The limit of the optimal Li--Yau constant for the fractional heat equation

For the fractional heat equation $\partial_t u + (-Δ)^{β/2}u=0$ on $\mathbb{R}^d$ with $β\in(0,2)$, Weber and Zacher introduced the optimal constant $C_{\rm LY}(β,d)$ in the Li--Yau type estimate $$(-Δ)^{β/2}\log u(t,\cdot)\leq \frac {C_{\rm LY}(β,d)}{t},\quad t>0.$$ They asked whether $C_{\rm LY}(β