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Magnetic dipole moment of the Δ + (1232) resonance

Magnetic dipole moment of the Δ + (1232) resonance. Marc Vanderhaeghen Johannes Gutenberg Universität Mainz. Crystal Ball coll. meeting, September 21-23, 2008, Mainz. TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: A A A A A. Overview.

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Magnetic dipole moment of the Δ + (1232) resonance

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  1. Magnetic dipole moment of the Δ+ (1232) resonance MarcVanderhaeghen Johannes Gutenberg Universität Mainz Crystal Ball coll. meeting, September 21-23, 2008, Mainz TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAA

  2. Overview 1) introduction : spin-3/2 e.m. transitions 2) full QCDlattice calculations for μΔ 3) Chiral EFT calculations 4) Observables 5) Quark transverse densities in Δ(1232) in coll. with • 2)C. Aubin, K. Orginos, V. Pascalutsa, M. Vdh(2008) • C. Alexandrou, T. Korzec, G. Koutsou, T. Leontiou, C. Lorcé, J. Negele, V. Pascalutsa, A. Tsapalis, M. Vdh(2008) • 3) & 4) V. Pascalutsa, M. Vdh (2004, 2008) • 5) C. Lorcé, V. Pascalutsa, M. Vdh (2008)

  3. spin-3/2 electromagnetic transition

  4. *ΔΔvertex  Δ Δ mass MΔ multipole transitions electric charge charge quadrupole magnetic dipole magnetic octupole

  5. magnetic momentfor higher spin particle g-factor , spin S classical value for g-factor : gP = 2 Weinberg value for point particle μ = 1 S = 1/2 S = 1 μ = 2 S = 3/2 μ = 3

  6. Status of μΔ

  7. spin-3/2 point particle SUGRA natural values for spin-3/2 point particle :

  8. QΔ linked with E2/M1 ratio for N -> Δ large Nc limit of QCD : Buchmann, Hester, Lebed (2002) Nc = 3 EXP : rn2 = - 0.113 (3) fm2 large Nc : Qp -> Δ+ = - 0.080 e . fm2 EXP : Qp -> Δ+ = - 0.085 (3) e . fm2 from exp. E2/M1 ratioTiator et al. (2003) large Nc limit relates QΔ+with Qp->Δ+ large Nc : QΔ+ = - 0.048 (2) e . fm2 GE2(0) = -1.87 ± 0.08

  9. full QCD lattice calculations for μΔ

  10. full QCD lattice calculations : Ω- anisotropic clover dynamical lattices (JLab) background field method Periodic b.c. : magnetic flux continuous over boundary B = n . 2 π / L2 : Damgaard, Heller (1988) μΩ in physical nuclear magnetons NERSC mΩ= 1.65 GeV Kyklades @ WM EXP. -2.02 ± 0.05 Aubin et al. (2008) JLab

  11. full QCD lattice calculations : Δ anisotropic clover dynamical lattices : 243 x 128,aS = 0.1, at = 0.036 fm background field method μΔfor mπ= 366 MeV μΔ++in physical nuclear magnetons Aubin et al. (2008)

  12. Chiral EFT calculations

  13. Magnetic Dipole Moment of (1232)- resonance • J P=3/2+ (P33), M = 1232 MeV,  = 115 MeV • N ->  transition:  N ->  (99%),  N ->  (<1%) Chiral Effective Field Theory (LO) Pascalutsa, Vdh (2004)

  14. chiralEffective Field Theory calculation of e p -> e p π0in Δ(1232) region in threshold region : momentum p ~ mπ in Δ region : p ~ MΔ - MN Power counting scheme : ε expansion Jenkins, Manohar; Hemmert et al.; … treat parametersΔ = MΔ– MN andmπonSAMEfooting δ expansion Pascalutsa. & Phillips (2003) inΔ region, treat parametersΔandmπon DIFFERENT footing LO calculation to NLO in δ expansion for e p -> e p π0 vertex corrections : unitarity & gauge invariance exactly preserved to NLO

  15. OR propagator p»m , 1/ = O(1/)[c.f., SN» 1/p = O(1/2)] » p» , 1/(p-- )= O(1/3 ) = + … = O(p3) = O(3 ) Chiral Lagrangians withand power counting Include the  as an explicit d.o.f. , [Jenkins & Manohar (1991)] described by a spin-3/2 (Rarita-Schwinger) isospin-3/2 (isoquartet) field δ- expansion Pascalutsa. & Phillips (2003)

  16. Chiral Lagrangians and LEC electric charge

  17. p ―›  π0 p : NLO EFT calculation loops : Pascalutsa, Vdh : PRD 77, 014027 (2008)

  18. Real part Imag. part full QCD lattice results and chiral behavior chiral EFT calc. Pascalutsa, Vdh(2004) background field calc. Nf = 2 + 1 dynamical Clover fermions Aubin et al. (2008) 3-point function calc. Nf = 2 dynamical Wilson fermions Alexandrou et al.(2008) 3-point function calc. domain-wall valence & staggered sea quarks 3-point function calc. quenched Wilson fermions

  19. Observables

  20. Low Energy Theorem : R -> 1 Σ -> Σπ Σcirc -> 0 for E’-> 0 : Observables p! (+!’+ )!0 p cross section ratio R linearphoton asymmetryΣ circularphoton asymmetryΣcirc(for a 3 body final state)

  21. p ―›  π0 p : NLO EFT calculation Pascalutsa, Vdh (2008) LO EFT :Re μΔ = 3 NLO EFT : Re μΔ = 1Re μΔ = 3 Re μΔ = 5

  22. p ―›  π0 p : Xsec and linear photon asymmetry EFT :Pascalutsa, Vdh (2008)

  23. p ―›  π+ n : Xsec and linear photon asymmetry

  24. p ―›  π0 p : circular photon asymmetry

  25. p ―›  π0 p : circular photon asymmetry circular photon asymmetryΣcirc zero in soft-photon limit linear in magnetic dipole moment EFT :Pascalutsa, Vdh (2008)

  26. Quark transverse densities in Δ(1232)

  27. quark transverse charge densities in Δ(1232) light-front q+ = q0 + q3 = 0 z p p’ photon only couples to forward moving quarks quark charge density operator longitudinally polarized Δ Lorcé et al. (2008) Aλλ(Q2)expressed in terms of GE0, GE2, GM1, GM3

  28. full QCD lattice calculations Alexandrou et al. (2008)

  29. full QCD lattice calculations Alexandrou et al. (2008)

  30. quark transverse densities inΔ(1232) Aλλ(Q2)expressed in terms of GE0, GE2, GM1, GM3 lattice calculations : Alexandrou et al. (2008) densities : Lorcé et al. (2008) λ= + 3/2 λ= +1/2 λ= + 3/2

  31. quark transverse charge densities in Δ(1232) transversely polarized Δ transverse spin e.g. along x-axis : multipole field pattern Lorcé et al. (2008)

  32. transversely polarizedΔ(1232) monopole dipole quadrupole octupole

  33. transversely polarized spin-3/2 electric dipole moment for spin-3/2 point particle : g = 2GM1 (0) = 3eΔ electric quadrupole moment for spin-3/2 point particleGM1 (0) = 3eΔand GE2(0) = -3eΔ transverse charge densities depend only on anomalous values of e.m. moments reflect internal structure

  34. transversely polarizedΔ(1232) lattice : Alexandrou et al. (2008)

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