The $n/d$-conjecture for central essential indecomposable hyperplane arrangements

Let $f\in\mathbb C[z_1,\ldots,z_n]\setminus\mathbb C$ be homogeneous of degree $d$, and suppose that the hypersurface $\{f=0\}$ is a central essential indecomposable hyperplane arrangement: it is a finite union of hyperplanes, all containing the origin, whose intersection is the origin, and which cannot be split after a linear coordinate change into a product of nonconstant polynomials in disjoint variable sets. Let $b_f(s)$ be the Bernstein–Sato polynomial. $n/d$-conjecture. One has

$$b_f\left(-\frac{n}{d}\right)=0.$$

The conjecture is important both because it would imply the strong monodromy conjecture for hyperplane arrangements and because the predicted root $-n/d$ is determined by combinatorial data. Its general status is open.