Lattice QCD constraints on the critical point from an improved precision equation of state

In this paper we employ lattice simulations to search for the critical point of QCD. We search for the onset of a first-order QCD transition on the phase diagram by following contours of constant entropy density from imaginary to real chemical potentials under conditions of strangeness neutrality. We scan the phase diagram and investigate whether these contours meet to determine the probability that the critical point is located in a certain region on the <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mrow> <a:mi>T</a:mi> <a:mo>−</a:mo> <a:msub> <a:mrow> <a:mi>μ</a:mi> </a:mrow> <a:mrow> <a:mi>B</a:mi> </a:mrow> </a:msub> </a:mrow> </a:math> plane. To achieve this we introduce a new, continuum extrapolated equation of state at zero density with improved precision using lattices with <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:msub> <c:mi>N</c:mi> <c:mi>τ</c:mi> </c:msub> <c:mo>=</c:mo> <c:mn>8</c:mn> </c:math> , 10, 12, 16 time slices, and supplement it with new data at imaginary chemical potential. The current precision allows us to exclude, at the <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"> <e:mn>2</e:mn> <e:mi>σ</e:mi> </e:math> level, the existence of a critical point at <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"> <g:msub> <g:mi>μ</g:mi> <g:mi>B</g:mi> </g:msub> <g:mo>&lt;</g:mo> <g:mn>450</g:mn> <g:mtext> </g:mtext> <g:mtext> </g:mtext> <g:mi>MeV</g:mi> </g:math> .