Lattice QCD in Background Fields

Electromagnetic properties of hadrons can be computed by lattice simulations of QCD in background fields. We demonstrate new techniques for the investigation of charged hadron properties in electric fields. Our current calculations employ large electric fields, motivating us to analyze chiral dynamics in strong QED backgrounds, and subsequently uncover surprising non-perturbative effects present at finite volume. Above we have reviewed lattice QCD computations in background fields. We have stressed the two basic features of such calculations; namely, the measurement of hadronic correlation functions in external fields, and the matching of the expected behavior for these correlation functions obtained from single-hadron effective actions. For ease we only considered pions in background electric fields. The neutral pion in infinite volume presents the simplest application of the background field method: a field-strength dependent shift of the pion energy is the only modification to the neutral pion correlation function. Measuring this shift allows one to deduce the electric polarizability. The charged pion electric polarizability can also be deduced by using the background field method. For this case, however, the calculated correlation function has non-standard behavior as a function of time. Nevertheless, this behavior of the correlation function is precisely that predicted for a relativistic charged particle in a constant electric field. Our computations are currently limited by systematic errors. As field quantization conditions must be met, the relatively small lattice volume employed leads to large values of the electric field. As one leaves the regime in which the field-strength dependence is perturbative, strong field chiral perturbation theory can be applied. In fact, chiral perturbation theory gives parameter-free predictions for hadron energies at next-to-leading order in the chiral expansion as a function of e (varepsilon)/mπ2. Small lattice volumes lead to another malady: finite size effects. Single pion effective actions are more complicated in finite volume. Quantum fluctuations allow virtual pions to wrap around the lattice and encounter background fields that differ topologically. Couplings of Wilson loops to pions must be included in the single pion effective action, and can potentially explain the oscillatory behavior seen in extracted energies as a function of the fit window. Lastly, our computations have been carried out at a single value for the pion mass, and with vanishing electric charges for the sea quarks. Further studies are required to extract physical results. Nevertheless, we have demonstrated new techniques for background field simulations which warrant such further studies. We additionally intend to study spin-1/2 baryons using generalizations of the methods presented here.