Vacuum free energy, quark condensate shifts and magnetization in three-flavor chiral perturbation theory to $\mathcal{O}(p^6)$ in a uniform magnetic field

Prabal Adhikari; Inga Strümke

doi:10.1016/j.nuclphysb.2023.116389

paper

Vacuum free energy, quark condensate shifts and magnetization in three-flavor chiral perturbation theory to $O (p^{6})$ in a uniform magnetic field

arXiv:2305.05427 · doi:10.1016/j.nuclphysb.2023.116389

Abstract

We study three-flavor QCD in a uniform magnetic field using chiral perturbation theory ( $χ$ PT). We construct the vacuum free energy density, quark condensate shifts induced by the magnetic field and the renormalized magnetization to $O (p^{6})$ 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 $2 + 1$ -flavor lattice QCD data, we find that the light quark condensate shift at $O (p^{6})$ is in better agreement than the shift at $O (p^{4})$ . We also find that the renormalized magnetization, due to its smallness, possesses large uncertainties at $O (p^{6})$ due to the uncertainties in the low-energy constants.

23 pages, 3 sets of figures, matches published version

Vacuum free energy, quark condensate shifts and magnetization in three-flavor chiral perturbation theory to O(p6) in a uniform magnetic field

Abstract

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Vacuum free energy, quark condensate shifts and magnetization in three-flavor chiral perturbation theory to $O (p^{6})$ in a uniform magnetic field