arXiv:1001.1131v2 [hep-lat] 25 Jan 2010 JLAB-THY-09-1111 UMD-40762-474 Extracting Nucleon Magnetic Moments and Electric Polarizabilities from Lattice QCD in Background Electric Fields W. Detmold, 1, 2, ∗ B. C. Tiburzi, 3, † and A. Walker-Loud 1, ‡ $^{1}$Department of Physics, College of William and Mary, Williamsburg, Virginia 23187-8795, USA $^{2}$Thomas Jefferson National Accelerator Facility, Newport News, Virginia 23606, USA $^{3}$Maryland Center for Fundamental Physics, Department of Physics, University of Maryland, College Park, Maryland 20742-4111, USA (Dated: October 24, 2018) Nucleon properties are investigated in background electric fields. As the magnetic moments of baryons affect their relativistic propagation in constant electric fields, electric polarizabilities cannot be determined without knowledge of magnetic moments. This is analogous to the experi- mental situation, for which determination of polarizabilities from the Compton amplitude requires subtraction of Born terms. With the background field method, we devise combinations of nucleon correlation functions in constant electric fields that isolate magnetic moments and electric polariz- abilities. Using an ensemble of anisotropic gauge configurations with dynamical clover fermions, we demonstrate how both observables can be determined from lattice QCD simulations in background electric fields. We obtain results for the neutron and proton, however, our study is currently lim- ited to electrically neutral sea quarks. The value we extract for the nucleon isovector magnetic moment is comparable to those obtained from measuring lattice three-point functions at similar pion masses. PACS numbers: 12.38.Gc $^{∗}$wdetmold@wm.edu $^{†}$bctiburz@umd.edu $^{‡}$walkloud@wm.edu 1 Abstract