Wild cluster tilted algebras of rank 3

Let HH be a connected wild hereditary algebra of rank 3, TT a square-free tilting HH-module and Γ=EndC(T) the endomorphism ring of TT in the cluster category CHCH of HH. It is shown that the Loewy length of the cluster tilted algebra ΓΓ is 3+r3+r, where rr denotes the number of regular indecomposable direct summands of TT.