  Point particle may interact to traceless symmetric tensors of arbitrary rank.
Free gauge theories of traceless symmetric tensors are constructed, that
provides a possibility for a new type of interactions, when particles exchange
by those gauge fields. The gauge theories are parameterized by the particle's
mass m and otherwise are unique for each rank s. For m=0, they are local gauge
models with actions of 2s-th order in derivatives, known in d=4 as "pure spin",
or "conformal higher spin" actions by Fradkin and Tseytlin. For nonzero m, each
rank-s model undergoes a unique nonlocal deformation which entangles fields of
all ranks, starting from s. There exists a nonlocal transform which maps m > 0
theories onto m=0 ones, however, this map degenerates at some m > 0 fields
whose polarizations are determined by zeros of Bessel functions. Conformal
covariance properties of the m=0 models are analyzed, the space of gauge fields
is shown to admit an action of an infinite-dimensional "conformal higher spin"
Lie algebra which leaves gauge transformations intact.
