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2021

QCD $\theta$-vacuum in a Uniform Magnetic Field

Adhikari, Prabal

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We study the $\theta$-vacuum of QCD using two-flavor chiral perturbation theory ($\chi$PT) in the presence of a uniform, background magnetic field calculating the magnetic field-dependent free energy density, the topological density, the topological susceptibility and the fourth cumulant at one-loop order.

We find that the topological susceptibility is enhanced by the magnetic field while the fourth topological cumulant is diminished at weak fields and enhanced at larger fields when $\theta=0$.
However, in the QCD vacuum with $\theta\neq 0$, the topological susceptibility can be either monotonically enhanced or diminished relative to their $\theta$-vacuum values.
The fourth cumulant also exhibits monotonic enhancement or suppression except for regions of $\theta$ near $0$ and $2\pi$, where it is both diminished and enhanced.

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