Natural electroweak symmetry breaking in generalised mirror matter models

It has recently been pointed out that the mirror or twin Higgs model is more technically natural than the standard model, thus alleviating the ``little'' hierarchy problem. In this paper we generalise the analysis to models with an arbitrary number of isomorphic standard model sectors, and demonstrate that technical naturalness increases with the number of additional sectors. We consider two kinds of models. The first has $N$ standard model sectors symmetric under arbitrary permutations thereof. The second has $p$ left-chiral standard model sectors and $p$ right-chiral or mirror standard model sectors, with $p$-fold permutation symmetries within both and a discrete parity transformation interchanging left and right. In both kinds of models the lightest scalar has an invisible width fraction 1/N, which will provide an important means of experimentally testing this class of models.