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The N to Delta transition form factors from Lattice QCD

The N to Delta transition form factors from Lattice QCD. Antonios Tsapalis University of Athens, IASA. EINN05, Milos, 21-9-2005. outline. Nucleon Deformation & N- D transition form factors LATTICE QCD: Hadronic states and transitions between them Limitations

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The N to Delta transition form factors from Lattice QCD

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  1. The N to Delta transition form factors from Lattice QCD Antonios Tsapalis University of Athens, IASA EINN05, Milos, 21-9-2005

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

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

  4. p(qqq) I = J = 938 MeV γ* Μ1, Ε2, C2 Μ1+ ,Ε1+,S1+πo d u u d u u Δ(qqq) I = J = 1232 MeV Spherical  M1 Deformed  M1 , E2 , C2 Deformation signal

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

  6. Lattice QCD • Rotate to Euclidean time: t -> -i t • Discretize space-time Fermions on sites X (m=1,2,3) Gauge fields on links t (m=4)

  7. Wilson formulation (1974) 3 a 2 4 1 Plaquette gauge action 1 2 Wilson-Dirac operator DW

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

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

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

  11. u u B(0) Hadrons and transitions in Lattice QCD B(x) d • 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

  12. g x N D • generate a nucleon at t=0 • inject a photon with momentum q at t=t1 • annihilate a Delta at time t=t2 • measure the 3-pt function • extract the form factors from suitable ratios • of 3-pt and 2-pt functions

  13. Quenched Results C. Alexandrou, Ph. de Forcrand, H. Neff, J. Negele, W. Schroers and A. Tsapalis PRL, 94, 021601 (2005) 323 x 64 lattice β = 6.0 200 gauge fields Wilson quarks La = 3.2 fm

  14. EMR (%) CMR (%)

  15. V. Pascalutsa & M. Vanderhaeghen, hep-ph/0508060 In Chiral Effective Field Theory d-expansion scheme is small L ~ 1 GeV fit low energy constants Non-analyticities in mp reconcile the heavy quark lattice results with experiment NLO results at Q2 = 0.1 GeV2

  16. Full QCD C. Alexandrou, R. Edwards, G. Koutsou, Th. Leontiou, H. Neff, J. Negele, W. Schroers and A. Tsapalis Hybrid scheme valence quarks sea quarks ‘domain wall’ quarks • 2 light + 1 heavy flavour • action with small • discretization error good chiral properties; lighter pions very CPU expensive V mp (GeV) 203 x 32 0.60 203 x 32 0.50 283 x 32 0.36 } a=0.125 fm

  17. GM1 : dynamical vs quenched @ mπ = 0.50 GeV

  18. GM1

  19. conclusions • The N to Delta transition form factors can be studied • efficiently using Lattice QCD • accurate determination of GM1in quenched theory ; • deviation from fitted experimental data (MAID) • 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)

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