Rho-meson screening mass in the presence of strong magnetic fields

We study the screening mass of the neutral rho-meson in the presence of strong magnetic fields using the Kroll-Lee-Zumino (KLZ) model. The rho-meson self-energy is computed at one-loop order within the lowest Landau level (LLL) approximation, considering the magnetic field as the dominant energy scale. Due to Lorentz symmetry breaking induced by the external field, we decompose the self-energy into three independent tensor structures, which give rise to three distinct modes. Additionally, the four-momentum splits into parallel and perpendicular components, leading to two types of screening masses: the parallel screening mass (<a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:msub><a:mi>p</a:mi><a:mn>0</a:mn></a:msub><a:mo>=</a:mo><a:mn>0</a:mn></a:math> and <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:msub><c:mi>p</c:mi><c:mo>⊥</c:mo></c:msub><c:mo stretchy="false">→</c:mo><c:mn>0</c:mn></c:math>) and the perpendicular screening mass (<f:math xmlns:f="http://www.w3.org/1998/Math/MathML" display="inline"><f:msub><f:mi>p</f:mi><f:mn>0</f:mn></f:msub><f:mo>=</f:mo><f:mn>0</f:mn></f:math> and <h:math xmlns:h="http://www.w3.org/1998/Math/MathML" display="inline"><h:msub><h:mi>p</h:mi><h:mo stretchy="false">∥</h:mo></h:msub><h:mo stretchy="false">→</h:mo><h:mn>0</h:mn></h:math>). Our results show that the zero and perpendicular modes exhibit a monotonically increasing behavior with the magnetic field strength, whereas the parallel mode remains essentially constant. These findings provide new insights into the behavior of vector mesons in strongly magnetized media, with implications for QCD under extreme conditions.