slide1 n.
Download
Skip this Video
Loading SlideShow in 5 Seconds..
Introduction The hypercentral Constituent Quark Model PowerPoint Presentation
Download Presentation
Introduction The hypercentral Constituent Quark Model

Loading in 2 Seconds...

play fullscreen
1 / 32

Introduction The hypercentral Constituent Quark Model - PowerPoint PPT Presentation


  • 92 Views
  • Uploaded on

Longitudinal and transverse helicity amplitudes of nucleon resonances in a constituent quark model - bare vs dressed resonance couplings. Introduction The hypercentral Constituent Quark Model Results for the longitudinal and transverse helicity amplitudes Bare vs dressed resonance couplings

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about 'Introduction The hypercentral Constituent Quark Model' - amber


An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
slide1
Longitudinal and transverse helicity amplitudes of nucleon resonances in a constituent quark model - bare vs dressed resonance couplings
  • Introduction
  • The hypercentral Constituent Quark Model
  • Results for the longitudinal and transverse helicity amplitudes
  • Bare vs dressed resonance couplings
  • How to introduce dressing
  • Conclusions

M. Giannini BRAG Meeting, Bonn 4 september 2007

slide2

Many models have been built and applied to the description of hadron properties:

Constituent Quark Models (CQM): quarks as effective

# Isgur-Karl, Capstick Isgur, Rome degrees of freedom

# algebric U(7)

# hypercentral

Goldstone Boson Exchange

# Instanton interaction

Skyrmion

Soliton models

Chiral models

Instanton models

# applied to spectrum

elastic ff

transition ff

a systematic approach is more

easily followed with CQMs

slide4

x =

 

hyperradius

slide5

Quark-antiquark lattice potential

G.S. Bali Phys. Rep. 343, 1 (2001)

V = - b/r + c r

hcqm electromagnetic properties
hCQM & Electromagnetic properties
  • Photocouplings
  • Helicity amplitudes (transition f.f.)
  • Elastic form factors of the nucleon
  • Structure functions

Fixed parameters predictions

helicity amplitudes
HELICITY AMPLITUDES

Definition

A1/2 = < N* Jz = 1/2 | HTem | N Jz = -1/2 > * §

A3/2 = < N* Jz = 3/2 | HTem | N Jz = 1/2 > * §

S1/2 = < N* Jz = 1/2 | HLem | N Jz = 1/2 > * 

N, N* nucleon and resonance as 3q states

HTemHlem model transition operator

 overall sign -> problem

§ results for the negative parity resonances: M. Aiello et al. J. Phys. G24, 753 (1998)

slide8

Photoproduction amplitude

π

N*

Theory:

states are defined up to a phase factor

N -> N ei N* -> N* ei

N

N

<N*|H|N>

<N*|H|N>

the overall sign is left unchanged

π

N*

Phenomenology:

Overall sign relative to Born amplitude

N

N

A1/2 A3/2 S1/2

In order to extract the helicity amplitudes the sign of the strong vertex is used

Need for : a definite way of extracting the photon vertex

a general consensus

slide10

D transverse helicity amplitudes (proton)

13

D13

D helicity amplitudes (neutron)

13

D longitudinal helicity amplitudes (proton)

D longitudinal helicity amplitudes (proton)

13

13

please note
please note
  • the calculated proton radius is about 0.5 fm

(value previously obtained by fitting the helicity amplitudes)

  • the medium Q2 behaviour is fairly well reproduced
  • there is lack of strength at low Q2 (outer region) in the e.m. transitions

specially for the A 3/2 amplitudes

  • emerging picture: quark core (0.5 fm) plus (meson or sea-quark) cloud

“On the other hand, the confinement radius of ≈ 0.5 fm, which is currently used in order to give

reasonable results for the photocouplings, is substantially lower than the proton charge radius

and this seems to indicate that other mechanisms, such as pair production and sea quark contributions

may be relevant.”

M. Aiello, M. Ferraris, M.M.G, M. Pizzo, E. Santopinto, Phys.Lett.B387, 215 (1996).

bare vs dressed quantities
Bare vs dressed quantities

QM calculations

  • the aim is the description of observablesnot a fit

(dressed quantities )

  • with success: spectrum, magnetic moments, …
  • the separation between bare and dressed quantities is meaningful within a definite theoretical approach
  • CQ have a mass, some dressing is implicitly taken into account

in fact CQs are effective degrees of freedom

  • something similar may occur in the spectrum

e.g. the consistent inclusion of quark loops effects in the meson description does not alter the form of the qqbar potential but renormalizes the string constant (Geiger-Isgur)

  • a consistent and systematic CQM approach may be helpful in order to put in evidence explicit dressing effects
slide21

Various approaches with mesons and baryons af effective degrees of freedom

Mainz-Dubna-Taiwan MAID -> 2007

Sato & Lee

………

e.g. MZ dynamical model

a systematic description (fit with free parameters) is obtained

with very good results

slide24
Explicit evaluation of the meson cloud contribution to the excitation of the nucleon resonances(Mainz Group and coworkers)
slide25

Explicit evaluation of the meson cloud contribution to

the excitation of the nucleon resonances(Mainz Group and coworkers)

=

+

~

R

B

~

t

v

R

R

t

t

how to introduce dressing
How to introduce dressing

hadronic approach: mesons and baryons (nucleon + resonances)

(equations for amplitudes, coupled channel calculations, lagrangians, …..

hybrid models

at the quark level

inclusion of higher Fock components in the baryon state

unquenching the quark model

Geiger-Isgur

Capstick, this meeting

Santopinto-Bijker, Nstar2007

conclusions
Conclusions
  • Phenomenological problems
    • Sign of helicity amplitudes
    • PDG values (often average of quite different sets)
    • Need for more data
  • A comparison of systematic CQM results and data
    • understanding where meson cloud or (better) q-qbar effects are important (transition and elastic ff, structure functions,…..)
    • a good basis for including consistently these effects provided by (h)CQM
conclusions cont
Conclusions (cont.)
  • Theoretical problems
    • Relativity (not important for helicity amplitudes)
    • Consistent inclusion of quark-antiquark pair creation effects
  • Consequences of the inclusion of quark-antiquark pair creation effects:
    • Shift of energy levels
    • Non zero width of resonances
    • Consistent evaluation of strong vertices
    • Direct calculation of scattering amplitudes
    • Direct calculation of scattering electroproduction
    • ……….
    • A substantial improvement in CQM calculations!