Irreducible twisted Heisenberg-Virasoro modules from tensor products

In this paper, we realize polynomial $\H$-modules $\Omega(\lambda,\alpha,\beta)$ from irreducible twisted Heisenberg-Virasoro modules $\A_{\alpha,\beta}$. It follows from $\H$-modules $\Omega(\lambda,\alpha,\beta)$ and $\mathrm{Ind}(M)$ that we obtain a class of natural non-weight tensor product modules $\big(\bigotimes_{i=1}^m\Omega(\lambda_i,\alpha_i,\beta_i)\big)\otimes \mathrm{Ind}(M)$. 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.