# Theory Center Research Highlights

### Spectra and Decays of Hadrons, and Confinement in QCD

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"Charmonium in lattice QCD and the non-relativistic quark-model"
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J.J. Dudek, E. Rrapaj

*Phys. Rev. D* **78**, 094504 (2008)

Using matrix elements of composite QCD operators, explicit lattice QCD computation and the bound-state quark model are compared in the case of heavy quark mesons. Lattice states are identified that correspond to states expected in a pure quark-antiquark picture as well as states which are interpreted as having an essential gluonic field component - the hybrid mesons.

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"Even parity excitations of the nucleon in lattice QCD"
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B.G. Lasscock, J.N. Hedditch, W. Kamleh, D.B. Leinweber, W. Melnitchouk,
A.G. Williams

*Phys. Rev. D* **76**, 054510 (2007)

The spectrum of the even parity excitations of the nucleon is studied in quenched lattice QCD. This analysis extends earlier work by including an expanded basis of nucleon interpolating fields, increasing the physical size of the lattice, including more configurations to enhance statistics and probing closer to the chiral limit. With a review of world lattice data, we conclude that there is little evidence of the Roper resonance in quenched lattice

Electric dipole transition matrix element between χ_{c0}
and J/ψ charmonium systems as a function of photon virtuality
*Q*^{2}. Lattice data (green and blue) is fitted with a
phenomenological form consistent with the quark model. The fitted curve
agrees with experimental data (purple) at the real photon point
*Q*^{2}=0

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"Radiative transitions in charmonium from lattice QCD"
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J.J. Dudek, R.G. Edwards, D.G. Richards

*Phys. Rev. D* **73**, 074507 (2006)

Radiative transitions between charmonium states offer an insight into
the internal structure of heavy-quark bound states within QCD. We compute,
for the first time within lattice QCD, the transition form-factors of
various multipolarities between the lightest few charmonium states. In
addition, we compute the experimentally unobservable, but physically
interesting vector form-factors of the η_{c}, J/ψ and
χ_{c0}. In general, after extrapolation of lattice data at
non-zero *Q*^{2} to the photopoint, our results agree within
errors with all well measured experimental values (see figure).
Furthermore, results are compared with the expectations of simple quark
models where we find that many features are in agreement.

We conclude that our methods are successful and propose to apply them to the problem of radiative transitions involving hybrid mesons, with the eventual goal of predicting hybrid meson photoproduction rates at the GlueX experiment.