Vacuum Properties of QCD in an Electromagnetic Field

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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.