Vacuum Properties of QCD in an Electromagnetic Field

Abstract

The non-trivial vacuum properties of Quantum Chromodynamics can be affected by a constant external magnetic field. The chiral condensate and the magnetization of the vacuum are the two properties studied in this work. The chiral condensate, which is the order parameter for chiral symmetry breaking--one of the most important properties of QCD--is an optimal quantity to study at intermediate field strengths. Using both models and chiral perturbation theory, it can be shown that an electric field suppresses the chiral condensate whereas a magnetic field enhances it. Higher-order calculations in χPT may have a substantial effect on the magnitude of the shift in the chiral condensate, but their exact effect is unknown due to the uncertainty in the parameters of the theory. The second parameter, the magnetization, is used at fields large enough for perturbative calculations to be valid; at these scales, there is large explicit chiral symmetry breaking and the chiral condensate cannot be used. The first-order magnetization shows a correction of the form B log B; the calculation to next order in perturbation theory shows a correction small enough that non-perturbative corrections dominate.