A symmetry-preserving approach to the two valence-body continuum bound-state problem is used to calculate the elastic electromagnetic form factors of the $\rho$-meson and subsequently to study the evolution of vector-meson form factors with current-quark mass. To facilitate a range of additional comparisons, $K^{*}$ form factors are also computed. The analysis reveals that vector mesons are larger than pseudoscalar mesons; composite vector mesons are nonspherical, with magnetic and quadrupole moments that deviate $\sim 30\%$ from point-particle values; in many ways, vector-meson properties are as much influenced by emergent mass as those of pseudoscalars; and vector-meson electric form factors possess a zero at spacelike momentum transfer. Qualitative similarities between the electric form factors of the $\rho$ and the proton, $G_E^p$, are used to argue that the character of emergent mass in the Standard Model can force a zero in $G_E^p$. Moreover, the existence of a zero in vector-meson electric form factors entails that a single-pole vector-meson dominance model can only be of limited use in estimating properties of off-shell vector mesons, providing poor guidance for systems in which the Higgs mechanism of mass generation is dominant.

• Received 12 November 2019

DOI:https://doi.org/10.1103/PhysRevD.100.114038