Traversable Wormhole Solutions in massive $F(T)$ gravity

We investigate traversable wormhole geometries in the framework of $F(T)$ gravity supplemented by a weak de Rham-Gabadadze-Tolley (dRGT) massive term. Using the static and spherically symmetric Morris-Thorne metric, we derive the field and conservation equations, separating the effective energy-momentum tensor into torsional and massive contributions. We analyze three representative classes of metric redshift functions, namely constant, logarithmic, and power-law forms, and two cases of the massive term, i.e. the general one and the uniform pressure case. The obtained solutions satisfy the flaring-out condition and remain asymptotically flat, while the effective matter sector can fulfill or only mildly violate the standard energy conditions. The results show that the inclusion of a small graviton mass provides an additional anisotropic pressure that can sustain the throat geometry without introducing exotic sources. In the limit of vanishing graviton mass, the configurations continuously reduce to the standard $F(T)$ wormhole solutions, confirming the consistency of the framework.