  We study two interacting identical run and tumble particles (RTP's) in one
dimension. Each particle is driven by a telegraphic noise, and in some cases,
also subjected to a thermal white noise with a corresponding diffusion constant
$D$. We are interested in the stationary bound state formed by the two RTP's in
the presence of a mutual attractive interaction. The distribution of the
relative coordinate $y$ indeed reaches a steady state that we characterize in
terms of the solution of a second-order differential equation. We obtain the
explicit formula for the stationary probability $P(y)$ of $y$ for two examples
of interaction potential $V(y)$. The first one corresponds to $V(y) \sim |y|$.
In this case, for $D=0$ we find that $P(y)$ contains a delta function part at
$y=0$, signaling a strong clustering effect, together with a smooth exponential
component. For $D>0$, the delta function part broadens, leading instead to weak
clustering. The second example is the harmonic attraction $V(y) \sim y^2$ in
which case, for $D=0$, $P(y)$ is supported on a finite interval. We unveil an
interesting relation between this two-RTP model with harmonic attraction and a
three-state single RTP model in one dimension, as well as with a four-state
single RTP model in two dimensions. We also provide a general discussion of the
stationary bound state, including examples where it is not unique, e.g., when
the particles cannot cross due to an additional short-range repulsion.
