Topological susceptibility and axion properties in the presence of a strong magnetic field within the three-flavor NJL model

We analyze the topological susceptibility and the axion properties in the presence of an external uniform magnetic field, considering a three-flavor Nambu-Jona-Lasinio model that includes strong <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>C</a:mi><a:mi>P</a:mi></a:math> violation through a ’t Hooft-like flavor mixing term. Both thermal and finite density effects are studied for magnetic fields up to <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mrow><c:mn>1</c:mn><c:mtext> </c:mtext><c:mtext> </c:mtext><c:msup><c:mi>GeV</c:mi><c:mn>2</c:mn></c:msup></c:mrow></c:math>, and the corresponding phase transitions are analyzed. To capture the inverse magnetic catalysis effect at finite temperatures and densities, a magnetic-field-dependent coupling constant is considered. Our analytical and numerical results are compared with those previously obtained from lattice QCD, chiral perturbation theory, and other effective models.