The N to Delta transition form factors from Lattice QCD

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

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Nucleon Deformation
Spectroscopic quadrupole moment vanishes
Intrinsic quadrupole moment w.r.t. body-fixed
frame exists
prolate
oblate
modelling required !
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?(qqq) I J 1232 MeV
Spherical ? M1
Deformed ? M1 , E2 , C2
Deformation signal
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EMR CMR Experimental Status
uncertainties in modelling final state
interactions
Thanks to N. Sparveris (Athens, IASA)
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Lattice QCD

• Rotate to Euclidean time t -gt -i t

• Discretize space-time

Fermions on sites
X (m1,2,3)
Gauge fields on links
t (m4)
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Wilson formulation (1974)
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a
2
4
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Plaquette gauge action
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2
Wilson-Dirac operator DW
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Generate an ensemble of gauge fields U
distributed with the Boltzmann weight
Calculate any n-point function of QCD
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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 gt 400 MeV
Overlap or Domain-Wall maintain chiral symmetry
but very CPU expensive
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The Transition Matrix Element
H.F.Jones and M.C.Scadron, Ann. Phys. (N.Y.) 81,1
(1973)
static D frame
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Hadrons and transitions in Lattice QCD
B(x)
d

• generate a baryon at t0
• annihilate the baryon at time t
• measure the 2-pt function
• extract the energy from the exponential
• decay of the state in Euclidean time

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• generate a nucleon at t0
• inject a photon with momentum q at tt1
• annihilate a Delta at time tt2
• measure the 3-pt function
• extract the form factors from suitable ratios
• of 3-pt and 2-pt functions

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

a0.125 fm
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GM1 dynamical vs quenched _at_ mp 0.50 GeV
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GM1
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conclusions

• The N to Delta transition form factors can be
  studied
• efficiently using Lattice QCD

• accurate determination of GM1 in 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)