Vacuum free energy, quark condensate shifts and magnetization in three-flavor chiral perturbation theory to In a Uniform Magnetic Field
Prabal Adhikari (Physics Department, Faculty of Natural Sciences and Mathematics, St. Olaf College, 1520 St. Olaf Avenue, Northfield, United States)
; Inga Strümke (Department of Computer Science, Faculty of Information Technology and Electrical Engineering, NTNU, Norwegian University of Science and Technology, Sem Sælandsvei 9, Trondheim, Norway)
We study three-flavor QCD in a uniform magnetic field using chiral perturbation theory (χPT). We construct the vacuum free energy density, quark condensate shifts induced by the magnetic field and the renormalized magnetization to in the chiral expansion. We find that the calculation of the free energy is greatly simplified by cancellations among two-loop diagrams involving charged mesons. In comparing our results with recent -flavor lattice QCD data, we find that the light quark condensate shift at is in better agreement than the shift at . We also find that the renormalized magnetization, due to its small-ness, possesses large uncertainties at due to the uncertainties in the low-energy constants.