The dynamics of partons inside the light $\rho$ meson is found to be essential for its properties and internal structure, both in free space and in the nuclear medium. In this paper, we systematically investigate the in-medium structure changes of ${\rho }^{+}$ mesons within the covariant Nambu-Jona-Lasinio (NJL) model, utilizing the Schwinger proper-time regularization scheme. We solve the Bethe-Salpeter equations to guarantee the bound meson-state condition. At the quark level, the nuclear medium effects are also derived within the same NJL model to maintain a consistent approach with the in-medium ${\rho }^{+}$ meson electromagnetic form factors. To this end, we analyze the spacelike electromagnetic form factors of the ${\rho }^{+}$ meson in free space and in a nuclear medium. We find that the charge radius and quadrupole moment of the ${\rho }^{+}$ meson increase with increasing nuclear matter density, while the magnetic moment decreases, in agreement with the existing previous theoretical predictions. The enhancement of the ${\rho }^{+}$ meson charge radius at normal density relative to that in free space is about 11% (0.08 fm), while the reduction of ${\rho }^{+}$ meson magnetic moment is about 8% ($0.20{\mu }_N$). Our predictions for the charge radius, magnetic moment, and quadrupole moment of the ${\rho }^{+}$ meson in both free space and nuclear medium, remain challenging to be verified experimentally.

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• Bethe-Salpeter equation
• Quantum chromodynamics
• Strong interaction
• Down quark
• Light quarks
• Mesons
• Electric moment
• Form factors
• Magnetic moment
• Quantum field theory
• Spontaneous symmetry breaking