Towards a reliable lower bound on the location of the critical endpoint

Abstract

We perform the first direct determination of the position of the leading singularity of the pressure in the complex chemical potential ${\mu }_B$ plane in lattice QCD using numerical simulations with 2-stout improved rooted staggered fermions. This provides a direct determination of the radius of convergence of the Taylor expansion of the pressure that does not rely on a finite-order truncation of the expansion. The analyticity issues in the complex ${\mu }_B$ plane of the grand canonical partition function of QCD with rooted staggered fermions are solved with a careful redefinition of the fermion determinant that makes it a polynomial in the fugacity on any finite lattice, without changing the continuum limit of the observables. By performing a finite volume scaling study at a single coarse lattice spacing, we show that the limiting singularity is not on the real line in the thermodynamic limit, thus showing that the radius of convergence of the Taylor expansion gives a lower bound on the location of a possible phase transition. In the vicinity of the crossover temperature at zero chemical potential, the radius of convergence turns out to be ${\mu }_B/T\approx 2$ and roughly temperature independent.

arXiv comment4 pages, 1 figure; Quark Matter 2019 - the XXVIIIth International Conference on Ultra-relativistic Nucleus-Nucleus Collisions

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Cited by in corpus (2)

• Apparent convergence of Padé approximants for the crossover line in finite density QCD
• Universality, Lee-Yang singularities and series expansions