Abstract
We perform the first direct determination of the position of the leading singularity of the pressure in the complex chemical potential μB 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 μB 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 μB/T≈2 and roughly temperature independent.
Highlights
The theoretical study of the phase diagram of QCD in the temperature (T )-baryon chemical potential plane is of considerable interest for the physics of high energy nuclear collisions and for the understanding of the early stages of the universe
It is further conjectured [3] that in the (T, μB) plane there is a line of crossovers, departing from (Tc, 0), that eventually turns into a line of first-order phase transitions
The point (TCEP, μCEP) separating the two lines is known as the critical endpoint (CEP), and the transition is expected to be of second order there
Summary
In the context of these extrapolation methods, one of the most sought-after quantities in the finite temperature lattice QCD community is the radius of convergence of the Taylor expansion of the pressure around μB = 0 [5, 11, 12]. 2. Lee-Yang zeros and the exact asymptotics of the Taylor expansion in a finite volume
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