The mass spectra of charged pions (${\pi }_{\pm }$) and kaons ($K_{\pm }$) at finite magnetic field, temperature, and quark chemical potential are investigated in frame of a three-flavor Nambu–Jona–Lasinio model. Based on the analytical formula, we observe that different behavior between charged mesons and neutral mesons is induced by the isospin symmetry breaking in magnetic field, and different behavior between ${\pi }_{\pm }$ and $K_{\pm }$ mesons comes from different mass of constituent $u/d$ and $s$ quarks. With vanishing temperature and quark chemical potential, the mass of charged pions $m_{{\pi }_{+}}=m_{{\pi }_{-}}$ and charged kaons $m_{K_{+}}=m_{K_{-}}$ increase monotonically with magnetic field ($eB<40m_{\pi }^2$). With fixed magnetic field and vanishing quark chemical potential, $m_{{\pi }_{+}}=m_{{\pi }_{-}}$ and $m_{K_{+}}=m_{K_{-}}$ show nonmonotonic behavior with increasing temperature, and several mass jumps at finite temperature caused by the discrete Landau level of constituent quarks. With fixed magnetic field and vanishing temperature, $m_{{\pi }_{+}}=m_{{\pi }_{-}}$ and $m_{K_{+}}=m_{K_{-}}$ remain constant at low-quark chemical potential, and then their mass jumps occur caused by the mass jump of constituent quarks. After that, $m_{{\pi }_{+}}\simeq m_{{\pi }_{-}}$ decreases with quark chemical potential, but $m_{K_{+}}$ ($m_{K_{-}}$) first increases and then decreases (decreases monotonically) with quark chemical potential, with apparent mass deviation $m_{K_{+}}\ne m_{K_{-}}$. Furthermore, we consider the inverse magnetic catalysis (IMC) effect on meson mass spectra by using a magnetic field dependent coupling parameter $G(eB)$ in four-fermion interaction term ${\mathcal{L}}_4$ or a magnetic field dependent coupling parameter $K(eB)$ in six-fermion interaction term ${\mathcal{L}}_6$. Including IMC effect does not lead to qualitative modification for the mass spectra at finite magnetic field, temperature, and quark chemical potential.

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• QCD phase transitions
• Quark model
• Strong interaction