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

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

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

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

 lectromagnetic properties of the  1.  , Q  ….. of the  E.g.,  + p →  +  0 + p  + p →  +  + p ( A2/TAPS)  1980’s (A2/TAPS, MAMI)

6 G M1, G E2 |G E2 | << |G M1 | 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

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12 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)

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 * 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 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?

15 Two aspects of the problem 1)Theoretical predictions QCD-motivated models, e.g., constituent quark models, bag models, skyrmion lattice QCD, large-N c 2)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 Q 2 =0, recent experiments give, REM = E2/M1 ≈ -2.5 %, (MAMI, LEGS) ( indication of a deformed  )

17 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%

18 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)

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

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

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

23 Pascalutsa and Vanderhaeghen, PR D 73, (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 Both on- & off-shell v , t  N two ingredients Dynamical model for  * N →  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-Salpeter formulation with driving term, with pseudovector  NN coupling, given by

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30 Chiral effective theory in the Δ-resonance region 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. (D. Phillips, V. Pascalutsa, M. Vanderhaeghen)

31 Only electric eNN coupling contributes in NLO

32 MAID DMT

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35 Threshold electromagnetic production Photoproduction HBChPT O ( )Dispersion relationExp. ( ) ±0.88± ±0.06±0.02 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

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39 Pion cloud effects bare excitation K-matrix

40 full

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

42 A 1/2 (10 -3 GeV -1/2 ) A 3/2 Q N →  (fm 2 ) N→ΔN→Δ 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. Q N→  =  Q   > 0, 1.13 >  > 0.4 (Dillon and Morpurgo)  is oblate !!!

43 For electroproduction : Q 2 -dependent

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51 Hadronic helicity conservation A 1/2 >> A 3/2 ? Not yet!

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

53 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.

54  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 SM | 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.  extension of dynamical model to higher energies.

55 The end

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) =. 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 pion cloud effects

57 Electromagnetic N →  (1232) Transition Shin Nan Yang Department of Physics National Taiwan University  Motivations  Model for  * N →  N  DMT (Dubna-Mainz-Taipei) dynamical model  Effective field theory  Results  Summary University of Maryland, College Park, MD, USA, March 12, 2007 Pascalutsa, Vanderhaeghen, SNY, Physic.Reports 437 (2007) 125, hep-ph/