Vanishing of higher Pontryagin classes for rationally contractible foliations

Let $M$ be a smooth manifold and let $E\subset TM$ be an integrable subbundle defining a foliation $\mathcal{F}$ whose leaves are rationally contractible, meaning that for every leaf $L$ and every $i$, $\pi_i(L)\otimes\textbf{Q}=0$. Let $Pont^*(M)(TM/E)$ be the higher Pontryagin ring generated by classes $y\cup p_i(TM/E)$ with $y\in H^j(M)$, and let $k=\dim(TM/E)$. Vanishing conjecture for higher Pontryagin classes. If the classifying space $BG$ of the holonomy groupoid satisfies the Novikov conjecture, then

$$Pont^q(M)(TM/E)=0$$

for $q>2k$. The assertion gives a dimension-dependent vanishing range for the higher Pontryagin ring of the normal bundle of the foliation, conditional on the Novikov conjecture for $BG$.