Irreducible twisted Heisenberg-Virasoro modules from tensor products

In this paper, we realize polynomial \H-modules $\mathrm{\Omega }(\lambda ,\alpha ,\beta )$ from irreducible twisted Heisenberg-Virasoro modules ${\text{A}}_{\alpha ,\beta }$. It follows from \H-modules $\mathrm{\Omega }(\lambda ,\alpha ,\beta )$ and $\mathrm{I}\mathrm{n}\mathrm{d}(M)$ that we obtain a class of natural non-weight tensor product modules $\big(\bigotimes_{i=1}^m\Omega(\lambda_i,\alpha_i,\beta_i)\big)\otimes $\mathrm{I}\mathrm{n}\mathrm{d}$(M)$. Then we give the necessary and sufficient conditions under which these modules are irreducible and isomorphic, and also give that the irreducible modules in this class are new.