Medium effects on the electromagnetic form factors of the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>ρ</mml:mi> </mml:math> meson

The dynamics of partons inside the light $\ensuremath{\rho}$ 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 ${\ensuremath{\rho}}^{+}$ 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 ${\ensuremath{\rho}}^{+}$ meson electromagnetic form factors. To this end, we analyze the spacelike electromagnetic form factors of the ${\ensuremath{\rho}}^{+}$ meson in free space and in a nuclear medium. We find that the charge radius and quadrupole moment of the ${\ensuremath{\rho}}^{+}$ meson increase with increasing nuclear matter density, while the magnetic moment decreases, in agreement with the existing previous theoretical predictions. The enhancement of the ${\ensuremath{\rho}}^{+}$ meson charge radius at normal density relative to that in free space is about 11% (0.08 fm), while the reduction of ${\ensuremath{\rho}}^{+}$ meson magnetic moment is about 8% ($0.20\text{ }\text{ }{\ensuremath{\mu}}_{N}$). Our predictions for the charge radius, magnetic moment, and quadrupole moment of the ${\ensuremath{\rho}}^{+}$ meson in both free space and nuclear medium, remain challenging to be verified experimentally.