Analog of Weyl Meson As Analog of the Dark Photon

The Lagrangian for conformal gravitation with two scalar fields, which is linear in scalar curvature, is considered. In this Lagrangian, the Weyl vector is replaced by a Weyl-gauge vector, which transforms like the Weyl vector, but does not enter into the Weyl connection. The space of such a model is an integrable Weyl space. Based on this Lagrangian, the relationship between the Weyl-gauge vector and the electromagnetic potential vector is considered. The probability of conversion of quanta of both types of vectors is considered. A possible variant is given for the case when such conversion can be observed under astrophysical conditions.