  We prove that in the Cayley graph of any braid group modulo its center
$B_n/Z(B_n)$, equipped with Garside's generating set, the axes of all
pseudo-Anosov braids are strongly contracting. More generally, we consider a
Garside group $G$ of finite type with cyclic center. We prove that in the
Cayley graph of $G/Z(G)$, equipped with the Garside generators, the axis of any
Morse element is strongly contracting. As a consequence, we prove that Morse
elements act loxodromically on the additional length graph of $G$.
