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We have started a program to compute the electromagnetic form factors of mesons. We discuss the techniques used to compute the pion form factor and present preliminary results computed with domain wall valence fermions on MILC asqtad lattices, as well as Wilson fermions on quenched lattices. These methods can easily be extended to rho-to-gamma-pi transition form factors.
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The existing theory of hard exclusive QCD processes is based on two assumptions: (i) $factorization$ into a $hard,block$ times light front distribution amplitudes (DAs); (ii) use of perturbative gluon exchanges within the hard block. However, unlike DIS and jet physics, the characteristic momentum transfer $Q$ involved in the factorized block is not large enough for this theory to be phenomenologically successful. In this work, we revisit the latter assumption (ii), by explicitly calculating the $instanton-induced$ contributions to the hard block, and show that they contribute substantially to the vector, scalar and gravitational form factors of the pseudoscalar, scalar and vector mesons, over a wide range of momentum transfer.
Lattice simulations of QCD have produced precise estimates for the masses of the lowest-lying hadrons which show excellent agreement with experiment. By contrast, lattice results for the vector and axial vector form factors of the nucleon show significant deviations from their experimental determination. We present results from our ongoing project to compute a variety of form factors with control over all systematic uncertainties. In the case of the pion electromagnetic form factor we employ partially twisted boundary conditions to extract the pion charge radius directly from the linear slope of the form factor near vanishing momentum transfer. In the nucleon sector we focus specifically on the possible contamination from contributions of higher excited states. We argue that summed correlation functions offer the possibility of eliminating this source of systematic error. As an illustration of the method we discuss our results for the axial charge, gA, of the nucleon.
Precision computation of hadronic physics with lattice QCD is becoming feasible. The last decade has seen percent-level calculations of many simple properties of mesons, and the last few years have seen calculations of baryon masses, including the nucleon mass, accurate to a few percent. As computational power increases and algorithms advance, the precise calculation of a variety of more demanding hadronic properties will become realistic. With this in mind, I discuss the current lattice QCD calculations of generalized parton distributions with an emphasis on the prospects for well-controlled calculations for these observables as well. I will do this by way of several examples: the pion and nucleon form factors and moments of the nucleon parton and generalized-parton distributions.
The role of the strange quarks on the low-energy interactions of the proton can be probed through the strange electromagnetic form factors. Knowledge of these form factors provides essential input for parity-violating processes and contributes to the understanding of the sea quark dynamics. We determine the strange electromagnetic form factors of the nucleon within the lattice formulation of Quantum Chromodynamics using simulations that include light, strange and charm quarks in the sea all tuned to their physical mass values. We employ state-of-the-art techniques to accurately extract the form factors for values of the momentum transfer square up to 0.8~GeV$^2$. We find that both the electric and magnetic form factors are statistically non-zero. We obtain for the strange magnetic moment $mu^s=-0.017(4)$, the strange magnetic radius $langle r^2_M rangle^s=-0.015(9)$~fm$^2$, and the strange charge radius $langle r^2_E rangle^s=-0.0048(6)$~fm$^2$.
We give an update on our ongoing efforts to compute the nucleons form factors and moments of structure functions using Nf=2 flavours of non-perturbatively improved Clover fermions. We focus on new results obtained on gauge configurations where the pseudo-scalar meson mass is in the range of 170-270 MeV. We will compare our results with various estimates obtained from chiral effective theories since we have some overlap with the quark mass region where results from such theories are believed to be applicable.
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