Exciting Hadrons

Vladimir Pascalutsa

European Centre for Theoretical Studies in Nuclear Physics and Related Areas Trento, Italy Supported by

Presented @ NUPECC Meeting ( ECT*, Trento, Italy, Mar 16, 2007)

The quest for understanding the strong interaction (

Q C D

) continues The running coupling of QCD: For

asymptotic freedom

Perturbative QCD (using factorization theorems) For

non-perturbative phenomena:

color confinement, spontaneous chiral symmetry breaking, generation of the nucleon mass (mass gap), hadron spectrum (mesons, baryons, pentaquarks, glueballs), nucleon structure (FFs, GPDs, spin content) nuclear forces Lattice QCD (severely limited by comp. power) Chiral Effective-Field Theory of QCD (very limited in energy, matching to QCD is a”?”) Models: quark, bag, NJL, chiral-soliton, instanton, AdS/QCD,…

Selected topics

• Nucleon mass and the 1 st nucleon excitation: lattice QCD vs chiral EFT • Nucleon structure: electromagnetic form factors, generalized parton distributions (GPDs) • Hadron spectrum: statistical properties (“quantum chaos”, “missing resonances”)

N and Δ masses : pion-mass dependence

ChEFT

physical world

V.P. & Vanderhaeghen, PLB 636 (2006)

Lattice : MILC

Electromagnetic excitation of the nucleon

N  * Δ 3 e.m. transitions : M1, E2, C2 non-zero values for R EM R SM =C2/M1 =E2/M1 : measure of non and spherical distribution of charges

Prediction of the m q dependence of R EM =E2/M1 and R SM =C2/M1 Q 2 = 0.1 GeV 2 Nicosia – MIT group [ Alexandrou et al., PRL 94 (2005)] quenched lattice QCD results : m π = 0.37, 0.45, 0.51 GeV linear extrapolation in m q ~ m π 2 ChEFT prediction [V.P. & Vanderhaeghen, PRL 95 (2005); PRD 73 (2006)] data points : MAMI , MIT-Bates

Rosenbluth vs polarization transfer measurements of G

E

/G

M

of proton

SLAC Rosenbluth data Jlab/Hall A Polarization data Jones et al. (2000) Gayou et al. (2002)

Two methods

,

two different results

!

Two-photon exchange calculation : elastic contribution

world Rosenbluth data N Polarization Transfer

Nucleon Form Factors: charge/current distribution

• C. Perdrisat

et al

.

JLab (E01-109) • SHMS in JLab / Hall C at 11 GeV curves : parameterizations

Generalized Parton Distributions (GPDs)

3-dim quark structure of nucleon

Elastic Scattering

transverse quark distribution in Coordinate space

DIS

longitudinal quark distribution in momentum space

GPDs

Fully-correlated quark distribution in both coordinate and momentum space

Hadron spectrum below 2.5 GeV (PDG 2002)

Quark models yield many more states, problem of “Missing Resonances” Search for this states motivated CEBAF (now Jefferson Lab) What about the statistical properties?

Nearest-neighbor spacing distribution of quantum billiard (circular vs hart-shaped)

Wave-function (quantum chaos)

Quantum chaos in hadrons

V.P., EPJA 16 (2003) C. Fernandez-Ramirez , A. Relano , PRL 98 (2007). Statistical analysis of baryon spectra in various quark models shows no correlation (failure of QMs), “missing resonances” will be missed!

Outlook

Hadrons are exciting and will be exciting for years to come, at LHC (CERN) DESY (Hamburg) GSI (Darmstadt) RHIC (Brookheaven) Jefferson Lab (Virginia) MAMI (Mainz) ELSA (Bonn) HIGS (Duke) …