Searching for the QCD critical endpoint using multi-point Padé approximations

Abstract

Using the multi-point Padé approach, we locate Lee-Yang edge singularities of the QCD pressure in the complex baryon chemical potential plane. These singularities are extracted from singularities in the net baryon-number density calculated in $N_f=2+1$ lattice QCD at physical quark mass and purely imaginary chemical potential. Taking an appropriate scaling ansatz in the vicinity of the conjectured QCD critical endpoint, we extrapolate the singularities on $N_{\tau }=6$ lattices to pure real baryon chemical potential to estimate the position of the critical endpoint (CEP). We find $T^{\mathrm{CEP}}=105_{-18}^{+8}$~ MeV and ${\mu }_B^{\mathrm{CEP}}=422_{-35}^{+80}$~ MeV, which compares well with recent estimates in the literature. For the slope of the transition line at the critical point we find $-0.16(24)$.

Comments: 10 pages, 7 figues