New $\mu$-Zariski pairs of surface singularities

To the best of the authors’ knowledge, all previously known examples of $\mu$-, ${\mu }^{\ast }$-, link-, or ordinary Zariski pairs of surface singularities in ${\mathbb{C}}^3$ consist of (possibly weighted) Lê-Yomdin singularities. In this paper, we present an example of a $\mu$-Zariski pair involving surface singularities that are not of Lê-Yomdin type.