronic helicity conservation: A 1/2  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? 5

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

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

Two aspects of the problem 1)Theoretical predictions QCD-motivated models, e.g., constituent quark models, bag models, skyrmion lattice QCD 2)Extraction from experiments dispersion relation dynamical model effective field theory 8

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 Q 2 =0, recent experiments give, REM = E2/M1 ≈ -2.5 %, ( indication of a deformed  ) 9

In constituent quark model, Fermi contact term Tensor force D-state component P D (%) Q(fm 2 ) N(938)  Too small !! -0.8% < REM < -0.3% 10

SU （ 6 ）： 0.0 MIT bag model ： 0.0 Large N c : 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 EMR ： E2/M1 RATIO (Theory) 11

Jones-Scadron f.f’s 12

13 helicity conserving

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QCD: hadron helicity conservation at high Q 2 and scaling 15

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

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

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

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

To order e, the t-matrix for  * N →  N is written as t  (E) = v  + v  g 0 (E) t  N (E), where, v  = transition potential, two ingredients t  N (E) =  N t-matrix, g 0 (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|, q E : photon and pion on-shell momentum Dynamical model for  * N →  N v , t  N 21 pion cloud effects

Both on- & off-shell 22

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

DMT Model (Dubna-Mainz-Taipei) 24

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

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MAID DMT 27

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…...…….. t B γπ K-matrix approx. _ _ _ _ t B γπ full 32

For electroproduction : Q 2 -dependent 33

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Hadronic helicity conservation A 1/2 >> A 3/2 ? 41

scaling: A 1/2 ~ Q -3 A 3/2 ~ Q -5 S 1+ ~ Q -3 42

Summary  Abundant precision data are now available from Bates (MIT), MAMI (Mainz), and Jlab on e.m. production of pion for Q 2 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 →  =  N, Q N →  = fm 2, and R EM = -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

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