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In typical statistical mechanical systems the grand canonical partitionfunction at finite volume is proportional to a polynomial of the fugacity$e^{\mu/T}$. The zero of this Lee-Yang polynomial closest to the origindetermines the radius of convergence of the Taylor expansion of the pressurearound $\mu=0$. The computationally cheapest formulation of lattice QCD, rootedstaggered fermions, with the usual definition of the rooted determinant, doesnot admit such a Lee-Yang polynomial. We argue that the radius of convergenceis then bounded by the spectral gap of the reduced matrix of the unrootedstaggered operator. This is a cutoff effect that potentially affects allestimates of the radius of convergence with the standard staggered rooting. Wesuggest a new definition of the rooted staggered determinant at finite chemicalpotential that allows for a definition of a Lee-Yang polynomial, and, thereforeof the numerical study of Lee-Yang zeros. We also describe an algorithm todetermine the Lee-Yang zeros and apply it to configurations generated with the2-stout improved staggered action at $N_t = 4$. We perform a finite-volumescaling study of the leading Lee-Yang zeros and estimate the radius ofconvergence of the Taylor expansion extrapolated to an infinite volume. We showthat the limiting singularity is not on the real line, thus giving a lowerbound on the location of any possible phase transitions at this latticespacing. In the vicinity of the crossover temperature at zero chemicalpotential, the radius of convergence turns out to be $\mu_B/T \approx 2$ androughly temperature independent. Our simulations are performed at strange quarkchemical potential $\mu_s=0$, but the method can be straightforwardly extendedto strangeness chemical potential $\mu_S=0$ or strangeness neutrality.

Radius of convergence in lattice QCD at finite $\mu_B$ with rooted staggered fermions