The N to Delta transition form factors from Lattice QCD Antonios Tsapalis University of Athens, IASA EINN05, Milos,

outline Nucleon Deformation & N-  transition form factors LATTICE QCD: Hadronic states and transitions between them Limitations Calculation of the N-  transition matrix element Results: Quenched QCD Dynamical Quarks included Outlook

Spectroscopic quadrupole moment vanishes Intrinsic quadrupole moment w.r.t. body-fixed frame exists prolate oblate modelling required ! Nucleon Deformation

u d u ud u γ * Μ1, Ε2, C2 Μ 1+, Ε 1+, S 1+ π o p(qqq) I = J = 938 MeV Δ(qqq) I = J = 1232 MeV Spherical  M1 Deformed  M1, E2, C2 Deformation signal

EMR & CMR Experimental Status Thanks to N. Sparveris (Athens, IASA) uncertainties in modelling final state interactions

Lattice QCD Rotate to Euclidean time: t  - i  Discretize space-time X (   Fermions on sites Gauge fields on links

Wilson-Dirac operator D W Plaquette gauge action Wilson formulation (1974) a

Generate an ensemble of gauge fields {U} distributed with the Boltzmann weight Calculate any n-point function of QCD

Limitations finite lattice spacing a ~ 0.1 fm (momentum cutoff ~  /a) finite lattice volume La ~ 2-3 fm finite ensemble of gauge fields U det(D W ) very expensive to include set det(DW) = 1 quenched approximation ignore quark loops D W breaks chiral symmetry heavy quarks ; m  > 400 MeV Overlap or Domain-Wall maintain chiral symmetry but very CPU expensive

The Transition Matrix Element magnetic dipole electric quadrupole scalar quadrupole static  frame H.F.Jones and M.C.Scadron, Ann. Phys. (N.Y.) 81,1 (1973)

Hadrons and transitions in Lattice QCD generate a baryon at t=0 annihilate the baryon at time t measure the 2-pt function extract the energy from the exponential decay of the state in Euclidean time B(x) B(0) u u d

 N x  generate a nucleon at t=0 inject a photon with momentum q at t=t 1 annihilate a Delta at time t=t 2 measure the 3-pt function extract the form factors from suitable ratios of 3-pt and 2-pt functions

Quenched Results 32 3 x 64 lattice β = gauge fields Wilson quarks La = 3.2 fm C. Alexandrou, Ph. de Forcrand, H. Neff, J. Negele, W. Schroers and A. Tsapalis PRL, 94, (2005)

EMR (%) CMR (%)

V. Pascalutsa & M. Vanderhaeghen, hep-ph/ NLO results at Q 2 = 0.1 GeV 2 In Chiral Effective Field Theory  expansion scheme is small  ~ 1 GeV Non-analyticities in m  reconcile the heavy quark lattice results with experiment fit low energy constants

Full QCD Hybrid scheme valence quarks ‘domain wall’ quarks sea quarks 2 light + 1 heavy flavour action with small discretization error 20 3 x x x V m  (GeV) a=0.125 fm } C. Alexandrou, R. Edwards, G. Koutsou, Th. Leontiou, H. Neff, J. Negele, W. Schroers and A. Tsapalis good chiral properties; lighter pions very CPU expensive

GM 1 : dynamical vs m π = 0.50 GeV

GM 1

conclusions accurate determination of GM 1 in quenched theory ; deviation from fitted experimental data (MAID) The N to Delta transition form factors can be studied efficiently using Lattice QCD EMR & CMR negative ; nucleon deformation calculation with dynamical quarks in progress ; smaller volumes  increased noise higher statistics is required in order to reach the level of precision necessary for the detection of unquenching effects (pion cloud)