Anisotropic quark propagation and Zeeman effect in an external magnetic field

We investigated the impact of a constant external magnetic field on the dressed propagators of up-, down-, and strange quarks. In the weak field limit, we derive a general momentum-space representation for the propagator and numerically solve the corresponding gap equation. Our analysis reveals that the vector term of the propagator can be decomposed into components parallel and perpendicular to the magnetic field, resulting in anisotropic effective masses, with the transverse mass consistently exceeding the longitudinal mass. This mass disparity exhibits a power law dependence on the magnetic field strength and is less pronounced for the strange quark compared to up and down quarks. Additionally, the magnetic field induces axial-vector and tensor terms, highlighting the Zeeman effect resulting from quark interactions with the magnetic field. These findings have important implications for (inverse) magnetic catalysis, and phenomena such as vector meson and pion condensations. Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. Article funded by SCOAP3 and published under licence by Chinese Physical Society and the Institute of High Energy Physics of the Chinese Academy of Science and the Institute of Modern Physics of the Chinese Academy of Sciences and IOP Publishing Ltd.