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In typical statistical mechanical systems the grand canonical partition function at finite volume is proportional to a polynomial of the fugacity $\exp(μ/T)$. The zero of this Lee-Yang polynomial closest to the origin determines the radius of convergence of the Taylor expansion of the pressure around $μ=0$. Rooted staggered fermions, with the usual definition of the rooted determinant, do not admit such a Lee-Yang polynomial. We show that the radius of convergence is then bounded by the spectral gap of the reduced matrix of the unrooted staggered operator. We suggest a new definition of the rooted staggered determinant at finite chemical potential that allows for a definition of a Lee-Yang polynomial. We perform a finite volume scaling study of the leading Lee-Yang zeros and estimate the radius of convergence extrapolated to infinite volume using stout improved staggered fermions on $N_t$=4 lattices. In the vicinity of the crossover temperature at zero chemical potential, the radius of convergence turns out to be at $μ_B/T$≈2 and roughly temperature independent.
