Dimension-free $H^\infty$-calculus of angle $<π/2$ for UMD-valued Ornstein--Uhlenbeck operators

Let $1<p<\infty$, let $X$ be a UMD Banach space, let $1<p<\infty$, and let $L_d$ be the generator of the Ornstein--Uhlenbeck semigroup $(P_d(t))_{t\geq 0}$ on $L^p(\mathbb R^d,γ_d;X)$. We prove that the operators $-L_d$ are $R$-sectorial with a common angle strictly smaller than $π/2$ and with bound