# Theory Center Research Highlights

### Lattice QCD

**
"Exotic and excited-state radiative transitions in charmonium
from lattice QCD"
**

J.J. Dudek, R.G. Edwards, C. Thomas

*Phys. Rev. D* **79**, 094504 (2009)

Extending the techniques used to obtain the excited state mass spectrum
of charmonium and the ground state radiative transitions, the amplitudes
for the transitions *A* → B γ* are extracted. The expected
patterns for conventional (heavy quark-antiquark) mesons are observed
along with the first QCD estimates of photocouplings of conventional
mesons to hybrid mesons (in which the gluonic field plays an explicit
role). These couplings are found to be large, supporting the
photoproduction mechanism proposed by the GlueX experiment. Ongoing
research work using the techniques developed in this study will test
this in the relevant light-quark sector.

**
"Two photon decays of charmonia from lattice QCD"
**

J.J. Dudek, R.G. Edwards

*Phys. Rev. Lett.* **97**, 172001 (2006)

Extracting the amplitude for a two-photon decay of a
meson from Euclidean Lattice QCD is not straightforward
as it corresponds to a correlator having no QCD
eigenstate in the final state. A method using
the Lehmann-Symanzik-Zimmermann reduction to relate a
photon to a linear superposition of QCD vector
eigenstates is tested and found successful in describing
the decays of pseudoscalar and scalar charmonium mesons,
η_{c}, χ_{c0}.

**
"Charmonium excited state spectrum in lattice QCD"
**

J.J. Dudek, R.G. Edwards, N. Mathur, D.G. Richards

*Phys. Rev. D* **77**, 034501 (2008)

The excited state mass spectrum of meson states built from the heavy charm quarks is extracted from a lattice QCD calculation. Utilizing a large basis of quark-gluon composite operators, the spectrum is reliably obtained by variational analysis of a matrix of correlation functions. The power of this technique is demonstrated by the first extraction of the near-degenerate pair of states ψ' and ψ''.

The figure shows the lattice measurement of the pion form factor (open symbols), with the bands showing the corresponding vector-meson-dominance fits. The solid symbols show the current experimental determination.

**
"Lattice computation of the pion form factor"
**

F.D.R. Bonnet, R.G. Edwards, G.T. Fleming, R. Lewis, D.G. Richards

*Phys. Rev. D* **72**, 054506 (2005)

The study of the pion form factor
*F _{π}(Q^{2})*
provides a good laboratory for investigating the onset of perturbative QCD
in exclusive processes, exploring the transtion from strong QCD
(confinement) to the pQCD regime. Its determination is an important
component of the Hall C experimental program both at 6 GeV and at 12 GeV.
Recently, members of the JLab Theory Center collaborated on a lattice
study of the pion form factor, employing the Jefferson Laboratory lattice
cluster facility. The calculation was performed in full QCD, with pion
masses down to around 300 MeV. They attained values of

*Q*comparable with the ongoing experiment JLab E01-004, and showed that a vector-meson-dominance form provided a faithful description of the data over the explored energy range. Future work will extend this calculation both to lighter quark masses, and to still larger energies commensurate with the 12 GeV experimental program, enabling a detailed study of this benchmark quantity in hadronic physics.

^{2}Lattice simulation results after correcting for finite-volume, finite lattice spacing and partial-quenching artifacts. The curve dispalys the continuum extrapolation to the physical pion mass.

**
"Chiral and continuum extrapolation of partially-quenched lattice results"
**

C.R. Allton, W. Armour, D.B. Leinweber, A.W. Thomas, R.D. Young

*Phys. Lett. B* **628**, 125 (2005)

The vector meson mass is extracted from a large sample of partially quenched, two-flavor lattice QCD simulations. For the first time, discretisation, finite-volume and partial quenching artefacts are treated in a unified framework which is consistent with the low-energy behaviour of QCD. This analysis incorporates the leading infrared behaviour dictated by chiral effective field theory. As the two-pion decay channel cannot be described by a low-energy expansion alone, a highly-constrained model for the decay channel of the rho-meson is introduced. The latter is essential for extrapolating lattice results from the quark-mass regime where the rho is observed to be a physical bound state.