Marginal scalar and Proca clouds around Reissner-Nordström black holes

Massive scalar test fields around Kerr black holes can form quasibound states with complex frequencies. Some of these states decay in time, but some others---in the superradiant regime---grow, causing a superradiant instability. Precisely at the threshold between decaying and growing modes, there exist bound states with real frequency, known as scalar clouds. Fully nonlinear counterparts of these clouds have been shown to yield Kerr black holes with scalar hair. Here, we consider massive, (electrically) charged, test scalar, and Proca fields on the background of Reissner-Nordstr\"om black holes. By computing the quasibound state frequencies, we establish that no such states exist in the superradiant regime for the Proca field---a similar behavior to that known for scalar fields. But decaying quasibound states with an arbitrarily small imaginary part of the frequency exist and thus are arbitrarily long lived. In the limit of a vanishing imaginary part of the frequency, the field does not trivialize, and we dub the corresponding configurations as marginal (charged) scalar or Proca clouds, since they are only marginally bound. We comment on the possible existence of nonlinear counterparts to these marginal clouds.