Nucleon Transition Formfactors with MAIDNucleon Transition Formfactors with MAID

from Low to High Q²from Low to High Q²

Lothar Tiator

Johannes Gutenberg Universität Mainz

Nucleon Resonance Structure in Exclusive Electroproduction at High Photon Virtualities

EmNN*2012, University of South Carolina, Columbia, SC, 2012

CRC 1044

2 very recent review articles on this subject:2 very recent review articles on this subject:

Electromagnetic excitation of nucleon resonancesLT, Dieter Drechsel, Sabit Kamalov and Marc Vanderhaeghen

European Journal Special Topics 198, 141-170 (2011)

Electroexcitation of nucleon resonancesInna Aznauryan and Volker Burkert

Progress in Particle and Nuclear Physics 67, 1-54 (2012)

theoretical poles and experimental bumpstheoretical poles and experimental bumps

poles in the

complex plane

bumps on the

physical axis

WW

WW

and and resonances with overall resonances with overall 33 andand 4 4 starsstarsbelow 2 GeV below 2 GeV (new, PDG2012)(new, PDG2012)

<- new in PDG2012<- upgraded from **

no pole

weakweak

weak

weak

1

2

3

8

97

4

5

6

weak

very strong

strong

strong

1

4

2

3

5

8

6

7 9

nucleon responsenucleon response

to real and virtual photonsto real and virtual photons

Inclusive Cross Section for Real and Virtual Photo AbsorptionInclusive Cross Section for Real and Virtual Photo AbsorptionInclusive Cross Section for Real and Virtual Photo AbsorptionInclusive Cross Section for Real and Virtual Photo Absorption

Inelastic Electron Scattering in the Resonance Region Inelastic Electron Scattering in the Resonance Region Inelastic Electron Scattering in the Resonance Region Inelastic Electron Scattering in the Resonance Region

in general:in general:

transition form factors can only be obtained bytransition form factors can only be obtained by

• partial wave analysis, e.g. MAID, JLabseparate S11, P11, P33, D13, F15, etc from angular distributions

• and background / resonance separationseparate bg and res parts in each partial wave

Form Factors in the Electroproduction ProcessForm Factors in the Electroproduction ProcessForm Factors in the Electroproduction ProcessForm Factors in the Electroproduction Process

Form Factors in MAID2007Form Factors in MAID2007Form Factors in MAID2007Form Factors in MAID2007

MM AA II DD

s-channel resonance contributionss-channel resonance contributionss-channel resonance contributionss-channel resonance contributions

unitarity is build in through coupling to other open channels:

e.g.

for S11(1535)

background - Ibackground - I

background - IIbackground - II

background - IIIbackground - III

other background contributions, not included in MAID:

- loop contributions from pion rescattering

- loop contributions from channel coupling with

- u-channel resonance contributions

- t-channel Regge contributions (more important for high W than high Q²)

background from unitarization (in K-matrix approximation):

(Born + Vec)(1 + i tN) = Born+Vec + i BV tN

data base for pion electroproductiondata base for pion electroproductiondata base for pion electroproductiondata base for pion electroproduction

(from Mainz, Bonn, Bates and JLab, mostly from CLAS)(from Mainz, Bonn, Bates and JLab, mostly from CLAS)

definition of the NN* transition form factors definition of the NN* transition form factors definition of the NN* transition form factors definition of the NN* transition form factors

helicity amplitudes:helicity amplitudes:

Sachs form factors:Sachs form factors:

covariant form factors:covariant form factors:

for spin ½ resonances as Roper P11 or S11 we get only 2 ff

helicity amplitudes and form factors helicity amplitudes and form factors helicity amplitudes and form factors helicity amplitudes and form factors

N to Delta (1232) transition form factorsN to Delta (1232) transition form factorsN to Delta (1232) transition form factorsN to Delta (1232) transition form factors

MAID analysis

JLab analysis

one of few cases with disagreement

between Mainz and JLab analysis

MAID

Sato-Lee

N to Delta (1232) transition form factorsN to Delta (1232) transition form factorsN to Delta (1232) transition form factorsN to Delta (1232) transition form factors

MAID analysis

JLab analysis

MAID analysis revisited

for narrow energy range ~ 1232 MeV

one of few cases with disagreement

between Mainz and JLab analysis

MAID

Sato-Lee

perturbative QCDperturbative QCDperturbative QCDperturbative QCD

helicity asymmetry and pQCD limithelicity asymmetry and pQCD limithelicity asymmetry and pQCD limithelicity asymmetry and pQCD limit

