Electromagnetic N 1232 Transition Shin Nan Yang Department

Electromagnetic N → (1232) Transition Shin Nan Yang Department of Physics National Taiwan University Pascalutsa, Vanderhaeghen, SNY, Physic. Reports 437 (2007) 125, hep-ph/0609004. Lattice QCD Journal Club, NTU, April 20, 2007 1

Motivation QCD Hadronic phenomena l low energies ─ Ch. PT l high energies, high momentum transfer─ p. QCD l medium energies ․LQCD ․Phenomenology : hadron models, reaction theory Δ(1232) physics 2

: 1 st, most prominent and non-overlapping resonance Discovered by Fermi in 1952 in πp scatterings 1232 3 2

Properties of (1232) l M = 1232 Me. V, = 120 Me. V l I(JP) = l Electromagnetic properties of the ? 4

Electromagnetic properties of the 1. , Q …. . of the E. g. , + p → + 0 + p +p → + +p ( A 2/TAPS) (A 2/TAPS, MAMI) 1980’s 5

|GE 2| << |GM 1| GM 1, GE 2 photo- and electro -production of pion 6

Parity and angular momentum of multipole radiation l electric multipole of order (l, m), parity = (-1)l l magnetic multipole of order (l, m), parity = (-1)l+1 Allowed multipole orders are l = 1 and 2, with parity = + 7

S S S D (deformed) (S=1/2, L=2) J=3/2 8

helicity conserving 9

Jones-Scadron f. f’s 10

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2 N → , Q N → in the * N → transition E. g. , + N → + N , e+N →e+N+ For electroproduction, Coulomb quadrupole transition C 2 is allowed, in addition to magnetic dipole M 1 and electric quadrupole E 2 transitions. QN → = Q , > 0 1. 13 > > 0. 4 (Dillon and Morpurgo) 12

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* N → transition l In a symmetric SU(6) quark model the electromagnetic excitation of the could proceed only via M 1 transition. l If the is deformed, then the photon can excite a nucleon into a through electric E 2 and Coulomb C 2 quadrupole transitions. l At Q 2 = 0, recent experiments give, Rem = E 2/M 1 -2. 5 %, ( indication of a deformed ) l p. QCD 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 Rem = E 1+(3/2)/M 1+(3/2) → 1, Rsm = S 1+(3/2)/M 1+(3/2) → const. What region of Q 2 correspond to the transition from nonperturbative to p. QCD descriptions? 14

Two aspects of the problem 1) Theoretical predictions ü QCD-motivated models, e. g. , constituent quark models, bag models, skyrmion ü lattice QCD, large-Nc 2) Extraction from experiments ü dispersion relation ü dynamical model ü effective field theory 15

SU(6) constituent quark model Both N and ∆ are members of the [56]-plet and the three quarks are in the (1 s)3 states p In a symmetric SU(6) quark model the e. m. excitation of the could proceed only via M 1 transition large-Nc QCD has an exact SU(6) spin-flavor symmetry p If the is deformed, then the photon can excite a nucleon into a through electric E 2 and Coulomb C 2 quardrupole transitions. p At Q 2 =0, recent experiments give, REM = E 2/M 1 ≈ -2. 5 %, (MAMI, LEGS) ( indication of a deformed ) 16

In constituent quark model, Tensor force Fermi contact term D-state component PD(%) N(938) 0. 4 (1232) 1. 9 Q(fm 2) 0 -0. 089 -0. 8% < REM < -0. 3% Too small !! 17

EMR：E 2/M 1 RATIO (Theory) SU（6）： MIT bag model： Large Nc : Non. rel. quark model： Relativized quark model： Cloudy bag model Chiral constituent quark model Skyrme model： PQCD： LQCD 0. 0 -0. 8% ~ -0. 3% -0. 1% -2. 0 to -3. 0% -1. 0 to -4. 0% -2. 5 to -6. 0% pion cloud models -100% 18

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

Lattice QCD Alexandrou et al , PR D 66, 094503 (2002) 20

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Alexandrou et al. , PR D 94, 021601 (2005) 22

Pascalutsa and Vanderhaeghen, PR D 73, 034003 (2006) 23

Extraction from experiments Ø dispersion relation (analyticity, crossing symmetry) Ø dynamical model (SL, DMT, DUO) Ø effective field theory (QCD symmetry, perturbative) SL: Sato-Lee DMT: Dubna-Mainz-Taipei DUO: dynamical Utrecht-Ohio 24

Dynamical model for * N → N Both on- & off-shell two ingredients v , t N 25

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) = 26

DMT Model (Dubna-Mainz-Taipei) 27

N Model (Taipei-Argonne) Three-dimensional Bethe-Salpeter formulation with driving term, with pseudovector NN coupling, given by 28

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

Only electric e. NN coupling contributes in NLO 31

MAID DMT 32

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Threshold electromagnetic production Photoproduction HBCh. PT O ( ) Dispersion relation Exp. ( ) -1. 1 -1. 22 -1. 33± 0. 88± 0. 03 -0. 43 -0. 56 -0. 45± 0. 06± 0. 02 • LET (Gauge Inv. + PCAC)： Electroproduction 35

HBCh. PT：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? 36

Cooper-Jennings reduction scheme 37

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bare excitation K-matrix Pion cloud effects 39

full 40

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

A 1/2 (10 -3 Ge. V-1/2) A 3/2 QN → (fm 2) N→Δ PDG -135 -255 -0. 072 3. 512 LEGS -135 -267 -0. 108 3. 642 MAINZ -131 -251 -0. 0846 3. 46 DMT -134 (-80) -256 (-136) -0. 081 (0. 009) 3. 516 (1. 922) SL -121 (-90) -226 (-155) -0. 051 (0. 001) 3. 132 (2. 188) Comparison of our predictions for the helicity amplitudes, QN → 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 !!! 42

For electroproduction : Q 2 -dependent 43

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

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

Summary Ø 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 (Ge. V/c)2. Ø Existing data give clear indication of a deformed Δ. Ø DMT dynamical model describes well the existing data on pion photo- and electroproduction data from threshold up to 1 Ge. V photon lab. energy. it predicts N → = 3. 516 N , QN → = -0. 081 fm 2 , 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. 53

Ø Existing data between Q 2 = 0 -6 (Ge. V/c)2 indicate l hadronic helicity conservation and scaling are still not yet observed in this region of Q 2. REM still remains negative. l | RSM | strongly increases with Q 2. l Ø Impressive progress have been made in the lattice QCD calculation for N → Δ e. m. transition form factors Ø More data at higher Q 2 will be available from Jlab upgrade Ø Other developments: N →Δ generalized parton distributions (GPDs), two-photon exchange effects, chiral effective field theory approach. Ø extension of dynamical model to higher energies 54

The end 55

Dynamical model for * N → N To order e, the t-matrix for * N → N is written as where, t (E) = v + v g 0(E) t N (E), v = transition potential, (1) two ingredients t N (E) = N t-matrix, g 0 (E) = . v , t N Multipole decomposition of (1) gives the physical amplitude in channel =( , l , j) pion cloud effects where ( ), R( ) : N scattering phase shift and reaction matrix in channel k=| k|, q. E : photon and pion on-shell momentum 56

Electromagnetic N → (1232) Transition Shin Nan Yang Department of Physics National Taiwan University Ø Motivations Ø Model for * N → N DMT (Dubna-Mainz-Taipei) dynamical model Effective field theory Ø Results Ø Summary Pascalutsa, Vanderhaeghen, SNY, Physic. Reports 437 (2007) 125, hep-ph/0609004. University of Maryland, College Park, MD, USA, March 12, 2007 57