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We study different estimators of the radius of convergence of the Taylorseries of the pressure in finite density QCD. We adopt the approach in whichthe radius of convergence is estimated first in a finite volume, and theinfinite-volume limit is taken later. This requires an estimator for the radiusof convergence that is reliable in a finite volume. Based on general argumentsabout the analytic structure of the partition function in a finite volume, wedemonstrate that the ratio estimator cannot work in this approach, and proposethree new estimators, capable of extracting reliably the radius of convergence,which coincides with the distance from the origin of the closest Lee-Yang zero.We also provide an estimator for the phase of the closest Lee-Yang zero,necessary to assess whether the leading singularity is a true critical point.We demonstrate the usage of these estimators on a toy model, namely 4 flavorsof unimproved staggered fermions on a small $6^3 \times 4$ lattice, where boththe radius of convergence and the Taylor coefficients to any order can beobtained by a direct determination of the Lee-Yang zeros. Interestingly, whilethe relative statistical error of the Taylor expansion coefficients steadilygrows with order, that of our estimators stabilizes, allowing for an accurateestimate of the radius of convergence. In particular, we show that despite themore than 100\% error bars on high-order Taylor coefficients, the givenensemble contains enough information about the radius of convergence.

Reliable estimation of the radius of convergence in finite density QCD