P33 (hard) spin-flavor excitation, pQCD may show up at much larger Q²

D13, F15 (soft) orbital excitation in the quark model

D15, P13 behave differently (A3/2 dominates at Q²~ 3 GeV²)

empirical parametrizationsempirical parametrizationsempirical parametrizationsempirical parametrizations

the magnetic N form factors has a very simple form

for all other resonances we use the general form:

numerical examples for a few resonances:

(complete results are found in our Review EPJ ST 198 (2011) 141)

Q²max

10 GeV²

5 GeV² 5 5 5 5 5 5 ? 4 ? 4 4 4

empirical parametrizations for large Q²empirical parametrizations for large Q²empirical parametrizations for large Q²empirical parametrizations for large Q²

the Maid parametrization with Gaussian forms for large Q²

is convenient and leads to fewer terms

However, it violates pQCD, which predicts:

A1/2(Q²) ~ 1/Q3

A3/2(Q²) ~ 1/Q5

S1/2(Q²) ~ 1/Q3

new ansatz:

transition FFs for N -> N*(1440)transition FFs for N -> N*(1440) and N -> N*(1535) excitationand N -> N*(1535) excitation

from MAID and JLab analysisfrom MAID and JLab analysis

transition FFs for N -> N*(1440)transition FFs for N -> N*(1440) and N -> N*(1535) excitationand N -> N*(1535) excitation

from MAID and JLab analysisfrom MAID and JLab analysis

transition FFs for N -> N*(1520)transition FFs for N -> N*(1520) and N -> N*(1680) excitationand N -> N*(1680) excitationtransition FFs for N -> N*(1520)transition FFs for N -> N*(1520) and N -> N*(1680) excitationand N -> N*(1680) excitation

data : practically allunderlying cross

sectionsthat went into the fitsare from CLAS

MAIDMAIDJLab

analysis :

new JLab Mokeev et al.

spatial distribution of charge and magnetizationspatial distribution of charge and magnetizationspatial distribution of charge and magnetizationspatial distribution of charge and magnetization

spherical charge densities in a 3-dim sphere:

transverse charge densities on a 2-dim disc:

traditional way for nuclei A>>1 with ff in the Breit frame

F(Q2) = GE(Q2), GM(Q2) : Sachs ff

more correct way for light systems with ff in the infinite momentum frame

F(Q2) = F1(Q2), F2(Q2) : Dirac/Pauli ff

r

by

bx

transverse transition densitiestransverse transition densities for thefor the Nucleon Nucleon andand N -> Roper N -> Roper excitationexcitation

transverse transition densitiestransverse transition densities for thefor the Nucleon Nucleon andand N -> Roper N -> Roper excitationexcitation

transition form factors on the latticetransition form factors on the latticetransition form factors on the latticetransition form factors on the lattice

Constantia Alexandrou et al., 2008 Huey-Wen Lin et al., 2008

N-Roper quenched with mp=720 MeV

N-Roper quenched with mp=720 MeVN-Delta

unquenched with mp=360 MeV

N-Delta unquenched with mp=360 MeV

F2

F1

GM

pion cloud problem at small Q²pion cloud problem at small Q²

N -> DeltaN -> Delta N -> RoperN -> Roper

lattice update 2011/12lattice update 2011/12lattice update 2011/12lattice update 2011/12

Constantia Alexandrou et al., 2011

Huey-Wen Lin et al., 2011N -> DeltaN -> Delta

N -> RoperN -> Roper

preliminary result 2012with large error

Summary Summary Summary Summary

with the unitary isobar model we have analyzed and

electroproduction data in the range 0 < Q² < 5 GeV²(in the range up to 8 GeV²)

for most 4* resonances we have obtained single-Q² amplitudes A1/2, A3/2, S1/2

and Q²-dependent transition form factors

this kind of analysis should also work up to Q² = 10 GeV²at least for helicity 1/2 : A1/2(Q²) and S1/2(Q²)

A3/2N(Q²) is perhaps the only 3/2 transition form factor

surviving at Q² = 10 GeV²

transition FFs for N -> N*(1675)transition FFs for N -> N*(1675) and N -> N*(1720) excitationand N -> N*(1720) excitationtransition FFs for N -> N*(1675)transition FFs for N -> N*(1675) and N -> N*(1720) excitationand N -> N*(1720) excitation