Topological susceptibility and fourth cumulant in a uniform magnetic field

We study the topological susceptibility and fourth cumulant of the QCD vacuum in a background magnetic field (H) using three-flavor chiral perturbation theory (χPT) for arbitrary quark masses and n-flavor χPT with degenerate quark masses. We find that the enhancement by the magnetic field of the topological susceptibility relative to the H=0 vacuum value is larger in the three-flavor χPT compared to two-flavor χPT. Additionally, in comparing the fourth cumulant, we find that its suppression is comparable for magnetic fields, eH≲0.8mπ2, and weaker for larger magnetic fields in three-flavor χPT with its enhancement beginning at a significantly lower critical magnetic field compared to two-flavor χPT. We also find that the enhancement of the topological susceptibility in n-flavor χPT with degenerate quarks is significantly larger and the suppression of the topological cumulant significantly greater at weak fields with the critical magnetic field pushed out to larger magnetic fields compared to both two and three-flavor χPT.